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@article{weintraub2025virtual,
abstract = {This paper considers an 𝑁 -pursuer–𝑀 -evader scenario involving 𝐿 virtual targets. The virtual targets serve as an intermediary target for the pursuers, allowing the pursuers to delay their final assignment to the evaders. However, upon reaching the virtual target, the pursuers must decide which evader to capture. It is assumed that there are more pursuers than evaders and that the pursuers are faster than the evaders. The objective is two-part: first, assign each pursuer to a virtual target and evader such that the pursuer team’s energy is minimized, and, second, choose the virtual targets’ locations for this minimization problem. The approach taken is to consider the Apollonius geometry between each pursuer’s virtual target location and each evader. Using the constructed Apollonius circles, the pursuer’s travel distance and maneuver at a virtual target are obtained. These metrics serve as a gauge for the total energy required to capture a particular evader and are used to solve the joint virtual target selection and pursuer–evader assignment problem. This paper provides a mathematical definition of this problem, the solution approach taken, and an example. Following the example, a Monte Carlo analysis is performed, demonstrating the efficacy of the algorithm and its suitability for real-time applications.},
author = {Weintraub, Isaac E. and Von Moll, Alexander and Casbeer, David W. and Manyam, Satyanarayana G.},
date = {2025-01-22},
journal = {Journal of Aerospace Information Systems},
publisher = {AIAA},
title = {Virtual Target Selection for a Multiple-Pursuer--Multiple-Evader Scenario},
year = {2025},
}
@inproceedings{mora2025influence,
abstract = {This paper explores a multi-agent containment problem, where a fast evader, modeled having constant speed and using constant heading, attempts to escape a circular containment region that is orbited by a slower team of pursuers with a nonzero capture radius. Two distinct multi-agent dynamic models cases are explored, the first uses a unicycle dynamics model with strict constraints, while the second uses a double integrator model with looser constraints and consensus laws implemented with a communication network. This paper considers the scenario wherein some of the pursuers get compromised and turn into malicious agents that suffer a delay in initiating the capture pursuit. A boost countermeasure is proposed and its effectiveness is investigated. This work provides a foundation for a consensus case that incorporates more restrictions in motion and extensions to larger teams of pursuers, as well as a more dynamic evader model.},
author = {Mora, Braulio and Chakravarthy, Animesh and Von Moll, Alexander and Weintraub, Isaac E. and Casbeer, David},
eventtitle = {SciTech},
date = {2025-01-03},
doi = {10.2514/6.2025-1348},
location = {Orlando},
booktitle = {SciTech},
publisher = {AIAA},
title = {Influence of Malicious Agents in a Team Seeking to Contain an Evader},
year = {2025},
}
@book{sargent2024dynamic,
abstract = {This book is about dynamic programming and its applications in economics, finance, and adjacent fields like operations research. It brings together recent innovations in the theory of dynamic programming and also provides related applications and computer code.},
author = {Sargent, Thomas J. and Stachurski, John},
date = {2024-11-26},
publisher = {QuantEcon},
title = {Dynamic Programming},
year = {2024},
}
@book{powell2011approximate,
author = {Powell, Warren B.},
doi = {10.1002/9781118029176},
isbn = {['9780470604458', '9781118029176']},
journal = {Wiley Series in Probability and Statistics},
month = {8},
publisher = {Wiley},
title = {Approximate Dynamic Programming},
url = {https://doi.org/10.1002/9781118029176},
year = {2011},
}
@article{fonod2020wingman-based,
author = {Fonod, Robert and Shima, Tal},
doi = {10.1109/taes.2019.2935642},
issue = {3},
journal = {IEEE Transactions on Aerospace and Electronic Systems},
month = {6},
pages = {1754--1766},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
title = {Wingman-Based Estimation and Guidance for a Sensorless PN-Guided Pursuer},
url = {https://doi.org/10.1109/taes.2019.2935642},
volume = {56},
year = {2020},
}
@article{zidek2017drift,
author = {Zidek, Robert A.E. and Kolmanovsky, Ilya V.},
doi = {10.1016/j.automatica.2017.06.015},
journal = {Automatica},
language = {en},
month = {9},
pages = {108--115},
publisher = {Elsevier BV},
title = {Drift counteraction optimal control for deterministic systems and enhancing convergence of value iteration},
url = {https://doi.org/10.1016/j.automatica.2017.06.015},
volume = {83},
year = {2017},
}
@article{jingjinyu2012rendezvous,
author = {Jingjin Yu, None and LaValle, S. M. and Liberzon, D.},
doi = {10.1109/tac.2011.2158172},
issue = {2},
journal = {IEEE Transactions on Automatic Control},
month = {2},
pages = {421--434},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
title = {Rendezvous Without Coordinates},
url = {https://doi.org/10.1109/tac.2011.2158172},
volume = {57},
year = {2012},
}
@article{berger2021near-optimal,
author = {Berger, Jean and Barkaoui, Mohamed and Lo, Nassirou},
doi = {10.1080/01605682.2019.1685362},
issue = {3},
journal = {Journal of the Operational Research Society},
language = {en},
month = {3},
pages = {688--700},
publisher = {Informa UK Limited},
title = {Near-optimal search-and-rescue path planning for a moving target},
url = {https://doi.org/10.1080/01605682.2019.1685362},
volume = {72},
year = {2021},
}
@book{hajek2008pursuit,
author = {Hájek, Otomar},
publisher = {Courier Corporation},
title = {Pursuit games: an introduction to the theory and applications of differential games of pursuit and evasion},
year = {2008},
}
@article{dubins1957curves,
author = {Dubins, L. E.},
doi = {10.2307/2372560},
issue = {3},
journal = {American Journal of Mathematics},
month = {7},
pages = {497},
publisher = {JSTOR},
title = {On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents},
url = {https://doi.org/10.2307/2372560},
volume = {79},
year = {1957},
}
@article{thrun2002probabilistic,
abstract = {<jats:p>Planning and navigation algorithms exploit statistics gleaned from uncertain, imperfect real-world environments to guide robots toward their goals and around obstacles.</jats:p>},
author = {Thrun, Sebastian},
doi = {10.1145/504729.504754},
issue = {3},
journal = {Communications of the ACM},
language = {en},
month = {3},
pages = {52--57},
publisher = {Association for Computing Machinery (ACM)},
title = {Probabilistic robotics},
url = {https://doi.org/10.1145/504729.504754},
volume = {45},
year = {2002},
}
@article{anderson2014stochastic,
author = {Anderson, Ross P. and Milutinovic, Dejan},
doi = {10.1109/tac.2014.2314224},
issue = {10},
journal = {IEEE Transactions on Automatic Control},
month = {10},
pages = {2801--2806},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
title = {A Stochastic Approach to Dubins Vehicle Tracking Problems},
url = {https://doi.org/10.1109/tac.2014.2314224},
volume = {59},
year = {2014},
}
@inproceedings{exarchos2014asymmetric,
author = {Exarchos, Ioannis and Tsiotras, Panagiotis},
booktitle = {2014 IEEE 53rd Annual Conference on Decision and Control (CDC)},
doi = {10.1109/cdc.2014.7040055},
journal = {53rd IEEE Conference on Decision and Control},
month = {12},
pages = {4272--4277},
publisher = {IEEE},
title = {An asymmetric version of the two car pursuit-evasion game},
url = {https://doi.org/10.1109/cdc.2014.7040055},
venue = {Los Angeles, CA, USA},
year = {2014},
}
@inproceedings{milutinovic2017stochastic,
author = {Milutinović, Dejan and Casbeer, David W. and Kingston, Derek and Rasmussen, Steven},
booktitle = {2017 IEEE Conference on Control Technology and Applications (CCTA)},
doi = {10.1109/ccta.2017.8062595},
journal = {2017 IEEE Conference on Control Technology and Applications (CCTA)},
month = {8},
pages = {1031--1037},
publisher = {IEEE},
title = {A stochastic approach to small UAV feedback control for target tracking and blind spot avoidance},
url = {http://dx.doi.org/10.1109/ccta.2017.8062595},
venue = {Mauna Lani Resort, HI, USA},
year = {2017},
}
@article{buzikov2021time-optimal,
abstract = {<jats:sec>
<jats:title>Abstract</jats:title>
<jats:p> The problem of intercepting a target moving along a prescribed trajectory by a Dubins car
is stated and formalized as a time-optimal control problem with an arbitrary car velocity direction
at the interception. The conditions available in the literature under which the optimal trajectory
is a geodesic line drawn from the initial position of the car to the interception point are refined.
