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112
A survey of industrial model predictive control technology
, 2003
"... This paper provides an overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors. A brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control an ..."
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Cited by 277 (4 self)
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This paper provides an overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors. A brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control and identification technology. A general MPC control algorithm is presented, and approaches taken by each vendor for the different aspects of the calculation are described. Identification technology is reviewed to determine similarities and differences between the various approaches. MPC applications performed by each vendor are summarized by application area. The final section presents a vision of the next generation of MPC technology, with an emphasis on potential business and research opportunities.
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 135 (6 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...
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 36 (0 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.
Optimization over state feedback policies for robust control with constraints
, 2005
"... This paper is concerned with the optimal control of linear discretetime systems, which are subject to unknown but bounded state disturbances and mixed constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with memory of prior states is e ..."
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Cited by 33 (4 self)
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This paper is concerned with the optimal control of linear discretetime systems, which are subject to unknown but bounded state disturbances and mixed constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with memory of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This result implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods without having to introduce any conservatism in the problem formulation. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closedloop system is inputtostate stable (ISS) and the constraints are satisfied for all time and for all allowable disturbance sequences. The cost that is chosen to be minimized in the associated finite horizon optimal control problem is a quadratic function in the disturbancefree state and input sequences. It is shown that the value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic or given by a 1norm or ∞norm bound, or a secondorder cone program (SOCP) if the disturbance set is ellipsoidal or given by a 2norm bound.
State and output feedback nonlinear model predictive control: An overview
 European Journal of Control
, 2003
"... The purpose of this paper is twofold. In the first part we give a review on the current state of nonlinear model predictive control (NMPC). After a brief presentation of the basic principle of predictive control we outline some of the theoretical, computational, and implementational aspects of this ..."
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Cited by 23 (2 self)
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The purpose of this paper is twofold. In the first part we give a review on the current state of nonlinear model predictive control (NMPC). After a brief presentation of the basic principle of predictive control we outline some of the theoretical, computational, and implementational aspects of this control strategy. Most of the theoretical developments in the area of NMPC are based on the assumption that the full state is available for measurement, an assumption that does not hold in the typical practical case. Thus, in the second part of this paper we focus on the output feedback problem in NMPC. After a brief overview on existing output feedback NMPC approaches we derive conditions that guarantee stability of the closedloop if an NMPC state feedback controller is used together with a full state observer for the recovery of the system state.
Robust Dynamic Programming for MinMax Model Predictive Control of Constrained Uncertain Systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
"... We address minmax model predictive control (MPC) for uncertain discretetime systems by a robust dynamic programming approach, and develop an algorithm that is suitable for linearly constrained polytopic systems with piecewise affine cost functions. The method uses polyhedral representations of the ..."
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Cited by 18 (1 self)
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We address minmax model predictive control (MPC) for uncertain discretetime systems by a robust dynamic programming approach, and develop an algorithm that is suitable for linearly constrained polytopic systems with piecewise affine cost functions. The method uses polyhedral representations of the costtogo functions and feasible sets, and performs multiparametric programming by a duality based approach in each recursion step. We show how to apply the method to robust MPC, and give conditions guaranteeing closed loop stability. Finally, we apply the method to a tutorial example, a parking car with uncertain mass.
Decentralized robust receding horizon control for multivehicle guidance
"... Abstract — This paper presents a decentralized robust Model Predictive Control algorithm for multivehicle trajectory optimization. The algorithm is an extension of a previous robust safe but knowledgeable (RSBK) algorithm that uses the constraint tightening technique to achieve robustness, an invar ..."
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Cited by 17 (8 self)
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Abstract — This paper presents a decentralized robust Model Predictive Control algorithm for multivehicle trajectory optimization. The algorithm is an extension of a previous robust safe but knowledgeable (RSBK) algorithm that uses the constraint tightening technique to achieve robustness, an invariant set to ensure safety, and a costtogo function to generate an intelligent trajectory around obstacles in the environment. Although the RSBK algorithm was shown to solve faster than the previous robust MPC algorithms, the approach was based on a centralized calculation that is impractical for a large group of vehicles. This paper decentralizes the algorithm by ensuring that each vehicle always has a feasible solution under the action of disturbances. The key advantage of this algorithm is that it only requires local knowledge of the environment and the other vehicles while guaranteeing robust feasibility of the entire fleet. The new approach also facilitates a significantly more general implementation architecture for the decentralized trajectory optimization, which further decreases the delay due to computation time.
On robust optimization and the optimal control of constrained linear systems with bounded state disturbances
 in Proc. European Control Conference
, 2003
"... receding horizon control, model predictive control, discretetime systems. The first part of this paper studies a specific class of uncertain quadratic and linear programs, where the uncertainty enters the constraints in an affine manner and the uncertainty set is a polytope. It is shown that one ca ..."
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Cited by 16 (9 self)
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receding horizon control, model predictive control, discretetime systems. The first part of this paper studies a specific class of uncertain quadratic and linear programs, where the uncertainty enters the constraints in an affine manner and the uncertainty set is a polytope. It is shown that one can convert the resulting semiinfinite optimization problem into a standard QP or LP with a finite number of decision variables and a finite number of constraints. This transformation is achieved in a computationally tractable way by solving as many LPs as there are constraints in the optimization problem without uncertainty. It is also shown that if the uncertainty set is given by upper and lower bounds only,then one need not solve any LPs in order to do this transformation; computing the 1norms of the rows of the matrix by which the uncertainty enters the constraints is sufficient. The second part of the paper reviews and extends some definitions and results on inputtostate stability for nonlinear discretetime systems. The third part of the paper shows how one can translate a class of robust finitehorizon optimal control problems (RFHOCPs) into the class of robust convex optimization problems that was studied in the first part of the paper. It is assumed that the system under consideration is linear, that there is a persistent, but bounded state disturbance that assumes values in a polytope and that there are mixed affine constraints on the input and state. By using the results from the previous sections, it is shown that one can set up a receding horizon controller (RHC) that is inputtostate stable (ISS) and guarantees robust constraint satisfaction for all time. The number of decision variables and constraints in the RFHOCP that define the RHC law increases linearly with the horizon length. 1
An ellipsoid algorithm for probabilistic robust controller design
 Systems & Control Letters
"... The ellipsoid algorithm for probabilistic robust controller design ∗ ..."
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Cited by 13 (0 self)
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The ellipsoid algorithm for probabilistic robust controller design ∗
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 12 (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...