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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 369 (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.
Linear Controller Design: Limits of Performance Via Convex Optimization
, 1990
"... this paper, we first give a very brief overview of control engineering. The goal of control engineering is to improve, or in some cases ena ble, the performance of a system by the addition of sensors, which measure various signals in the system and external command signals, control processors, whic ..."
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Cited by 180 (25 self)
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this paper, we first give a very brief overview of control engineering. The goal of control engineering is to improve, or in some cases ena ble, the performance of a system by the addition of sensors, which measure various signals in the system and external command signals, control processors, which process the measu red signals to drive actuators, which affect the behav ior of the system. A schematic diagram of a general control system is shown in Fig. 1. The use of the sensed response of the system (and not just the command signals) in the computation of the actuator signals is called feedback control, an old idea which has been developed and applied with great success in this century [1], [2]. Control engineering involves 1. Modeling or identification. The designer develops mathematical models of the relevant aspects of system to be controlled. This can be done using knowl edge of the system (for example by applying Newton 's equations of motion to a mechanical system), and experimentally by observing responses of the Manuscript received November 30,1988; revised August 4,1989. This work was supported in part by the National Science Foundation (NSF) under ECS8552465, the Air Force Office of Scientific Research (AFOSR) under 890228, Boeing Electronics Company under LF0937, and Bell Communications Research, and the National Science and Engineering Research Council (Canada) 1967 Science and Engineering Scholarship. The authors arewith the Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305, USA. IEEE Log Number 8933936. system to various excitations, a procedure known as s)zstem identification [3]. In some cases, several models are developed, varying in complexity and accu racy. 2. Control configuration: selection and placement of sensors an...
Forecasting the Forecast of Others
 Journal of Political Economy
, 1983
"... you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact inform ..."
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Cited by 126 (1 self)
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you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
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 122 (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...
Contributions to the Theory of Optimal Control
, 1960
"... This paper was in fact the first to introduce the RDE as an algorithm for computing the state feedback gain of the optimal controller for a general linear system with a quadratic performance criterion. RDE had emerged earlier in the study of the second variations in the calculus of variations, but i ..."
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Cited by 84 (1 self)
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This paper was in fact the first to introduce the RDE as an algorithm for computing the state feedback gain of the optimal controller for a general linear system with a quadratic performance criterion. RDE had emerged earlier in the study of the second variations in the calculus of variations, but its use in general linear systems, where the optimal trajectory needs to be generated by a control input, was new. The analysis throughout the paper concentrates on timevarying systems, and uses the HamiltonJacobi theory to arrive at RDE and to deduce optimality of the LQ control gain. We now know, however, that an alternative way to prove optimality in least squares is by showing how RDE allows one to "complete the square" (see, e.g., [5], [18]).
On the Mechanics of Forming and Estimating Dynamic Linear Economies
"... This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to sever ..."
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Cited by 77 (19 self)
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This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to several example economies.
Adaptive dynamic programming
 IEEE Trans. Syst. Man Cyber. 2002
"... Abstract—Unlike the many soft computing applications where it suffices to achieve a “good approximation most of the time, ” a control system must be stable all of the time. As such, if one desires to learn a control law in realtime, a fusion of soft computing techniques to learn the appropriate co ..."
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Cited by 44 (2 self)
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Abstract—Unlike the many soft computing applications where it suffices to achieve a “good approximation most of the time, ” a control system must be stable all of the time. As such, if one desires to learn a control law in realtime, a fusion of soft computing techniques to learn the appropriate control law with hard computing techniques to maintain the stability constraint and guarantee convergence is required. The objective of the present paper is to describe an adaptive dynamic programming algorithm (ADPA) which fuses soft computing techniques to learn the optimal cost (or return) functional for a stabilizable nonlinear system with unknown dynamics and hard computing techniques to verify the stability and convergence of the algorithm. Specifically, the algorithm is initialized with a (stabilizing) cost functional and the system is run with the corresponding control law (defined by the Hamilton–Jacobi–Bellman equation), with the resultant state trajectories used to update the cost functional in a soft computing mode. Hard computing techniques are then used to show that this process is globally convergent with stepwise stability to the optimal cost functional/control law pair for an (unknown) input affine system with an input quadratic performance measure (modulo the appropriate technical conditions). Three specific implementations of the ADPA are developed for 1) the linear case, 2) for the nonlinear case using a locally quadratic approximation to the cost functional, and 3) the nonlinear case using a radial basis function approximation of the cost functional; illustrated by applications to flight control. Index Terms—Adaptive control, adaptive critic, dynamic programming, nonlinear control, optimal control. I.
