|On the Uniqueness and Stability of Mayer Optimal Control Problem with Quasi-convexity Functional
Khelifa Djendel and Zhongcheng Zhou*
International Journal of Control, Automation, and Systems, vol. 21, no. 1, pp.31-39, 2023
Abstract : We consider in this paper Mayer optimal control problem for linear systems with convex compact polyhedral control set. Under quasi convexity of the functional, we give some assumptions to guarantee the uniqueness and analyse the stability for a class of Mayer-type problem via Pontryagin Maximum Principle relying on the controllability index of linear systems. Moreover, we present the error evaluates for the Euler discretization method and it turns out that its accuracy based on the controllability index related with the optimal solution. In addition, we give an example with numerical tests to confirm the theoretical result.
Euler method, linear control system, optimal control, quasi-convex, uniqueness and stability analysis.