Unified Optimization of Upper Stability Bound and Tracking Performance Index for Singularly Perturbed Systems

In this paper, the problem of unified optimization of upper stability bound $\varepsilon^{\ast}$ and tracking performance index $J^{\ast}$ for singularly perturbed systems is considered. First, an optimal output tracking controller is given based on the method of minimum value principle, such that the original system achieves asymptotically stable and asymptotic tracking of the tracking system and the minimum value of quadratic performance index can be obtained. Furthermore, based on Nash game theory, an algorithm to optimize ($\varepsilon^{\ast}, J^{\ast}$) simultaneously which transfers multi-objective problem into a single objective problem as well we determines the objective weights. Finally, one numerical example is given to illustrate the correctness and feasibility of the proposed results.