Algebraic equations for calculating the optimal interception time are obtained. The optimal
control is synthesized based on these equations. A software module is developed for constructing
the optimal car trajectories for various target trajectories.
</jats:p>
</jats:sec>},
author = {Buzikov, M. E. and Galyaev, A. A.},
doi = {10.1134/s0005117921050015},
issue = {5},
journal = {Automation and Remote Control},
language = {en},
month = {5},
pages = {745--758},
publisher = {Pleiades Publishing Ltd},
title = {Time-Optimal Interception of a Moving Target by a Dubins Car},
url = {http://dx.doi.org/10.1134/s0005117921050015},
volume = {82},
year = {2021},
}
@book{krasovskii1988game-theoretical,
author = {Krasovskii, Nikolai N and Subbotin, Andrei I and Kotz, Samuel},
publisher = {Springer},
title = {Game-theoretical control problems},
year = {1988},
}
@inproceedings{petrosyan1965family,
author = {Petrosyan, Leon Aganesovich},
booktitle = {Doklady Akademii Nauk},
number = {1},
organization = {Russian Academy of Sciences},
pages = {52--54},
title = {A family of differential survival games in the space R^n},
volume = {161},
year = {1965},
}
@article{munts2019time-optimal,
author = {Munts, Nataly V. and Kumkov, Sergey S.},
doi = {10.1007/s13235-018-00295-8},
issue = {3},
journal = {Dynamic Games and Applications},
language = {en},
month = {9},
pages = {751--770},
publisher = {Springer Science and Business Media LLC},
title = {On Time-Optimal Problems with Lifeline},
url = {http://dx.doi.org/10.1007/s13235-018-00295-8},
volume = {9},
year = {2019},
}
@misc{krassovskii1974positional,
author = {Krassovskii, NN and Subbotin, AI},
note = {in Russian},
publisher = {Nauka, Moskva},
title = {Positional Differential Games},
year = {1974},
}
@book{petrosjan1993differential,
author = {Petrosjan, Leon A},
doi = {10.1142/1670},
isbn = {['9789810209797', '9789814355834']},
language = {en},
month = {9},
publisher = {WORLD SCIENTIFIC},
title = {Differential Games of Pursuit},
url = {http://dx.doi.org/10.1142/1670},
year = {1993},
}
@inproceedings{beaver2024lq-ocp:,
author = {Beaver, Logan E.},
booktitle = {2024 American Control Conference (ACC)},
doi = {10.23919/acc60939.2024.10644883},
journal = {2024 American Control Conference (ACC)},
month = {7},
pages = {821--826},
publisher = {IEEE},
title = {LQ-OCP: Energy-Optimal Control for LQ Problems},
url = {http://dx.doi.org/10.23919/acc60939.2024.10644883},
venue = {Toronto, ON, Canada},
year = {2024},
}
@inproceedings{luders2010chance,
author = {Luders, Brandon and Kothari, Mangal and How, Jonathan},
booktitle = {AIAA Guidance, Navigation, and Control Conference},
doi = {10.2514/6.2010-8160},
journal = {AIAA Guidance, Navigation, and Control Conference},
month = {8},
publisher = {American Institute of Aeronautics and Astronautics},
title = {Chance Constrained RRT for Probabilistic Robustness to Environmental Uncertainty},
url = {http://dx.doi.org/10.2514/6.2010-8160},
venue = {Toronto, Ontario, Canada},
year = {2010},
}
@article{bakker2025operator-theoretic,
abstract = {Differential game theory offers an approach for modeling interactions between two or more agents that occur in continuous time. The goal of each agent is to optimize its objective cost functional. In this paper, we present two different methods, based on the Koopman Operator (KO), to solve a zero-sum differential game. The first approach uses the resolvent of the KO to calculate a continuous-time global feedback solution over the entire domain. The second approach uses a discrete-time, data-driven KO representation with control to calculate open- loop control policies one trajectory at a time. We demonstrate these methods on a turret defense game from the literature, and we find that the methods’ solutions replicate the behavior of the analytical solution provided in the literature. Following that demonstration, we highlight the relative advantages and disadvantages of each method and discuss potential future work for this line of research.},
author = {Bakker, Craig and Rupe, Adam and Von Moll, Alexander and Gerlach, Adam},
date = {2025-04-01},
location = {None},
journal = {Journal of Computational Physics},
publisher = {Elsevier},
title = {Operator-Theoretic Methods for Differential Games},
year = {2025},
}
@article{yazdaniyan2020numerical,
author = {Yazdaniyan, Z. and Shamsi, M. and Foroozandeh, Z. and de Pinho, Maria do Rosário},
doi = {10.1016/j.cam.2019.112535},
journal = {Journal of Computational and Applied Mathematics},
language = {en},
month = {4},
pages = {112535},
publisher = {Elsevier BV},
title = {A numerical method based on the complementarity and optimal control formulations for solving a family of zero-sum pursuit-evasion differential games},
url = {http://dx.doi.org/10.1016/j.cam.2019.112535},
volume = {368},
year = {2020},
}
@inproceedings{munishkin2016stochastic,
author = {Munishkin, Alexey A. and Milutinović, Dejan and Casbeer, David W.},
booktitle = {2016 International Conference on Unmanned Aircraft Systems (ICUAS)},
doi = {10.1109/icuas.2016.7502568},
journal = {2016 International Conference on Unmanned Aircraft Systems (ICUAS)},
month = {6},
pages = {211--218},
publisher = {IEEE},
title = {Stochastic optimal control navigation with the avoidance of unsafe configurations},
url = {http://dx.doi.org/10.1109/icuas.2016.7502568},
venue = {Arlington, VA, USA},
volume = {137},
year = {2016},
}
@inproceedings{manyam2025shortest,
abstract = {In this paper the shortest time strategy of turn- constrained vehicle for reaching a circle moving on a straight line is posed and solved. The shortest curvature constrained path to a circle is comprised of a left or right turning arc of minimum turn radius (L/R) and straight-line segment (S). An analysis of each of the candidate Dubins modes, L, R, LS, and RS is provided. Under the condition that the agent’s initial position is not on the path of the moving circle, we prove that the length of the shortest Dubins path to the circle is a continuous function of the position of the target center. Leveraging this continuity, we propose an algorithm that uses the bisection search and finds the time-optimal solution. A lower bound to the solution is obtained when the agent’s initial position lies on the path of the moving circle, and a heuristic approach is discussed for such instances.},
author = {Manyam, Satyanarayana G. and Casbeer, David W. and Von Moll, Alexander and Weintraub, Isaac},
eventtitle = {American Control Conference},
date = {2025-07-08},
note = {Accepted},
location = {Denver, CO},
booktitle = {American Control Conference},
publisher = {IFAC},
title = {Shortest Dubins Path to a Moving Circle with Free Final Heading},
year = {2025},
}
@article{kim2019algorithm,
author = {Kim, Ik Sung},
journal = {Communications of the Korean Mathematical Society},
number = {3},
pages = {1029--1047},
publisher = {Korean Mathematical Society},
title = {An algorithm for circle fitting in ℝ 3},
volume = {34},
year = {2019},
}
@inproceedings{surve2025heterogeneous,
