Linear quadratic Nash game-based tracker for multiparameter singularly perturbed sampled-data systems: Digital redesign approach

In this paper, a linear quadratic Nash game-based tracker for multiparameter singularly perturbed sample-data systems is developed. A generalized cross-coupled multiparameter algebraic Riccati equation (GCMARE) with two quadratic cost functions is solved by applying the LQR design methodology for the optimal tracker design. Firstly, the asymptotic expansions of the GCMARE are newly established, and the proposed algorithm is able to effectively solve the GCMARE with the quadratic convergence rate. Then, the low-gain digital controller with a high design performance is realized through the prediction-based digital redesign method. Finally, for further improving the tracking performance, the chaos-evolutionary-programming algorithm (CEPA) is utilized to optimally tune the parameters of the tracker. An example is presented to demonstrate the effectiveness of the proposed methodology.