J Jurre Hanema

A Robust MPC for Input-Output LPV Models

In this note, a discrete-time robust model predictive control (MPC) design approach is proposed to control systems described by linear parameter-varying models in input-output form subject to constraints. To ensure the stability of the closed-loop system, a quadratic terminal cost along with an ellipsoidal terminal constraint are included in the control optimization problem. The MPC design problem is formulated as a linear matrix inequality problem. The proposed MPC scheme is applied on a continuously stirred tank reactor as an illustrative example.

An MPC approach for LPV systems in input-output form

In this paper, a discrete-time model predictive control (MPC) design approach is proposed to control systems described by linear parameter-varying (LPV) models in input-output form subject to constraints. To ensure stability of the closed-loop system, a quadratic terminal cost along with an ellipsoidal terminal constraint are included in the control optimization problem. The proposed scheme is a robust LPV-MPC scheme, which considers future values of the scheduling variable being uncertain and varying inside a prescribed polytope. The MPC design problem is formulated as a linear matrix inequality (LMI) problem. The effectiveness of the proposed LPV-MPC design is demonstrated using a numerical example.

Tube-based anticipative model predictive control for linear parameter-varying systems

Currently available model predictive control methods for linear parameter-varying systems assume that the future behavior of the scheduling trajectory is unknown over the prediction horizon. In this paper, an anticipative tube MPC algorithm for polytopic linear parameter-varying systems under full state feedback is developed. In contrast to existing approaches, the method explicitly takes into account expected future variations in the scheduling variable: its current value is measured exactly, while the future values over the prediction horizon are assumed to belong to a sequence of sets describing expected deviations from a nominal trajectory. Through this mechanism, the controller “anticipates” upon future changes in the system dynamics. The algorithm constructs a tube homothetic to a terminal set and employs gain scheduled vertex control laws. A worst-case cost is minimized: the corresponding optimization problem is a single linear program with complexity linear in the prediction horizon. Numerical examples show the validity of the approach.

MPC for linear parameter-varying systems in input-output representation

In this paper, we propose a method for model predictive control of linear parameter-varying (LPV) systems described in an input-output (IO) representation and subject to input- and output constraints. By assuming exact knowledge of the future trajectory of the scheduling variable, the on-line computations reduce to the solution of a nominal predictive control problem. An incremental non-minimal state-space representation is used as a prediction model, giving a controller with integral action suitable for tracking piecewise-constant reference signals. Closed-loop asymptotic stability is guaranteed by a terminal cost and terminal set constraint, and the computation of an ellipsoidal terminal set is discussed. Numerical examples demonstrate the properties of the proposed approach. When exact future knowledge of the scheduling variable is not available, we argue and show that good practical performance can be obtained by a scheduling prediction strategy.