abstract = {We consider the problem of minimum time inter- cept of multiple mobile targets that are translating in a fixed direction, i.e., moving with identical constant speeds in the same direction. Every target has to be intercepted by a heterogeneous pursuer assembly – a mobile vehicle that carries another pursuer whose speed is higher than that of the vehicle. Aside from this novel problem formulation, our main contributions are as follows. First, we formally establish that the optimal heterogeneous intercept problem is equivalent to solving an appropriately defined Euclidean Traveling Salesperson Problem with Neighborhoods (ETSPN). We show that each neighborhood is an ellipse with a specified center and lengths of the major and minor axis. Second, we provide novel upper bounds on the optimal length as a function of the problem parameters, i.e., the number of targets, the speed ratio between the target and the assembly, the speed between the pursuer and the assembly, the geometry of the region containing the targets and the time required for the pursuer to intercept a target. Finally, we offer insight into the approach through a numerical visualization and a discussion on improving the upper bounds.},
author = {Surve, Prajakta and Frost, Richard L. and Bopardikar, Shaunak D. and Von Moll, Alexander and Casbeer, David W.},
eventtitle = {American Control Conference},
date = {2025-07-08},
note = {Submitted for Review},
location = {Denver, CO},
booktitle = {American Control Conference},
publisher = {IFAC},
title = {Heterogeneous Pursuit of Multiple Translating Targets},
year = {2025},
}
@article{milutinovic2025stochastic,
abstract = {This work formulates the feedback control strategies for vehicles to reach a goal point amongst a field of dynamic risk regions. Whereas previous work has considered deterministic versions of this problem, we consider the scenario in the context of uncertainty. This uncertainty could be due to unknown wind or other external disturbances. The risk regions’ dynamics are tightly coupled to the state of the vehicle and as a result the task of navigating through a field dynamically changes as the vehicle traverses through it. Rather than using a nonlinear program solver, the approach taken here is one of formulating the problem as a stochastic optimal control problem wherein a feedback control law is derived. This feedback control law allows a single or multiple vehicles to reach the desired goal location efficiently and with minimal risk incursion. When inside a risk region, there is a probability rate of the vehicle being neutralized. The stochastic dynamical system is modeled as a hybrid system, i.e., regime switching diffusion. The hybrid system is comprised of continuous spatial dynamics and discrete operational states corresponding to “normal” and “neutralized”. The optimal control problem is discretized into a field of vehicle states and control. Using Value Iteration, the control signal at each discrete location is optimized, providing a feedback control strategy over the field. Following a discussion of the methods and approaches, this problem is formulated, simulations are performed, and conclusions and remarks are made.},
author = {Milutinović, Dejan and Von Moll, Alexander and Weintraub, Isaac E. and Casbeer, David},
date = {2025-07-08},
note = {Submitted for Review},
journal = {Journal of Aerospace Information Systems},
publisher = {AIAA},
title = {Stochastic Optimal Avoidance of Multiple Engagement Zones},
year = {2025},
}
@article{kushner1990numerical,
author = {Kushner, Harold J.},
doi = {10.1137/0328056},
issue = {5},
journal = {SIAM Journal on Control and Optimization},
language = {en},
month = {9},
pages = {999--1048},
publisher = {Society for Industrial & Applied Mathematics (SIAM)},
title = {Numerical Methods for Stochastic Control Problems in Continuous Time},
url = {http://dx.doi.org/10.1137/0328056},
volume = {28},
year = {1990},
}
@inproceedings{weintraub2025min-time,
abstract = {A turn constrained vehicle is initially located inside a polygon region and desires to escape in minimum time. First, the method of characteristics is used to describe the time-optimal strategies for reaching a line of infinite length. Next, the approach is extended to polygons constructed of a series of line segments. Using this construction technique, the min-time path to reach each edge is obtained; the resulting minimum of the set of optimal trajectories is then selected for escaping the polygon.},
author = {Weintraub, Isaac and Von Moll, Alexander and Casbeer, David and Manyam, Satyanarayana G. and Pachter, M. and Taylor, Colin},
eventtitle = {American Control Conference},
date = {2025-07-08},
note = {Accepted},
location = {Denver, CO},
booktitle = {American Control Conference},
publisher = {IFAC},
title = {Min-Time Escape of a Dubins Car from a Polygon},
url = {https://arxiv.org/abs/2410.01589},
year = {2025},
}
@article{umbach2003methods,
author = {Umbach, D. and Jones, K.N.},
doi = {10.1109/tim.2003.820472},
issue = {6},
journal = {IEEE Transactions on Instrumentation and Measurement},
language = {en},
month = {12},
pages = {1881--1885},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
title = {A few methods for fitting circles to data},
url = {http://dx.doi.org/10.1109/tim.2003.820472},
volume = {52},
year = {2003},
}
@article{cockayne1975plane,
author = {Cockayne, E. J. and Hall, G. W. C.},
doi = {10.1137/0313012},
issue = {1},
journal = {SIAM Journal on Control},
language = {en},
month = {1},
pages = {197--220},
publisher = {Society for Industrial & Applied Mathematics (SIAM)},
title = {Plane Motion of a Particle Subject to Curvature Constraints},
url = {http://dx.doi.org/10.1137/0313012},
volume = {13},
year = {1975},
}
@article{surve2023quaternion,
author = {Surve, Prajakta and Maity, Arnab and Kumar, Shashi Ranjan},
doi = {10.1016/j.ifacol.2023.10.1725},
issue = {2},
journal = {IFAC-PapersOnLine},
language = {en},
pages = {1174--1179},
publisher = {Elsevier BV},
title = {Quaternion based Three-Dimensional Impact Time and Field-of-View Constrained Guidance},
url = {http://dx.doi.org/10.1016/j.ifacol.2023.10.1725},
volume = {56},
year = {2023},
}
@article{surve2024polynomial,
author = {Surve, Prajakta and Maity, Arnab and Kumar, Shashi Ranjan},
doi = {10.1016/j.ast.2024.109018},
journal = {Aerospace Science and Technology},
language = {en},
month = {4},
pages = {109018},
publisher = {Elsevier BV},
title = {Polynomial shaping based three-dimensional impact angle and field-of-view constrained guidance},
url = {http://dx.doi.org/10.1016/j.ast.2024.109018},
volume = {147},
year = {2024},
}
@inbook{shevchenko2020alternative,
author = {Shevchenko, Igor},
doi = {10.1007/978-3-030-51941-4_17},
isbn = {['9783030519407', '9783030519414']},
journal = {Static \& Dynamic Game Theory: Foundations \& Applications},
month = {11},
pages = {283--294},
publisher = {Springer International Publishing},
title = {An Alternative Pursuit Strategy in the Game of Obstacle Tag},
