Constrained optimal control of switched systems and its application

Abstract

In this paper, we consider an optimal co with state and control constraints, where a prespecified sequence of active subsystems is given. Both the switching instants and the control function are to be chosen such that the cost functional is minimized. Firstly, we convert the problem into a conventional optimal control problem based on parameterization of the switching instants. Next, through discretizing the control space, applying a time-scaling transformation and using the smoothing technique, the optimal control problem is approximated by a non-linear optimization problem with linear constraints and bounds on the variables. Furthermore, an algorithm that finds a suboptimal solution to the original problem is proposed. One major advantage with the new algorithm implementation is the only need to solve a non-linear optimization problem with linear constraints and bounds on the variables. The gradients of these linear constraints and the objective function can be easily obtained. Therefore, the original optimization problem can be solved efficiently using any gradient-based method, such as sequential quadratic programming algorithm. Finally, a flight planning example illustrates the efficiency of the proposed approach.

Keywords:

• switched systems
• optimal control
• control parameterization
• smoothing technique
• flight planning

Acknowledgments

The authors wish to thank the anonymous referees for carefully reading this article and providing valuable comments and suggestions which helped us improve the presentation. This work was supposed by the Chinese National Outstanding Youth Foundation under Grant No. 61125306, the Major Program of Chinese National Natural Science Foundation under Grant Nos. 91016004 and 11190015.