Hybrid Intelligent Optimization Method for Nonlinear Path-constrianed Switched Systems

A hybrid intelligent dynamic optimization method is proposed to find the optimal input and switching times for path-constrained nonlinear switched systems within a finite number of iterations. Firstly, the path constraint is discretized into multiple point constraints, then a negative value is used to restrict the right-hand side of the path constraint. Secondly, the transformed problem is solved by deterministic optimization method to obtain the local optimal control input and switching times, and then simulated annealing (SA) is used to detect the current local minimum and jump to a better local minimum with a certain probability. After that, such a search process is repeated until finding the global optimal solution that rigorously satisfies the path constraint. Thirdly, the finite convergence of the method is proved mathematically. Finally, the effectiveness of the method in improving the solution accuracy and guaranteeing rigorous satisfaction of the path constraint of is analyzed by a numerical example.

I. Introduction

Dynamic optimization of switched systems refers to find the optimal switching times and the optimal input to optimize the cost function. Such problems have been widely used in various fields, such as biological systems [1], flight control [2], chemical processes [3] and robotic systems [4].