url = {http://dx.doi.org/10.1007/978-3-030-51941-4_17},
year = {2020},
}
@article{weiss2005adjoint,
author = {Weiss, Martin},
doi = {10.2514/1.7342},
issue = {2},
journal = {Journal of Guidance, Control, and Dynamics},
language = {en},
month = {3},
pages = {236--248},
publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
title = {Adjoint Method for Missile Performance Analysis on State-Space Models},
url = {http://dx.doi.org/10.2514/1.7342},
volume = {28},
year = {2005},
}
@inproceedings{milutinovic2025policy,
abstract = {This work formulates the feedback control strategies for vehicles to reach a goal point amongst a field of dynamic risk regions. Whereas previous work has considered deterministic versions of this problem, we consider the scenario in the context of uncertainty. This uncertainty could be due to unknown wind or other external disturbances. The risk regions’ dynamics are tightly coupled to the state of the vehicle and as a result the task of navigating through a field dynamically changes as the vehicle traverses through it. Rather than using a nonlinear program solver, the approach taken here is one of formulating the problem as a stochastic optimal control problem wherein a feedback control law is derived. This feedback control law allows a single or multiple vehicles to reach the desired goal location efficiently and with minimal risk incursion. When inside a risk region, there is a probability rate of the vehicle being neutralized. The stochastic dynamical system is modeled as a hybrid system, i.e., regime switching diffusion. The hybrid system is comprised of continuous spatial dynamics and discrete operational states corresponding to “normal” and “neutralized”. The optimal control problem is discretized into a field of vehicle states and control. Using Value Iteration, the control signal at each discrete location is optimized, providing a feedback control strategy over the field. Following a discussion of the methods and approaches, this problem is formulated, simulations are performed, and conclusions and remarks are made.},
author = {Milutinović, Dejan and Von Moll, Alexander and Weintraub, Isaac E. and Casbeer, David},
eventtitle = {SciTech},
date = {2025-01-08},
doi = {10.2514/6.2025-1544},
location = {Orlando, FL},
booktitle = {SciTech},
publisher = {AIAA},
title = {Policy for Optimal Avoidance of Multiple Engagement Zones},
year = {2025},
}
@inproceedings{hansen2025optimal,
abstract = {This work considers a two-actor scenario of a faster, unmanned turn-constrained pursuer with an engagement zone (EZ) and a non-maneuvering mobile evader. The pursuer aims to capture an evader with a circular EZ. The pursuer’s EZ is dynamic and shifts as a function of the evader’s velocity vector magnitude and direction. Using nonlinear optimal control techniques, the optimal trajectory and minimum time to engage the evader are determined for various pursuer initial headings and positions through MATLAB simulation. The results build a control strategy given the scenario, with analytic solution validation. Results lay a foundation to model pursuer-evader capture scenarios with a dynamic EZ, leading to general guidelines for real-time control strategies. Finally, an algorithm to find a dispersal surface in any pursuer/evader scenario establishes a comparison angle for the pursuer to guarantee optimal turn direction to engage the evader.},
author = {Hansen, Alexander and Zollars, Michael and Weintraub, Isaac E. and Von Moll, Alexander},
eventtitle = {SciTech},
date = {2025-01-08},
doi = {10.2514/6.2025-1350},
location = {Orlando, FL},
booktitle = {SciTech},
publisher = {AIAA},
title = {An Optimal Strategy for Off-Board Proximal Sensing of a Target: Part 2},
year = {2025},
}
@inproceedings{weintraub2025optimal,
abstract = {The time-optimal strategy for a pursuer, endowed with a guided off-board sensor, is found to place the range-limited sensor platform onto a non-maneuvering target. Leveraging optimal control theory, a feedback control strategy is obtained for the pursuer using the indirect optimal control method. The target is assumed to have constant speed and move slower than the off-board sensor and the pursuer. The limited-range off-board sensor is assumed to be faster than the pursuer and the target. The pursuer is assumed to have unlimited range and is faster than the target but slower than the off-board sensor platform. All agents' communication, location, and heading are assumed known by all; the scenario assumes communication between the pursuer and off-board sensor is ideal. This work presents how the optimal control approach can be leveraged as well as highlighted in example simulations and an accompanying discussion of those results.},
author = {Weintraub, Isaac E. and Von Moll, Alexander and Hansen, Alexander and Zollars, Michael},
eventtitle = {SciTech},
date = {2025-01-08},
doi = {10.2514/6.2025-1349},
location = {Orlando, FL},
booktitle = {SciTech},
publisher = {AIAA},
title = {An Optimal Strategy for Off-Board Proximal Sensing of a Target: Part 1},
year = {2025},
}
@article{pachter2024synthesis,
author = {Pachter, Meir and Weintraub, Isaac E.},
doi = {10.1007/s10957-024-02490-7},
journal = {Journal of Optimization Theory and Applications},
language = {en},
month = {7},
publisher = {Springer Science and Business Media LLC},
title = {The Synthesis of Optimal Control Laws Using Isaacs’ Method for the Solution of Differential Games},
url = {http://dx.doi.org/10.1007/s10957-024-02490-7},
year = {2024},
}
@article{dhananjay2014accurate,
author = {Dhananjay, N. and Ghose, D.},
doi = {10.2514/1.g000082},
issue = {4},
journal = {Journal of Guidance, Control, and Dynamics},
language = {en},
month = {7},
pages = {1378--1383},
publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
title = {Accurate Time-to-Go Estimation for Proportional Navigation Guidance},
url = {http://dx.doi.org/10.2514/1.g000082},
volume = {37},
year = {2014},
}
@article{stenger2020optimal,
author = {Stenger, Jerome and Gamboa, Fabrice and Keller, M. and Iooss, Bertrand},
doi = {10.1615/int.j.uncertaintyquantification.2020030800},
issue = {1},
journal = {International Journal for Uncertainty Quantification},
language = {en},
pages = {35--53},
publisher = {Begell House},
title = {Optimal Uncertainty Quantification of a Risk Measurement from a Thermal-Hydraulic Code Using Canonical Moments},
url = {http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2020030800},
volume = {10},
year = {2020},
}
@book{dette1997theory,
author = {Dette, Holger and Studden, William J},
publisher = {John Wiley & Sons},
title = {The theory of canonical moments with applications in statistics, probability, and analysis},
volume = {338},
year = {1997},
}
@inproceedings{weintraub2024minimum,
abstract = {A turn-constrained evader strives to escape a circular region in minimum time.},
author = {Weintraub, Isaac E. and Von Moll, Alexander and Pachter, Meir},
eventtitle = {National Aerospace Electronics Conference},
