Bang-Bang Property and Time-Optimal Control for Caputo Fractional Differential Systems

Abstract

In this paper, by using the controllability method, a bang-bang property and a time optimal control problem for time fractional differential systems (FDS) are considered. First, we formulate our problem and prove the existence theorem. We then state and prove the bang-bang theorem. Finally, we state the optimality conditions that characterize the optimal control. Some application examples are given to illustrate our results.

Keywords

• time optimal control problems
• Bang-Bang theorem
• fractional optimal control
• Dirichlet parabolic equations
• classical control theory
• optimality conditions