Robust min-max model predictive control of linear systems with constraints

Abstract

In this paper the method of design the robust MPC controller for nonzero targets tracking is presented. The proposed method is based on dual mode paradigm in which the inner unconstrained controller is designed together with the robust feasible and invariant region. This robust feasible and invariant set unsure that the unconstrained controller does not violate the process constraints. So, the theory of robust invariant sets is investigated and the algorithm for finding needed robust invariant and feasible is presented. The outer controller is based on the solution of a min-max finite horizon optimisation problem. The mentioned min-max formulation of MPC involves minimisation of maximum of disturbance influence which range over the given polytope of possible disturbance realisations In the formulation of the robust MPC is a new linear cost function used that allow computation of the min-max optimisation problem using only single linear program. At the end, the illustrative real-time experiment is given.