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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...
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 109 (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...
Fast Model Predictive Control Using Online Optimization
, 2008
"... A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well known technique for implementing fast MPC is to compute the entire control law offline, in which c ..."
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Cited by 55 (19 self)
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A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well known technique for implementing fast MPC is to compute the entire control law offline, in which case the online controller can be implemented as a lookup table. This method works well for systems with small state and input dimensions (say, no more than 5), and short time horizons. In this paper we describe a collection of methods for improving the speed of MPC, using online optimization. These custom methods, which exploit the particular structure of the MPC problem, can compute the control action on the order of 100 times faster than a method that uses a generic optimizer. As an example, our method computes the control actions for a problem with 12 states, 3 controls, and horizon of 30 time steps (which entails solving a quadratic program with 450 variables and 1260 constraints) in around 5msec, allowing MPC to be carried out at 200Hz. 1
DNSbased predictive control of turbulence: an optimal benchmark for feedback algorithms
, 1999
"... this paper describes and demonstrates one approach of determining such control strategies via optimal control theory and iterative direct numerical simulations. 2. Optimal and robust control in the predictive control framework 2.1. The seminal idea and an analogy to the game of chess The general i ..."
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Cited by 49 (6 self)
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this paper describes and demonstrates one approach of determining such control strategies via optimal control theory and iterative direct numerical simulations. 2. Optimal and robust control in the predictive control framework 2.1. The seminal idea and an analogy to the game of chess The general idea of the recedinghorizon predictive control setting (as formulated in continuous time) is shown in Figure 1. To put this approach into a more intuitive context, and to appreciate better the importance of the (somewhat mathematical) gradientbased optimization approach to the present problem, it is useful at the outset to compare and contrast the present approach to massivelyparallel bruteforce algorithms recently developed to play the game of chess. The parallels and the shortcomings of this analogy highlight well the problem at hand. t = 0 t = T ) Optimization of controls on horizon [0; T ]. . . . t = T a t = T a + T ) Optimization of controls on horizon [T a ; T a + T ]. . . . t = 2T a t = 2T a + T ) Optimization of controls on horizon [2T a ; 2T a + T ]. . . . t = 3T a : : : etc. Figure 1. The sequence of events in recedinghorizon predictive control. The heavy solid arrows indicate the flow advancement. The evolution of the "actual" flow response to several "test" distribution of controls is explored during the iterative flow prediction (dashed line) and adjoint computation (dotdashed line) stages, during which the control is optimized by a gradient algorithm. Once this iteration converges, the flow is "advanced" some portion Ta of the period T over which the control was optimized, and the optimization process is begun anew. The goal when playing chess is to capture the other player's king through an alternating series of discrete moves with the opponen...
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 46 (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
RealTime Optimization and Nonlinear Model Predictive Control of Processes Governed By DifferentialAlgebraic Equations
, 2001
"... Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast offline method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performan ..."
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Cited by 41 (18 self)
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Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast offline method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briey reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of realtime optimization. Special strategies have been developed to effectively minimize the online computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical realtime problems they have proven much faster than fast offline strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice.
TD Models of Reward Predictive Responses in Dopamine Neurons
"... This article focuses on recent modeling studies of dopamine neuron activity and their influence on behavior. Activity of midbrain dopamine neurons is phasically increased by stimuli that increase the animal's reward expectation and is decreased below baseline levels when the reward fails to occ ..."
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Cited by 35 (0 self)
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This article focuses on recent modeling studies of dopamine neuron activity and their influence on behavior. Activity of midbrain dopamine neurons is phasically increased by stimuli that increase the animal's reward expectation and is decreased below baseline levels when the reward fails to occur. These characteristics resemble the reward prediction error signal of the temporal difference (TD) model, which is a model of reinforcement learning. Computational modeling studies show that such a dopaminelike reward prediction error can serve as a powerful teaching signal for learning with delayed reinforcement, in particular for learning of motor sequences.
Model Predictive Control for MaxPlusLinear Systems
, 1999
"... Model predictive control (MPC) is a very popular controller design method in the process industry. An important advantage of MPC is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discretetime models. In this paper we extend MPC to a class of discrete e ..."
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Cited by 33 (16 self)
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Model predictive control (MPC) is a very popular controller design method in the process industry. An important advantage of MPC is that it allows the inclusion of constraints on the inputs and outputs. Usually MPC uses linear discretetime models. In this paper we extend MPC to a class of discrete event systems, i.e. we present an MPC framework for maxpluslinear systems. In general the resulting optimization problem is nonlinear and nonconvex. However, if the control objective and the constraints depend monotonically on the outputs of the system, the MPC problem can be recast as problem with a convex feasible set. If in addition the objective function is convex, this leads to a convex optimization problem, which can be solved very efficiently.
Model predictive control for optimal coordination of ramp metering and variable speed limits
 Transportation Research C
"... Model predictive control for optimal coordination of ramp metering and variable speed control ∗ ..."
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Cited by 31 (15 self)
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Model predictive control for optimal coordination of ramp metering and variable speed control ∗