date = {2024-07-08},
location = {Dayton, OH},
booktitle = {National Aerospace Electronics Conference},
publisher = {IEEE},
title = {Minimum Time Escape from a Circular Region of a Dubins Car},
url = {https://arxiv.org/abs/2405.05725},
year = {2024},
}
@article{stenger2018optimal,
abstract = {We gain robustness on the quantification of a risk measurement by accounting for all sources of uncertainties tainting the inputs of a computer code. We evaluate the maximum quantile over a class of distributions defined only by constraints on their moments. The methodology is based on the theory of canonical moments that appears to be a well-suited framework for practical optimization.},
archiveprefix = {arXiv},
author = {Stenger, Jerome and Gamboa, Fabrice and Keller, Merlin and Iooss, Bertrand},
eprint = {1811.12788v1},
file = {1811.12788v1.pdf},
month = {Nov},
primaryclass = {math.ST},
title = {Optimal Uncertainty Quantification on moment class using canonical moments},
url = {http://arxiv.org/abs/1811.12788v1},
year = {2018},
}
@inproceedings{mclain2000trajectory,
author = {McLain, Timothy and Beard, Randal},
booktitle = {AIAA Guidance, Navigation, and Control Conference and Exhibit},
doi = {10.2514/6.2000-4369},
journal = {AIAA Guidance, Navigation, and Control Conference and Exhibit},
month = {8},
publisher = {American Institute of Aeronautics and Astronautics},
title = {Trajectory planning for coordinated rendezvous of unmanned air vehicles},
url = {http://dx.doi.org/10.2514/6.2000-4369},
venue = {Dever,CO,U.S.A.},
year = {2000},
}
@article{zhou2024koopman,
author = {Zhou, Min and Lu, Mingfei and Hu, Guanjie and Guo, Zongyi and Guo, Jianguo},
doi = {10.1109/tcst.2024.3401609},
journal = {IEEE Transactions on Control Systems Technology},
pages = {1--8},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
title = {Koopman Operator-Based Integrated Guidance and Control for Strap-Down High-Speed Missiles},
url = {http://dx.doi.org/10.1109/tcst.2024.3401609},
year = {2024},
}
@mastersthesis{zittrouer2022differential,
abstract = {A study of defensive architectures for combating hypersonic glide vehicles (HGVs) via interception with a ground-based interceptor (GBI) is presented. Pursuit-evasion differential games are formulated for numerical simulation of the interception engagements. A one-sided optimal control problem wherein the evader HGV is optimized and the pursuer GBI employs a suboptimal proportional navigation control strategy is solved. The solution space is characterized by varying the pursuer initial velocity advantage relative to the evader. A two-sided optimal control problem in which both players behave optimally is solved via the semi-direct collocation with nonlinear programming (semi- DCNLP) method. The resulting state and control trajectories are candidate minimax solutions to a GBI-HGV kinetic kill engagement.
Subsequently, an overarching survey of the defensive architecture is discussed, specifically in terms of a detection and tracking network, the deployment of ground-, space- and air-based interceptor batteries, and the firing doctrine. This holistic defensive architecture is explored in the context of classical combat aircraft survivability analysis. Probabilities of kill for a GBI against an HGV are computed in case studies considering a direct hit and proximity kill mechanism with varying levels of degraded threat detection and tracking.},
author = {Zittrouer, Stephen T.},
institution = {Air Force Institute of Technology},
title = {Differential Game-Based Defensive Architecture Study Employing Ground-Based Interceptors},
year = {2022},
}
@article{shishika2024deception,
abstract = {Can deception exist in differential games? We provide a case study for a Turret-Attacker differential game, where two Attackers seek to score points by reaching a target region while a Turret tries to minimize the score by aligning itself with the Attackers before they reach the target. In contrast to the original problem solved with complete information, we assume that the Turret only has partial information about the maximum speed of the Attackers. We investigate whether there is any incentive for the Attackers to move slower than their maximum speed in order to “deceive” the Turret into taking suboptimal actions. We first describe the existence of a dilemma that the Turret may face. Then we derive a set of initial conditions from which the Attackers can force the Turret into a situation where it must take a guess.},
author = {Shishika, Daigo and Von Moll, Alexander and Maity, Dipankar and Dorothy, Michael},
date = {2024-12-31},
location = {None},
journal = {arXiv},
publisher = {arXiv},
title = {Deception in Differential Games: Information Limiting Strategy to Induce Dilemma},
url = {https://arxiv.org/abs/2405.07465},
year = {2024},
}
@inproceedings{wolek2025maximum,
abstract = {This paper considers the optimal control problem of steering a Dubins vehicle with a decaying speed that depends linearly on the turn-rate to a terminal point and heading with maximum kinetic energy. Pontryagin's Minimum Principle is applied and the extremals are identified as sequences of straight segments and spiral-shaped turns. A method is proposed to exactly transcribe the continuous optimization into a series of finite dimensional optimizations; each of which solves for locally optimal extremal that satisfies the terminal condition. Next, an application of this path planning approach to gliding flight is examined. A technique is established to map the planar paths to three-dimensional trajectories for an aerodynamic glider model with angle-of-attack and bank-angle controls. The maximum kinetic energy obtained using the mapping is compared to a baseline glider guidance technique through numerical simulations.},
author = {Wolek, Artur and Casbeer, David and Weintraub, Isaac and Von Moll, Alexander},
eventtitle = {SciTech},
date = {2025-01-12},
doi = {10.2514/6.2025-1351},
note = {Accepted},
location = {Orlando, USA},
booktitle = {SciTech},
publisher = {AIAA},
title = {Maximum Kinetic Energy Paths for a Dubins Vehicle with Decaying Speed},
year = {2025},
}
@techreport{vonmoll2023multi-agent,
abstract = {Mission operations include a myriad of priorities that are subject to change in the field, of which four are commonly used by pilots: Signature Management (SM), Optimize Killing (OK), Weapon Engagement Zone Denial (WEZD), and Mutual Support (MS). The scope of this project includes three of these priorities, namely OK, WEZD, and MS in an effort to mature autonomy in these areas for unmanned platforms. Furthermore, the inclusion of uncertainty of sensor reliability, asset location, target location/strategy, and other factors are a focus of this effort. Air and missile threats in contested airspace represent a challenge for a number of Air Force missions [1]. In concert, some of the tasks include Defensive Counterair (DCA), Offensive Counterair (OCA), Intelligence, Surveillance, and Reconnaissance (ISR), Air Mobility Operations (AMO), Strike, and Interdiction. Although not comprehensive, these tasks are required for achieving air superiority to support and defend enemy or friendly airspace. As defined in JP 3-01 [2], in OCA, enemy Integrated Air Defense Systems (IADS) attempt to destroy, disrupt, or neutralize penetrations of their airspace. This is an attempt to degrade OCA operations. One way to address enemy IADS is through Suppression of Enemy Air Defense (SEAD). SEAD missions neutralize, destroy, or temporarily degrade surface-based enemy Air Defenses (ADs) by destructive or disruptive means.},
