Browsing by Author "Idczak, Dariusz"

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Access status: Open Access ,
On a linear-quadratic problem with Caputo derivative
(2016) Idczak, Dariusz; Walczak, Stanisław
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.
Access status: Open Access ,
Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods
(2014) Idczak, Dariusz; Walczak, Stanisław
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.