Robust model predictive control for a class of disturbed systems

Abstract

This paper proposes a robust model predictive control method for a class of linear discrete time, uncertain and disturbed systems. A relationship between the system disturbance, the states and control input exists, which is used to remove, through several manipulations, the disturbance from the control optimization problem. Moreover, in comparison with other several previous studies, the disturbance does not act directly on the system, a system disturbance matrix being introduced. In principle, the main objective is to find a control law by solving a min-max problem in which a robust performance objective is to be minimized. Instead, an equivalent optimization problem is solved and an upper bound is found for the robust performance objective using a Lyapunov function. With the upper bound, the equivalent control optimization problem is formulated. The solutions of the equivalent optimization problem are used to construct the control law. A Matlab simulation, using Yalmip toolbox, indicates that the states are stabilized to zero and the control input tends to zero.

Keywords

• robust model predictive control
• linear matrix inequality
• uncertain system
• disturbance
• schur complement.