author = {Von Moll, Alexander and Weintraub, Isaac},
date = {2023-12-01},
location = {None},
journal = {Defense Technical Information Center},
publisher = {Defense Technical Information Center},
title = {Multi-Agent Risk-aware Teaming under Uncertainty (MARTY)},
url = {https://avonmoll.github.io/files/marty.pdf},
year = {2023},
}
@book{lasota2013chaos,
author = {Lasota, Andrzej and Mackey, Michael C},
publisher = {Springer Science & Business Media},
title = {Chaos, fractals, and noise: stochastic aspects of dynamics},
volume = {97},
year = {2013},
}
@article{gerlach2023introduction,
abstract = {This document serves to provide and introduction to the Frobenius-Perron ("push-forward") and Koopman ("pull-back") operators. The terminology and mathematics required to understand and use these operators is foreign to most engineers. Thus, this tutorial tries to be explicit in defining and providing intuition to new mathematical concepts as they are introduced. Exercises with solutions are also provided so the reader can test their understanding.},
author = {Gerlach, Adam R.},
date = {2023-05-09},
location = {None},
journal = {None},
publisher = {None},
title = {An Introduction to the Frobenius-Perron and Koopman Operators},
year = {2023},
}
@inproceedings{vonmoll2024constrained,
abstract = {In this paper, we extend existing turret defense differential game formulations involving a turn-constrained turret and mobile agent to include specified final time and a constraint. For the purposes of this analysis, the specified final time may represent some exogenous input, perhaps representing the time at which some other event will take place. As for the constraint, it represents a keep-out zone for the mobile agent. The scenario is formulated as a two-player, zero-sum differential game and solved via the method of characteristics (i.e., back-propagation of equilibrium trajectories). Three different trajectory types make up the solution: trajectories that end with the turret aligned with the mobile agent, trajectories that end with the mobile agent on the constraint boundary, and regular trajectories.},
author = {Von Moll, Alexander and Gerlach, Adam R. and Bakker, Craig and Rupe, Adam and Pachter, Meir},
eventtitle = {Modeling, Estimation and Control Conference},
date = {2024-10-27},
note = {Accepted},
location = {Chicago, USA},
booktitle = {Modeling, Estimation and Control Conference},
publisher = {IFAC},
title = {Constrained Turret Defense with Fixed Final Time},
year = {2024},
}
@inproceedings{wolek2024sampling-based,
abstract = {Existing methods for avoiding dynamic engagement zones (EZs) and minimizing risk leverage the calculus of variations to obtain optimal paths. While such methods are deterministic, they scale poorly as the number of engagement zones increases. Furthermore, optimal-control based strategies are sensitive to initial guesses and often converge to local, rather than global, minima. This paper presents a novel sampling-based approach to obtain a feasible flight plan for a Dubins vehicle to reach a desired location in a bounded operating region in the presence of a large number of engagement zones. The dynamic EZs are coupled to the vehicle dynamics through its heading angle. Thus, the dynamic two-dimensional obstacles in the (x, y) plane can be transformed into three-dimensional static obstacles in a lifted (x, y, ψ) space. This insight is leveraged in the formulation of a Rapidly-exploring Random Tree (RRT∗) algorithm. The algorithm is evaluated with a Monte Carlo experiment that randomizes EZ locations to characterize the success rate and average path length as a function of the number of EZs and as the computation time made available to the planner is increased.},
author = {Wolek, Artur and Weintraub, Isaac E. and Von Moll, Alexander and Casbeer, David and Manyam, Satyanarayana G.},
eventtitle = {Modeling, Estimation and Control Conference},
date = {2024-10-27},
note = {Accepted},
location = {Chicago, USA},
booktitle = {Modeling, Estimation and Control Conference},
publisher = {IFAC},
title = {Sampling-Based Risk-Aware Path Planning Around Dynamic Engagement Zones},
year = {2024},
}
@article{vanparys2015distributionally,
author = {Van Parys, Bart and Kuhn, Daniel and Goulart, Paul and Morari, Manfred},
doi = {10.1109/tac.2015.2444134},
journal = {IEEE Transactions on Automatic Control},
pages = {1--1},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
title = {Distributionally Robust Control of Constrained Stochastic Systems},
url = {http://dx.doi.org/10.1109/tac.2015.2444134},
year = {2015},
}
@article{imado1998high-g,
author = {Imado, Fumiaki and Uehara, Sachio},
doi = {10.2514/2.4351},
issue = {6},
journal = {Journal of Guidance, Control, and Dynamics},
language = {en},
month = {11},
pages = {876--881},
publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
title = {High-g Barrel Roll Maneuvers Against Proportional Navigation from Optimal Control Viewpoint},
url = {http://dx.doi.org/10.2514/2.4351},
volume = {21},
year = {1998},
}
@inproceedings{milutinovic2024pursuit-evasion,
abstract = {In classical works on a planar differential pursuit-evasion game with a faster pursuer, the intercept point resulting from the equilibrium strategies lies on the Apollonius circle. This property was exploited for the construction of the equilibrium strategies for two faster pursuers against one evader. Extensions for planar multiple-pursuer single-evader scenarios have been considered. We study a pursuit-evasion game on a sphere and the relation of the equilibrium intercept point to the Apollonius domain on the sphere. The domain is a generalization of the planar Apollonius circle set. We find a condition resulting in the intercept point belonging to the Apollonius domain, which is the characteristic of the planar game solution. Finally, we use this characteristic to discuss pursuit and evasion strategies in the context of two pursuers and a single slower evader on the sphere and illustrate it using numerical simulations.},
author = {Milutinović, Dejan and Von Moll, Alexander and Manyam, Satyanarayana G. and Casbeer, David W. and Weintraub, Isaac E. and Pachter, Meir},
eventtitle = {Conference on Decision and Control},
date = {2024-12-16},
note = {Accepted},
location = {Milan, Italy},
booktitle = {Conference on Decision and Control},
publisher = {IEEE},
title = {Pursuit-Evasion on a Sphere and When it Can Be Considered Flat},
