Ellipsoidal tube‐based output feedback robust MPC for linear systems with bounded disturbances and noises

Abstract

AbstractThis paper designs an ellipsoidal tube‐based output feedback robust model predictive control approach for linear systems with bounded disturbances and noises subject to physical constraints. The ellipsoidal tube‐based output feedback robust model predictive control approach combines the off‐line optimization to compute controller parameters and deal with system uncertainties, and the on‐line optimization to stabilize the nominal system with time‐varying tightened constraints. In the off‐line optimization, the state observer gain, ancillary feedback controller gain, and tightened constraint sets on the nominal system are synthesized in one optimization. Then, an ellipsoidal terminal constraint set with terminal controller gain and terminal cost matrix, and tightened constraint sets related to different sizes of estimation error bounds are computed. In the on‐line model predictive control optimization with time‐varying tightened constraints, a sequence of nominal control inputs is receding horizon optimized to steer the nominal system state to the ellipsoidal terminal constraint set. When the current nominal system state is bounded within the ellipsoidal terminal constraint set, the nominal control inputs are switched to the feedbacks on the closed‐loop nominal system states. Recursive feasibility of the proposed algorithm and robust stability of the controlled system are guaranteed.