Hybrid Intelligent Optimization of Path-Constrained Switched Systems With Free Switching Sequences

In this article, a hybrid intelligent optimization method is proposed for the dynamic optimization of path-constrained switched systems with free switching sequences. This method combines improved particle swarm optimization and differential evolution (IPSO-DE) method with a gradient-based dynamic optimization method, which can simultaneously obtain the global optimal solution, i.e., optimal control input, optimal switching instants, and optimal switching sequences. First, control vector parameterization (CVP), switching time parameterization (STP), and switching sequence smoothing techniques are employed to transform the original problem into a continuous finite-dimensional dynamic one. Second, the path constraints are discretized into a finite number of point constraints, and the IPSO-DE algorithm is proposed to search for the global optimal solution of the continuous dynamic problem with discretized constraints. Then, the obtained optimal solution serves as the initial point to calculate the gradients of the objective function with respect to control input, switching instants, and switching sequences. Third, the gradient-based deterministic method is applied to obtain the global optimal solution that satisfies the first-order optimality condition. Fourth, the finite termination of the hybrid intelligent optimization method is proven. Finally, the effectiveness of the proposed method is verified through three numerical examples.