url = {https://arxiv.org/abs/2403.15188},
year = {2024},
}
@inbook{kovshov2000geodesic,
author = {Kovshov, A. M.},
doi = {10.1007/978-1-4612-1336-9_5},
isbn = {['9781461271000', '9781461213369']},
journal = {Advances in Dynamic Games and Applications},
pages = {97--113},
publisher = {Birkhäuser Boston},
title = {Geodesic Parallel Pursuit Strategy in a Simple Motion Pursuit Game on the Sphere},
url = {http://dx.doi.org/10.1007/978-1-4612-1336-9_5},
year = {2000},
}
@inproceedings{merkulov2024reinforcement,
author = {Merkulov, Gleb and Iceland, Eran and Michaeli, Shay and Riechkind, Yosef and Gal, Oren and Barel, Ariel and Shima, Tal},
booktitle = {AIAA SCITECH 2024 Forum},
doi = {10.2514/6.2024-0125},
journal = {AIAA SCITECH 2024 Forum},
month = {1},
publisher = {American Institute of Aeronautics and Astronautics},
title = {Reinforcement Learning Based Decentralized Weapon-Target Assignment and Guidance},
url = {http://dx.doi.org/10.2514/6.2024-0125},
venue = {Orlando, FL},
year = {2024},
}
@article{levchenkov1990differential,
author = {Levchenkov, A. Y. and Pashkov, A. G.},
doi = {10.1007/bf00939563},
issue = {3},
journal = {Journal of Optimization Theory and Applications},
language = {en},
month = {6},
pages = {501--518},
publisher = {Springer Science and Business Media LLC},
title = {Differential game of optimal approach of two inertial pursuers to a noninertial evader},
url = {http://dx.doi.org/10.1007/bf00939563},
volume = {65},
year = {1990},
}
@article{aravind1994symmetrical,
abstract = {The following is a well known pursuit problem: n bugs are at rest at the vertices of a regular polygon. At a certain instant each bug starts crawling towards its neighbour on the right with a constant speed, always altering its course so as to be headed directly towards its neighbour. How long does it take for the bugs to meet at the center of the polygon and what paths do they trace out in getting there? The earliest reference I could find to this problem was in a collection of mathematical puzzles edited by L.A.Graham. A more recent reference to it occurs in the amusing and informative collection of geometrical curiosities by David Wells. The “n-bug” problem was also discussed briefly in two of Martin Gardner’s columns in Scientific American. The cover of the July 65 issue of that magazine shows the equiangular spirals traced out by four bugs as they “square dance” their way towards their tryst at the centre.},
author = {Aravind, P.K.},
doi = {10.2307/3619428},
issue = {481},
journal = {The Mathematical Gazette},
language = {en},
month = {3},
pages = {30--36},
publisher = {Cambridge University Press (CUP)},
title = {A symmetrical pursuit problem on the sphere and the hyperbolic plane},
url = {http://dx.doi.org/10.2307/3619428},
volume = {78},
year = {1994},
}
@article{aliyev2023geometric,
abstract = {In the paper, some geometric properties of the plane interception curve defined by a nonlinear ordinary differential equation are discussed. Its parametric representation is used to find the limits of some triangle elements associated with the curve. These limits have some connections with the lemniscate constants A,B and Gauss's constant G, which were used to compare with the classical pursuit curve. The analogous spherical geometry problem is solved using a spherical curve defined by the Gudermannian function. It is shown that the results agree with the angle-preserving property of Mercator and Stereographic projections. The Mercator and Stereographic projections also reveal the symmetry of this curve with respect to Spherical and Logarithmic Spirals. The geometric properties of the spherical curve are proved in two ways, analytically and using a lemma about spherical angles. A similar lemma for the planar case is also mentioned. The paper shows symmetry/asymmetry between the spherical and planar cases and the derivation of the properties of these curves as limiting cases of some plane and spherical geometry results.},
archiveprefix = {arXiv},
author = {Aliyev, Yagub N.},
doi = {10.3390/axioms12070704},
eprint = {2305.07873v1},
file = {2305.07873v1.pdf},
month = {May},
note = {Axioms (ISSN 2075-1680) Special Issue "Advances in Mathematics and Its Applications II"},
primaryclass = {math.DG},
title = {Geometric Properties of Planar and Spherical Interception Curves},
url = {http://arxiv.org/abs/2305.07873v1},
year = {2023},
}
@article{vlassakis2020two-on-one,
author = {Vlassakis, Mark and Pachter, Meir},
doi = {10.1016/j.ifacol.2020.12.1687},
issue = {2},
journal = {IFAC-PapersOnLine},
language = {en},
pages = {3463--3468},
publisher = {Elsevier BV},
title = {Two-on-One Pursuit when the Pursuers Have the Same Speed as the Evader},
url = {http://dx.doi.org/10.1016/j.ifacol.2020.12.1687},
volume = {53},
year = {2020},
}
@article{vonmoll2024complete,
abstract = {In the Lady in the Lake scenario, a mobile agent, 𝐿, is pitted against an agent, 𝑀, who is constrained to move along the perimeter of a circle. 𝐿 is assumed to begin inside the circle and wishes to escape to the perimeter with some finite angular separation from 𝑀 at the perimeter. This scenario has, in the past, been formulated as a zerosum differential game wherein 𝐿 seeks to maximize terminal separation and 𝑀 seeks to minimize it. Its solution is well-known. However, there is a large portion of the state space for which the canonical solution does not yield a unique equilibrium strategy. This paper provides such a unique strategy by solving an auxiliary zero-sum differential game. In the auxiliary differential game, 𝐿 seeks to reach a point opposite of 𝑀 at a radius for which their maximum angular speeds are equal (i.e., the antipodal point). 𝐿 wishes to minimize the time to reach this point while 𝑀 wishes to maximize it. The solution of the auxiliary differential game is comprised of a Focal Line, a Universal Line, and their tributaries. The Focal Line tributaries’ equilibrium strategy for 𝐿 is semi-analytic, while the Universal Line tributaries’ equilibrium strategy is obtained in closed form.},
author = {Von Moll, Alexander and Pachter, Meir},
date = {2024-07-09},
doi = {10.1007/s13235-024-00614-2},
note = {Presented at the International Symposium on Dynamic Games and Applications},
location = {Valladolid, Spain},
journal = {Dynamic Games and Applications},
publisher = {Springer},
title = {Complete Solution of the Lady in the Lake Scenario},
url = {https://arxiv.org/abs/2401.14994},
year = {2024},
}
@inproceedings{pachter1987pincer,
author = {Pachter, M. and Bar-itzhack, I.},
booktitle = {26th IEEE Conference on Decision and Control},
doi = {10.1109/cdc.1987.272778},
journal = {26th IEEE Conference on Decision and Control},
month = {12},
publisher = {IEEE},
title = {Pincer movement pursuit-An outline},
url = {http://dx.doi.org/10.1109/cdc.1987.272778},
venue = {Los Angeles, California, USA},
year = {1987},
}
@article{mutalik2021mathcan,
author = {Mutalik, Pradeep},
journal = {Quanta Magazine},
month = {Aug},