The Policy Iteration Algorithm for Average Reward Markov Decision Processes with General State Space
 IEEE Trans. Automat. Control
, 1997
"... The average cost optimal control problem is addressed for Markov decision processes with unbounded cost. It is found that the policy iteration algorithm generates a sequence of policies which are cregular (a strong stability condition) , where c is the cost function under consideration. This result ..."
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Cited by 33 (13 self)
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The average cost optimal control problem is addressed for Markov decision processes with unbounded cost. It is found that the policy iteration algorithm generates a sequence of policies which are cregular (a strong stability condition) , where c is the cost function under consideration. This result only requires the existence of an initial cregular policy, and an irreducibility condition on the state space. Furthermore, under these conditions the sequence of relative value functions generated by the algorithm is bounded from below, and "nearly" decreasing, from which it follows that the algorithm is always convergent. Under further conditions, it is shown that the algorithm does compute a solution to the optimality equations, and hence an optimal average cost policy. These results provide elementary criteria for the existence of optimal policies for Markov decision processes with unbounded cost, and recover known results for the standard LQG problem. When these results are specialize...
The Dynamics of Perception and Action
 Psychological Review
, 2006
"... How might one account for the organization in behavior without attributing it to an internal control structure? The present article develops a theoretical framework called behavioral dynamics that integrates an informationbased approach to perception with a dynamical systems approach to action. Fo ..."
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Cited by 28 (0 self)
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How might one account for the organization in behavior without attributing it to an internal control structure? The present article develops a theoretical framework called behavioral dynamics that integrates an informationbased approach to perception with a dynamical systems approach to action. For a given task, the agent and its environment are treated as a pair of dynamical systems that are coupled mechanically and informationally. Their interactions give rise to the behavioral dynamics, a vector field with attractors that correspond to stable task solutions, repellers that correspond to avoided states, and bifurcations that correspond to behavioral transitions. The framework is used to develop theories of several tasks in which a human agent interacts with the physical environment, including bouncing a ball on a racquet, balancing an object, braking a vehicle, and guiding locomotion. Stable, adaptive behavior emerges from the dynamics of the interaction between a structured environment and an agent with simple control laws, under physical and informational constraints.
Optimal taxation in an RBC model: A linearquadratic approach
 Journal of Economic Dynamics and
, 2006
"... We reconsider the optimal taxation of income from labor and capital in the stochastic growth model analyzed by Chari et al. (1994, 1995), but using a linearquadratic (LQ) approximation to derive a loglinear approximation to the optimal policy rules. The example illustrates how inaccurate “naive ” ..."
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Cited by 27 (1 self)
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We reconsider the optimal taxation of income from labor and capital in the stochastic growth model analyzed by Chari et al. (1994, 1995), but using a linearquadratic (LQ) approximation to derive a loglinear approximation to the optimal policy rules. The example illustrates how inaccurate “naive ” LQ approximation — in which the quadratic objective is obtained from a simple Taylor expansion of the utility function of the representative household — can be, but also shows how a correct LQ approximation can be obtained, which will provide a correct local approximation to the optimal policy rules in the case of small enough shocks. We also consider the numerical accuracy of the LQ approximation in the case of shocks of the size assumed in the calibration of Chari et al. We find that the correct LQ approximation yields results that are quite accurate, and similar in most respects to the results obtained by Chari et al. using a more computationally intensive numerical method.