Optimal control with regional pole constraints via the mapping theory. (English) Zbl 0849.93028
Summary: The design of optimal linear, time-invariant systems with regional pole constraint is studied. The performance index consists of two parts. One part is used to penalise the sustained error, and the other part is used to guarantee that the optimal solution will not occur on the boundary of the admissible controller set and to improve the robustness property of the closed-loop system. The necessary condition that the optimal control law must satisfy is derived. Furthermore, the robustness analysis of the regional pole restriction under unstructured perturbation is studied. Based on Gersgorin’s theorem, a new method is presented, which calculates allowable bounds of the unstructured perturbation, so that all the perturbed poles shall still remain inside some regions.