title = {Math can, in theory, help you escape a hungry bear},
url = {https://www.quantamagazine.org/math-can-in-theory-help-you-escape-a-hungry-bear-20210825/},
year = {2021},
}
@article{pachter2019classical,
author = {Pachter, Meir and Coates, Sean},
doi = {10.1007/s13235-018-0264-8},
issue = {3},
journal = {Dynamic Games and Applications},
language = {en},
month = {9},
pages = {800--850},
publisher = {Springer Science and Business Media LLC},
title = {The Classical Homicidal Chauffeur Game},
url = {http://dx.doi.org/10.1007/s13235-018-0264-8},
volume = {9},
year = {2019},
}
@article{nakamura-zimmerer2021neural,
abstract = {Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not well understood. In this paper we use numerical simulations to demonstrate that typical test accuracy metrics do not effectively capture the ability of an NN controller to stabilize a system. In particular, some NNs with high test accuracy can fail to stabilize the dynamics. To address this we propose two NN architectures which locally approximate a linear quadratic regulator (LQR). Numerical simulations confirm our intuition that the proposed architectures reliably produce stabilizing feedback controllers without sacrificing optimality. In addition, we introduce a preliminary theoretical result describing some stability properties of such NN-controlled systems.},
archiveprefix = {arXiv},
author = {Nakamura-Zimmerer, Tenavi and Gong, Qi and Kang, Wei},
doi = {10.23919/ACC53348.2022.9867619},
eprint = {2109.07466v2},
file = {2109.07466v2.pdf},
month = {09},
primaryclass = {math.OC},
title = {Neural network optimal feedback control with enhanced closed loop stability},
url = {http://arxiv.org/abs/2109.07466v2},
year = {2021},
}
@article{vonmoll2024basic,
abstract = {This paper establishes a concise definition for an Engagement Zone which describes a region of space for which a Mobile Agent must alter its current motion strategy or otherwise risk engaging with a known Threat. In the event of an engagement, the Mobile Agent may have to actively evade the Threat in order to guarantee survival. Provided the Engagement Zone definition, several fundamental engagement models are described and their corresponding Engagement Zones are derived. In each of the engagement models, the Mobile Agent is treated as an Evader; they include pursuit-evasion against a range-limited Pursuer moving with simple motion and faster speed, a variation in which the Pursuer is slower, and a turret-evasion scenario against a range-limited, turn-rate-limited Turret. The slow Pursuer Engagement Zone is applied to a path planning scenario wherein the Mobile Agent must reach a desired target in minimum time while navigating outside the dynamically changing Engagement Zone. Numerical results demonstrate the advantage of Engagement Zone-based navigation over other path plans based on circumnavigation.},
author = {Von Moll, Alexander and Weintraub, Isaac},
date = {2024-09-12},
doi = {10.2514/1.I011394},
issue = {10},
pages = {885--891},
location = {None},
journal = {Journal of Aerospace Information Systems},
publisher = {AIAA},
title = {Basic Engagement Zones},
url = {https://arxiv.org/abs/2311.06165},
volume = {21},
year = {2024},
}
@article{olsder1988use,
author = {Olsder, Geert Jan and Papavassilopoulos, George P},
doi = {10.1016/0022-247x(88)90097-2},
issue = {2},
journal = {Journal of Mathematical Analysis and Applications},
language = {en},
month = {12},
pages = {466--478},
publisher = {Elsevier BV},
title = {About when to use the searchlight},
url = {http://dx.doi.org/10.1016/0022-247x(88)90097-2},
volume = {136},
year = {1988},
}
@inproceedings{hespanha2000deception,
author = {Hespanha, Joao P. and Ateskan, Yusuf S. and Kizilocak, H.},
booktitle = {2nd DARPA-JFACC Symposium on Advances in Enterprise Control},
eventtitle = {2nd DARPA-JFACC Symposium on Advances in Enterprise Control},
pages = {1-9},
title = {Deception in non-cooperative games with partial information},
year = {2000},
}
@techreport{scott2017countering,
author = {Scott, Kevin D.},
institution = {Joint Chiefs of Staff, United States of America},
title = {Countering Air and Missile Threats},
year = {2017},
}
@article{patle2019review:,
author = {Patle, B.K. and Babu L, Ganesh and Pandey, Anish and Parhi, D.R.K. and Jagadeesh, A.},
doi = {10.1016/j.dt.2019.04.011},
issue = {4},
journal = {Defence Technology},
language = {en},
month = {8},
pages = {582--606},
publisher = {Elsevier BV},
title = {A review: On path planning strategies for navigation of mobile robot},
url = {http://dx.doi.org/10.1016/j.dt.2019.04.011},
volume = {15},
year = {2019},
}
@article{patil2023risk-minimizing,
abstract = {This paper addresses a continuous-time risk-minimizing two-player zero-sum stochastic differential game (SDG), in which each player aims to minimize its probability of failure. Failure occurs in the event when the state of the game enters into predefined undesirable domains, and one player's failure is the other's success. We derive a sufficient condition for this game to have a saddle-point equilibrium and show that it can be solved via a Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) with Dirichlet boundary condition. Under certain assumptions on the system dynamics and cost function, we establish the existence and uniqueness of the saddle-point of the game. We provide explicit expressions for the saddle-point policies which can be numerically evaluated using path integral control. This allows us to solve the game online via Monte Carlo sampling of system trajectories. We implement our control synthesis framework on two classes of risk-minimizing zero-sum SDGs: a disturbance attenuation problem and a pursuit-evasion game. Simulation studies are presented to validate the proposed control synthesis framework.},
archiveprefix = {arXiv},
author = {Patil, Apurva and Zhou, Yujing and Fridovich-Keil, David and Tanaka, Takashi},
doi = {10.1109/CDC49753.2023.10383399},
eprint = {2308.11546v1},
file = {2308.11546v1.pdf},
month = {Aug},
primaryclass = {math.OC},
title = {Risk-Minimizing Two-Player Zero-Sum Stochastic Differential Game via Path Integral Control},
url = {http://arxiv.org/abs/2308.11546v1},
year = {2023},
}
@inproceedings{li2023safety-critical,
author = {Li, Yihe and Peng, Zhouhua and Liu, Lu and Wang, Haoliang and Gu, Nan and Wang, Anqing and Wang, Dan},
booktitle = {2023 8th International Conference on Automation, Control and Robotics Engineering (CACRE)},
doi = {10.1109/cacre58689.2023.10208636},
journal = {2023 8th International Conference on Automation, Control and Robotics Engineering (CACRE)},
month = {7},
publisher = {IEEE},
title = {Safety-Critical Path Planning of Autonomous Surface Vehicles Based on Rapidly-Exploring Random Tree Algorithm and High Order Control Barrier Functions},
url = {http://dx.doi.org/10.1109/cacre58689.2023.10208636},
venue = {Hong Kong, China},
year = {2023},
}
@article{wachter2006implementation,
author = {Wächter, Andreas and Biegler, Lorenz T.},