Optimal control problem for linear fractional-order systems

Abstract

The optimal control problem for linear dynamic systems of fractional order is investigated. This problem is reduced to the classical moment problem. This paper validates the conditions making possible to formulate and resolve the obtained moment problem. Some particular cases of one- and two-dimensional fractional-order systems are discussed and the explicit solutions for the problems of optimal control were obtained. In particular, this paper studies the problem to minimize the norm of control for the assigned time interval and the problem of control with the minimal time of the object transition into the desirable state with the given limitation of the norm of control. It is also shown that the moment method may be also applied to the systems of fractional order with distributed parameters. The problem of optimal control for the transfer-type equation with a fractional derivative in time is formulated and the respective moment problem is analyzed.