Regular Papers

International Journal of Control, Automation and Systems 2023; 21(1): 31-39

Published online January 6, 2023

https://doi.org/10.1007/s12555-021-0570-6

© The International Journal of Control, Automation, and Systems

On the Uniqueness and Stability of Mayer Optimal Control Problem with Quasi-convexity Functional

Khelifa Djendel and Zhongcheng Zhou*

Southwest University

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.

Keywords Euler method, linear control system, optimal control, quasi-convex, uniqueness and stability analysis.

Article

Regular Papers

International Journal of Control, Automation and Systems 2023; 21(1): 31-39

Published online January 1, 2023 https://doi.org/10.1007/s12555-021-0570-6

Copyright © The International Journal of Control, Automation, and Systems.

On the Uniqueness and Stability of Mayer Optimal Control Problem with Quasi-convexity Functional

Khelifa Djendel and Zhongcheng Zhou*

Southwest University

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.

Keywords: Euler method, linear control system, optimal control, quasi-convex, uniqueness and stability analysis.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

Stats or Metrics

Share this article on

  • line

Related articles in IJCAS

IJCAS

eISSN 2005-4092
pISSN 1598-6446