On a Solution of an Optimal Control Problem for a Linear Fractional-Order System
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We consider an optimal control problem for a dynamical system described by a linear differential equation with the Caputo fractional derivative of an order \(\alpha \in (0, 1)\). A cost functional to be minimized evaluates a deviation of a system’s terminal state from a given target point. In order to construct a solution, we turn from the considered problem to an auxiliary optimal control problem for a first-order linear system with concentrated delays, which approximates the original system and, after that, we reduce this auxiliary problem to an optimal control problem for an ordinary differential system. Moreover, on this basis, we propose a feedback scheme of optimal control of the original system. The efficiency of the approach is illustrated by an example, and the results of numerical simulations are presented.
KeywordsOptimal control problem Linear system Caputo fractional derivative Approximation Feedback control Numerical method
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