The Optimal Control Problem for Linear Distributed Systems of Fractional Order

Optimal control problem considered for the plant which described by one-dimensional transfer equation with Caputo fractional derivative. The equation defined on finite segment. Investigation evaluates for both of cases when controls enter into right part of equation and depend on spatial coordinates and time and when controls enter into boundary conditions and depends on time only. Two types of optimal control problem studied: 1) the problem of plant transfer from initial state to given one with minimal transfer time and control norm restriction; 2) the problem of plant transfer from initial state to given one with minimal control norm at given transfer time. It’s assumed that admissible controls belong to the function class which p-integrable in given domain. It’s shown that assigned optimal control problem can be reduced to the known problem of moments and to corresponding problem of conditional minimization for convex multivariable function. For the problem of moments conditions of statement possibility and solvability derived. This work can be useful for control systems development for plants which dynamics can reveal anomalous diffusion.

fractional order equations, Caputo fractional derivative, problem of moments, optimal control