Code for Kernel repurducing Utilities includes the src code
An efficient approach adopting Reproducing Kernel Hilbert Space, RKHS, to estimate the parameters of Differential Equations from noisy realizations of the system's output is presented in this thesis. Initially, this thesis studies the previous works on parameter and state estimation using RKHS. This approach estimates the parameters, order n, the output trajectory and the derivatives of the system up to n-1, where n is the true order. The presented approach is able to handle error in the variable using local fitting and regularization. The suggested method uses Bayesian Information Criterion, BIC, to evaluate possible order for unknown systems. Lastly, to increase the accuracy and computational speed, the approach applies hyper-parameter search and cross-validation to tune its cost function's coefficients. The MATLAB software package has been implemented to evaluate the suggested approach.