A New Numerical Method for Optimal Control of a Class of Hybrid Systems

Optimal control of uncertain hybrid systems is a major concern in control engineering. For optimal control of hybrid systems, there are a variety of direct methods, including parametric control and state-based parametric control. A reason that indirect methods are less used for optimal control of hybrid systems is difficulty in working with it and its primary valuing. The present study develops a new numerical method for optimal control of hybrid systems which decreases special restrictions of optimal control functions of hybrid systems per provided solution by a Bellman inequality. The obtained results show that an optimal control problem can be easily solved by converting it to an optimization problem. In addition, the used method obtained more accurate numerical value of the performance index. The results showed that the proposed method leads to greater convergence of the algorithm used in optimal control problems. The efficiency and performance of the proposed method was tested by an application example.