Hybrid Intelligent Optimization of Nonlinear Switched Systems With Guaranteed Feasibility

To address the challenge of globally optimal control of path-constrained switched systems, a hybrid intelligent dynamic optimization method is proposed by combining the biobjective particle swarm optimization (PSO) method and a gradient descent method, which simultaneously obtains globally optimal switching instants and input and guarantees rigorous satisfaction of the path constraints over the continuous time horizon. First, the path constraint of switched systems is discretized into multiple point constraints, and then the right-hand side of the path constraint ($\leq 0$) is substituted with a negative value ($\leq-\varepsilon$). Second, the single-objective constrained dynamic program of switched systems is transformed into a biobjective unconstrained dynamic program where each particle intelligently adjusts its objectives to detect the global optimum area satisfying the constraints, depending on its current position in the search space by the search mechanism of PSO. Third, the deterministic optimization method is deployed in the detected global optimum area to locate a feasible solution satisfying the Karush–Kuhn–Tucker (KKT) conditions to a specified tolerance of dynamic optimization of switched systems. Moreover, it is proved that the hybrid intelligent dynamic optimization method can obtain the optimal solution satisfying the first-order approximation KKT conditions within a finite number of iterations. Finally, the results of numerical simulations show the effectiveness of the presented method in terms of improving the solution accuracy and guaranteeing rigorous satisfaction of the path constraint.