Constrained parameterized optimal control of switched systems based on continuous Hopfield neural networks

This paper studies the problem of optimal control of switched systems under state constraints. It suggests a hybrid approach based on Continuous Hopfield Neural Network (CHNN). To deal with this issue, we need first to determine the optimal switching instants as well as the optimal control input, which guarantees the minimization of a performance criterion while respecting the constraints imposed on the system. Hence, this paper divides the issue under study into two stages. In the first, it starts with the transformation of the problem into an equivalent problem based on parameterization of the switching instants. This step would allow us to calculate the optimal control law and to determine the optimal cost’s derivatives’ expressions at the same time. These expressions are used in the second stage by the CHNN to define the optimal switching instants. In order to respect the state inequalities constraints of the system, the Karush-Kuhn-Tucker conditions and the Lagrange multipliers method associated with the Pontryagin Maximum Principle are used, which we apply on the equivalent problem. The results of this approach have been illustrated through a hydraulic system under state constraints.