Robust constrained model predictive control using linear matrix inequalities

Introduction to linear and nonlinear programming

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Predictive Control for Linear and Hybrid Systems

This paper gives an overview of robustness in Model Predictive Control (MPC). After reviewing the basic concepts of MPC, we survey the uncertainty descriptions considered in the MPC literature, and the techniques proposed for robust constraint handling, stability, and performance. The key concept of “closedloop prediction” is discussed at length. The paper concludes with some comments on future research directions.

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Robust model predictive control: A survey

The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to explicitly deal with model uncertainty. In this paper, the authors address the robustness issue in MPC by directly incorporating the description of plant uncertainty in the MPC problem formulation. The plant uncertainty is expressed in the time-domain by allowing the state-space matrices of the discrete-time plant to be arbitrarily time-varying and belonging to a polytope. The existence of a feedback control law minimizing an upper bound on the infinite horizon objective function and satisfying the input and output constraints is reduced to a convex optimization over linear matrix inequalities (LMIs). It is shown that for the plant uncertainty described by the polytope, the feasible receding horizon state feedback control design is robustly stabilizing.

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http://bme2.aut.ac.ir/~towhidkhah/mpc/seminars-ppt/seminar mpc/foroogh shamsi/references1/on linear programming and robust model-predictive control using impulse-responses.pdf

G. C. Papavasiliou

Papers

On linear programming and robust modelpredictive control using impulse-responses