Robust tube-based constrained predictive control via zonotopic set-membership estimation

Abstract

This paper proposes an approach to deal with the problem of robust output feedback model predictive control for linear discrete-time systems subject to state and input constraints, in the presence of unknown but bounded disturbances and measurement noises. The estimation of the states is built using a zonotopic set-membership estimation. This set is timedecreasing and is computed off-line as the solution of a Linear Matrix Inequality optimization problem. The control law is designed by using tube-based model predictive control such that the closed-loop stability is guaranteed and the state and input constraints are fulfilled. The proposed methodology is illustrated through numerical simulations.

Robust-Adaptive Interval Predictive Control for Linear Uncertain Systems

“…There exist many predictors based, e.g., on zonotope [18] or interval [17], [1] representation of the set of admissible values of x(s). Opting the simplicity of implementation and computational efficiency, we use an interval predictor here that ensures the property (7).…”

Output feedback model predictive control based on set‐membership state estimation

“…An approach for solving a joint state estimation and control problem using the semi‐definite programming by approximating the quadratic matrix inequalities into LMIs was presented in [29]. A tube‐based output feedback MPC design based on zonotopic set‐membership estimation was developed in [30].…”

“…Inspired by this, a novel output feedback MPC based on ellipsoidal set‐membership state estimation is proposed for time‐varying systems with unknown but bounded external process disturbances and measurement noises in this paper. The difference between the proposed method and the tube‐based MPC [10, 30] lies in the basic idea to compute the control inputs. In tube‐based MPC, there are two optimal control problems need to be considered.…”

Ellipsoidal set-membership state estimation for descriptor systems

“…In set-membership state estimation approaches, the evolution of the system state at each time instant is described by a set consistent with the model of the system, the bounded perturbations and measurement noises simultaneously. Among these sets are, for example, polytopes [30], zonotopes [31], [32], [33] and ellipsoids [34], [35]. Generally, the ellipsoidal set is privileged in literature for its simplicity [36].…”