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72
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 199 (5 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 96 (4 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 78 (4 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...
Application of interiorpoint methods to model predictive control
 JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
, 1998
"... We present a structured interiorpoint method for the efficient solution of the optimal control problem in model predictive control (MPC). The cost of this approach is linear in the horizon length, compared with cubic growth for a naive approach. We use a discretetime Riccati recursion to solve the ..."
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Cited by 46 (6 self)
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We present a structured interiorpoint method for the efficient solution of the optimal control problem in model predictive control (MPC). The cost of this approach is linear in the horizon length, compared with cubic growth for a naive approach. We use a discretetime Riccati recursion to solve the linear equations efficiently at each iteration of the interiorpoint method, and show that this recursion is numerically stable. We demonstrate the effectiveness of the approach by applying it to three process control problems.
Receding Horizon Control of Nonlinear Systems: A Control . . .
, 2000
"... n Automatic Control, pages 898 907, 1990. J. Shamma and M. Athans. Guaranteed properties of gain scheduled control for linear parametervarying plants. Automatica, pages 559 564, 1991. J. Shamma and M. Athans. Gainscheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, ..."
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Cited by 41 (4 self)
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n Automatic Control, pages 898 907, 1990. J. Shamma and M. Athans. Guaranteed properties of gain scheduled control for linear parametervarying plants. Automatica, pages 559 564, 1991. J. Shamma and M. Athans. Gainscheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, 12(3):101 107, June 1992. [Sch96] A. Schwartz. Theory and Implementation of Numerical Methods Based on RungeKutta Integration for Optimal Control Problems. PhD Disser tation, University of California, Berkeley, 1996. [SCH+00] M. Sznaier, J. Cloutier, R. Hull, D. Jacques, and C. Mracek. Reced ing horizon control lyapunov function approach to suboptimal regula tion of nonlinear systems. Journal of Guidance, Control, and Dynamics, 23(3):399 405, 2000. [SD90] M. Sznaier and M. J. Damborg. Heuristically enhanced feedback con trol of constrained discretetime linear systems. Automatica, 26:521 532, 1990. [SMR99] P. Scokaert, D. Mayne, and J. Rawlings. Suboptimal model predictive cont
APPLYING NEW OPTIMIZATION ALGORITHMS TO MODEL PREDICTIVE CONTROL
"... The connections between optimization and control theory have been explored by many researchers, and optimization algorithms have been applied with success to optimal control. The rapid pace of developments in model predictive control has given rise to a host of new problems to which optimization has ..."
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Cited by 27 (1 self)
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The connections between optimization and control theory have been explored by many researchers, and optimization algorithms have been applied with success to optimal control. The rapid pace of developments in model predictive control has given rise to a host of new problems to which optimization has yet to be applied. Concurrently, developments in optimization, and especially in interiorpoint methods, have produced a new set of algorithms that may be especially helpful in this context. In this paper, we reexamine the relatively simple problem of control of linear processes subject to quadratic objectives and general linear constraints. We show how new algorithms for quadratic programming can be applied efficiently to this problem. The approach extends to several more general problems in straightforward ways.
Nonlinear Optimal Control: A Control Lyapunov Function and Receding Horizon Perspective
 Asian Journal of Control
, 1999
"... Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). The online EulerLagrange computation of receding horizon control is naturally viewed in terms of optimal control, whe ..."
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Cited by 18 (0 self)
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Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). The online EulerLagrange computation of receding horizon control is naturally viewed in terms of optimal control, whereas researchers in CLF methods have emphasized such notions as inverse optimality. We focus on a CLF variation of Sontag's formula, which also results from a special choice of parameters in the socalled pointwise minnorm formulation. Viewed this way, CLF methods have direct connections with the HamiltonJacobiBellman formulation of optimal control. A single example is used to illustrate the various limitations of each approach. Finally, we contrast the CLF and receding horizon points of view, arguing that their strengths are complementary and suggestive of new ideas and opportunities for control design. The presentation is tutorial, emphasizing concepts and connections over details and t...
Explicit Suboptimal Linear Quadratic Regulation with State and Input Constraints
, 2000
"... Optimal feedback solutions to the infinite horizon LQR problem with state and input constraints based on receding horizon realtime quadratic programming are well known. In this paper we develop an explicit solution to the same problem, eliminating the need for realtime optimization. A suboptimal st ..."
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Cited by 13 (11 self)
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Optimal feedback solutions to the infinite horizon LQR problem with state and input constraints based on receding horizon realtime quadratic programming are well known. In this paper we develop an explicit solution to the same problem, eliminating the need for realtime optimization. A suboptimal strategy, based on a suboptimal choice of a finite horizon and imposing additional limitations on the allowed switching between active constraint sets on the horizon, is suggested in order to address the computer memory and processing capacity requirements of the explicit solution. It is shown that the resulting feedback controller is piecewise linear, and the piecewise linear structure is explored and exploited for computational analysis of stability and performance of the suboptimal constrained LQR. The piecewise linear structure can also be exploited for efficient realtime implementation of the controller.
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 12 (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.
Burstlevel Congestion Control Using Hindsight Optimization
, 2000
"... We consider the burstlevel congestioncontrol problem in a communication network with multiple traffic sources, each modeled as a fullycontrollable stream of fluid traffic. The controlled traffic shares a common bottleneck node with highpriority cross traffic described by a Markovmodulated fluid ..."
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Cited by 12 (5 self)
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We consider the burstlevel congestioncontrol problem in a communication network with multiple traffic sources, each modeled as a fullycontrollable stream of fluid traffic. The controlled traffic shares a common bottleneck node with highpriority cross traffic described by a Markovmodulated fluid (MMF). Each controlled source is assumed to have a unique roundtrip delay. The goal is to maximize a linear combination of the throughput, delay, traffic loss rate, and a fairness metric at the bottleneck node. We introduce a simulationbased congestioncontrol scheme capable of performing effectively under rapidlyvarying cross traffic by making use of the provided MMF model of that variation. In our scheme, the control problem is posed as a finitehorizon Markov decision process and is solved heuristically using a technique called Hindsight Optimization. We provide a detailed derivation of our congestioncontrol algorithm based on this technique. Our empirical study shows that the control scheme performs sign...