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Constrained model predictive control: Stability and optimality
 AUTOMATICA
, 2000
"... Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and t ..."
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Cited by 696 (15 self)
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Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant. An important advantage of this type of control is its ability to cope with hard constraints on controls and states. It has, therefore, been widely applied in petrochemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls. In this review, we focus on model predictive control of constrained systems, both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and/or timevarying systems. We concentrate our attention on research dealing with stability and optimality; in these areas the subject has developed, in our opinion, to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control. We distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature. In some cases the finite horizon optimal control problem solved online is exactly equivalent to the same problem with an infinite horizon; in other cases it is equivalent to a modified infinite horizon optimal control problem. In both situations, known advantages of infinite horizon optimal control accrue.
Model Predictive Control: Past, Present and Future
 Computers and Chemical Engineering
, 1997
"... More than 15 years after Model Predictive Control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the online optimization, stability and performance a ..."
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Cited by 210 (8 self)
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More than 15 years after Model Predictive Control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the online optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for nonlinear systems but for practical applications many questions remain, including the reliability and efficiency of the online computation scheme. To deal with model uncertainty "rigorously" an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage. Among the broader research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, nonlinear state estimation, and batch system control. Many practical problems like control objective prior...
Robust Constrained Model Predictive Control using Linear Matrix Inequalities
, 1996
"... The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty i ..."
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Cited by 140 (5 self)
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The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a statefeedback control law which minimizes a "worstcase" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worstcase" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon statefeedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions...
Chromatographic Methods
 In International
, 1992
"... Still the doctor — by a country mile! Preferences for health services in two country towns in northwest New South Wales he relative importance people place on particular healthcare services is a significant factor in meeting their healthcare needs and influencing their health behaviour. ..."
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Cited by 76 (1 self)
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Still the doctor — by a country mile! Preferences for health services in two country towns in northwest New South Wales he relative importance people place on particular healthcare services is a significant factor in meeting their healthcare needs and influencing their health behaviour.
Model Predictive Controllers: A Critical Synthesis of Theory and Industrial Needs
, 1998
"... After several years of efforts, constrained model predictive control (MPC), the de facto standard algorithm for advanced control in process industries, has finally succumbed to rigorous analysis. Yet successful practical implementations of MPC were already in place almost two decades before a rigoro ..."
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Cited by 16 (2 self)
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After several years of efforts, constrained model predictive control (MPC), the de facto standard algorithm for advanced control in process industries, has finally succumbed to rigorous analysis. Yet successful practical implementations of MPC were already in place almost two decades before a rigorous stability proof for constrained MPC was published. What is then the importance of recent theoretical results for practical MPC applications? In this publication we present a pedagogical overview of some of the most important recent developments in MPC theory, and discuss their implications for the future of MPC theory and practice. 1 (713) 743 4309, fax: (713) 743 4323, email: nikolaou@uh.edu.  2  TABLE OF CONTENTS 1 INTRODUCTION 3 2 WHAT IS MPC? 3 2.1 A TRADITIONAL MPC FORMULATION 6 2.2 EXPANDING THE TRADITIONAL MPC FORMULATION 7 2.3 MPC WITHOUT INEQUALITY CONSTRAINTS 8 3 STABILITY 10 3.1 WHAT IS STABILITY? 10 3.1.1 Stability with respect to initial conditions 11 3.1.2 Input...
Control applications of nonlinear convex programming
 the 1997 IFAC Conference on Advanced Process Control
, 1998
"... Since 1984 there has been a concentrated e ort to develop e cient interiorpoint methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interiorpoint methods (beyond their e ciency for LP): they extend gracefully to nonline ..."
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Cited by 7 (3 self)
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Since 1984 there has been a concentrated e ort to develop e cient interiorpoint methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interiorpoint methods (beyond their e ciency for LP): they extend gracefully to nonlinear convex optimization problems. New interiorpoint algorithms for problem classes such as semide nite programming (SDP) or secondorder cone programming (SOCP) are now approaching the extreme e ciency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to e ciently solve nonlinear convex optimization problems opens up new applications. In the rst example we show how SOCP can be used to solve robust openloop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the setpoint and feedback gains for a controller, and compare this method with the more standard approach. Our nal application concerns analysis and synthesis via linear matrix inequalities and SDP. Submitted to a special issue of Journal of Process Control, edited by Y. Arkun & S. Shah, for papers presented at the 1997 IFAC Conference onAdvanced Process Control, June 1997, Ban. This and related papers available via anonymous FTP at
A Framework for Robustness Analysis of Constrained Finite Receding Horizon Control
 IEEE Transactions on Automatic Control
, 1998
"... A framework for robustness analysis of input constrained finite receding horizon control is presented. Under the assumption of quadratic upper bounds on the finite horizon costs, we derive sufficient conditions for robust stability of the standard discretetime linearquadratic receding horizon cont ..."
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Cited by 2 (0 self)
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A framework for robustness analysis of input constrained finite receding horizon control is presented. Under the assumption of quadratic upper bounds on the finite horizon costs, we derive sufficient conditions for robust stability of the standard discretetime linearquadratic receding horizon control formulation. This is achieved by recasting conditions for nominal and robust stability as an implication between quadratic forms, lending itself to Sprocedure tools which are used to convert robustness questions to tractable convex conditions. Robustness with respect to plant/model mismatch as well as for state measurement error is shown to reduce to the feasibility of linear matrix inequalities. Simple examples demonstrate the approach. Keywords: predictive control, optimal control, linear systems, robustness, Sprocedure, LMI. 1 Introduction Receding horizon, moving horizon and model predictive control are names for a state feedback control technique where the control action is dete...
Robust model predictive control for input saturated and soften state constraints,” Asian
 Institute of Technology North Bangkok, 1518 Pibulsongkram, Bangsue, Bangkok 10800, Thailand Email address: vutrieuminh@kmitnb.ac.th Nitin Afzulpurkar: Mechatronics, Industrial System Engineering Group (ISE), School of Engineering and Technology, Asian Ins
, 2005
"... This paper starts with a brief review of robust model predictive control (RMPC) algorithsms for uncertain systems using linear matrix inequalities (LMIs) subject to input and/or output saturated constraints. However when RMPC has both input and state constraints, a difficulty will arise due to the i ..."
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Cited by 2 (2 self)
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This paper starts with a brief review of robust model predictive control (RMPC) algorithsms for uncertain systems using linear matrix inequalities (LMIs) subject to input and/or output saturated constraints. However when RMPC has both input and state constraints, a difficulty will arise due to the inability of the optimizer to satisfy the state constraints due to the constraints on inputs. Therefore, a novel RMPC scheme is presented that softens the state constraints as penalty terms are added to its objective function. These terms maintain state violation at low values until a constrained solution is returned. The state violation can be regulated by changing the value of the weighting factor. A novel robust predictive controller for input saturated and softened state constraints for linear time varying (LTV) systems with polytopic model uncertainties is presented.