Optimal control for a class of impulsive switched systems

Abstract

In this paper, an optimal switch-time control problem is solved for a class of impulsive switched autonomous systems. The considered systems jump at the switching times, and the sequence of active subsystems is pre-specified. The control variables consist of the impulse times and a set of scalars which determine the jump amplitudes. Moreover, the subsystems do not require a refractory period, which can bring more generality. Using the calculus of variation, the partial derivatives of the cost with respect to the control variables are derived, based on which the optimality conditions are given. Meanwhile, the obtained formulas can be used in some gradient descent algorithms to locate the optimal control variables. Finally, the viability of the proposed method is illustrated through two numerical examples.

KEYWORDS:

• Optimal control
• impulsive switched systems
• calculus of variation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under [Grant 61803238 and Grant 61873151].

Notes on contributors

Xiaomei Liu

Xiao-Mei Liu received her M.S. degree in Operational Research and Cybernetics from Ludong University, China, in 2010, and a Ph.D. degree in Control Theory and Control Engineering from Southeast University, China in 2014. She is currently a lecturer in the Business School, Shandong Normal University. Her research interests include switched systems theory, optimal switch-time control theory of switched stochastic systems, and robust control of systems with time-delay.

Shengtao Li

Sheng-Tao Li received his M.S. degree in Operational Research and Cybernetics from Ludong University, China, in 2010, and his Ph.D. degree in Control Theory and Control Engineering from Northeastern University, China in 2013. He is currently an associate professor at the College of Information Science and Engineering, Shandong Normal University. His research interests include robust control and nonlinear control systems.