On a linear-quadratic problem with Caputo derivative
Abstract. In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
Keywords: fractional Caputo derivative, linear-quadratic problem, existence and uniqueness of a solution, maximum principle, gradient method, projection of the gradient method.
Mathematics Subject Classification: 26A33, 49J15, 49K15, 49M37.