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.