A Hybrid Intelligent Method for Path-Constrained Switched Systems with Free Switching Sequences

In this article, a hybrid intelligent optimization method is proposed, which can simultaneously find the optimal input, switching instants, and switching sequences within a finite number of iterations. Firstly, the infinite-dimensional program is transformed into a finite-dimensional program through parameterization methods, and then, since the switching sequences are discrete variables, the discrete-continuous finite-dimensional program is converted into a continuous finite-dimensional program by introducing linear and quadratic constraints. Secondly, the path constraint is discretized into finite point constraints, and the right side of the constraint is replaced with a negative value. Thirdly, an improved differential evolution (IDE) is used for random search to find the global optimal region that satisfies the point constraints, and then a deterministic optimization method is used to find an approximate KKT optimal solution that rigorously satisfies path constraints in the global optimal region. Fourthly, the convergence of the hybrid intelligent method has been proven. Finally, a numerical example shows the effectiveness of the proposed method.

I. Introduction

The optimal control problem of nonlinear switching systems is applied in many fields. Such a problem has been a hot and difficult issue in recent years, due to its widespread application and the implicit representation of the variables to be optimized in the systems. Several methods for solving the optimal solution of this type of problem have been proposed in [1]–[4]. From these results, the optimization methods for nonlinear switched systems can be broadly divided into the following three categories: the deterministic method, the heuristic method, and the hybrid intelligent method. The deterministic method (DM) [1], [3] uses gradient information to quickly converge and accurately obtain the optimal solution. However, due to the dependence of the deterministic method on the selection of the initial search point, it may lead to the deterministic method falling into local optima. The heuristic method [2] has strong global search capabilities, but in the final optimization stage, a lot of computational work is required to find the optimal solution. The hybrid intelligent method (HIM) [4] can avoid local optima and satisfy optimality conditions. However, this work is based on fixed switching sequences and does not consider the path constraint. Therefore, this article develops a hybrid intelligent method that can solve the dynamic optimization problem of nonlinear switched systems with a path constraint and free switching sequences.