Opuscula Math. 34, no. 4 (2014), 763-775
Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods
Abstract. In the paper, we study a linear-quadratic optimal control problem of Mayer type given by a fractional control system. First, we prove a theorem on the existence of a solution to such a problem. Next, using the local implicit function theorem, we derive a formula for the gradient of a cost functional under constraints given by a control system and prove a maximum principle in the case of a control constraint set. The formula for the gradient is used to implement the gradient methods for the problem under consideration.
Keywords: fractional Riemann-Liouville derivative, Mayer problem, existence of an optimal solution, maximum principle, gradient method.
Mathematics Subject Classification: 26A33, 49J15, 49K15, 49M37.