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285
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 203 (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.
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 48 (18 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
Constrained state estimation for nonlinear discretetime systems: Stability and moving horizon approximations
 IEEE Transactions on Automatic Control
, 2003
"... Abstract—State estimator design for a nonlinear discretetime system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ o ..."
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Cited by 47 (1 self)
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Abstract—State estimator design for a nonlinear discretetime system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ online optimization using a moving horizon approximation. In this article we propose a general theory for constrained moving horizon estimation. Sufficient conditions for asymptotic and bounded stability are established. We apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation. Examples are used to illustrate the benefits of constrained state estimation. Our framework is deterministic. Index Terms—Constraints, model predictive control (MPC), moving horizon estimation (MHE), optimization, state estimation. I.
Optimal coordination of variable speed limits to suppress shock waves
 Transportation Research Record
, 2004
"... Optimal coordination of variable speed limits to suppress shock waves ∗ ..."
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Cited by 46 (27 self)
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Optimal coordination of variable speed limits to suppress shock waves ∗
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 43 (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
Optimal control of constrained piecewise affine systems with state and inputdependent disturbances
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Model Predictive Control of Coordinated MultiVehicle Formations
 In IEEE Conference on Decision and Control
, 2002
"... A generalized model predictive control (MPC) formulation is derived that extends the existing theory to a multivehicle formation stabilization problem. The vehicles are individually governed by nonlinear and constrained dynamics. The extension considers formation stabilization to a set of permis ..."
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Cited by 38 (9 self)
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A generalized model predictive control (MPC) formulation is derived that extends the existing theory to a multivehicle formation stabilization problem. The vehicles are individually governed by nonlinear and constrained dynamics. The extension considers formation stabilization to a set of permissible equilibria, rather than a unique equilibrium. Simulations for three vehicle formations with input constrained dynamics on configuration space SE(2) are performed using a nonlinear trajectory generation (NTG) software package developed at Caltech. Preliminary results and an outline of future work for scaling/decentralizing the MPC approach and applying it to an emerging experimental testbed are given.
Unconstrained Receding Horizon Control with No Terminal Cost
, 2001
"... In this paper, we discuss a stabilizing receding horizon scheme for unconstrained nonlinear systems. Using Dini's theorem on the uniform convergence of functions, we show that there always exist a finite horizon length for which the corresponding receding horizon scheme is stabilizing without using ..."
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Cited by 33 (9 self)
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In this paper, we discuss a stabilizing receding horizon scheme for unconstrained nonlinear systems. Using Dini's theorem on the uniform convergence of functions, we show that there always exist a finite horizon length for which the corresponding receding horizon scheme is stabilizing without using terminal costs and/or constraints.
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 32 (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.
Stabilizing Model Predictive Control of Hybrid Systems
"... Abstract—In this note, we investigate the stability of hybrid systems in closedloop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for dis ..."
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Cited by 29 (25 self)
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Abstract—In this note, we investigate the stability of hybrid systems in closedloop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1,norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory. Index Terms—Hybrid systems, Lyapunov stability, model predictive control (MPC), piecewise affine systems. I.