This paper examines the problem of the optimal control of nonlinear switched systems under mixed constraints. The solution to this problem consists mainly in determining two major factors; on the one hand, we need to determine the optimal control input, and on the other one, we have to find out the best switching instants that lead to minimizing a particular functional cost. In order to reach this objective, we use a hybrid approach that consists in dividing the problem in two stages. In the first one, we employ the method of Lagrange multipliers while considering the Karush Kuhn Tucker (KKT) conditions. This method must be accompanied by the bang bang control. This combination of these optimization methods enables us to obtain the optimal control input while respecting the simultaneously imposed constraints on the state and the input. In the second stage, a metaheuristic method is used to define the optimum switching instants, and this is what we call the particle swarm optimization (PSO). In order to approve this approach, different examples are applied in this study.
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