OPTIMAL CONTROL OF FRACTIONAL-ORDER SWITCHING SYSTEMS
In this paper, we consider an optimal control problem for a switching fractional-order system. For solving this problem, we do not make any assumptions about the number of switches nor about the mode sequence, they are determined by the solution of the problem. First, the fractional-order switching system is embedded into a large family of systems and it is shown that the set of trajectories of the fractional-order switching system is dense in the set of trajectories of the embedded system. Moreover, by using the embedding, we provide a rigorous development of sufficient and necessary conditions for optimality. Finally, we provide an example to demonstrate the effectiveness of our discussed techniques.
fractional-order systems, switched systems, optimal control, fractional-order Gronwall inequality.