Computation of Invariant Tubes for Robust Output Feedback Model Predictive Control

Abstract

This paper presents an algorithm to calculate tightened invariant tubes for output feedback model predictive controllers (MPC). We consider discrete-time linear time-invariant (DLTI) systems with bounded state and input constraints and subject to bounded disturbances. In contrast to existing approaches which either use pre-defined control and observer gains or compute the control and observer gains that optimize the volume of the invariant sets for the estimation and control errors separately, we consider the problem of optimizing the volume of these sets simultaneously. The nonlinearities associated with computing the control and observer gains are circumvented by the application of Farkas’ Theorem and an extended Elimination Lemma, to convert the nonconvex optimization problem into a convex semidefinite program. An update algorithm is then used to reduce the volume of the invariant tube through a finite number of iterations. Numerical examples are provided to illustrate the effectiveness of the proposed algorithm.