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167
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.
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 131 (24 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 86 (0 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 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...
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 60 (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 51 (14 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.
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 22 (9 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...
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 14 (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.
Exponential Stability in Discrete Time Filtering for NonErgodic Signals
 System and Control Letters
, 1999
"... In this paper we prove exponential asymptotic stability for discrete time filters for signals arising as solutions of ddimensional stochastic difference equations. The observation process is the signal corrupted by an additive white noise of su#ciently small variance. The model for the signal admit ..."
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Cited by 13 (5 self)
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In this paper we prove exponential asymptotic stability for discrete time filters for signals arising as solutions of ddimensional stochastic difference equations. The observation process is the signal corrupted by an additive white noise of su#ciently small variance. The model for the signal admits nonergodic processes. We show that almost surely, the total variation distance between the optimal filter and an incorrectly initialized filter converges to 0 exponentially fast as time approaches #. Key Words: nonlinear filtering, asymptotic stability, measure valued processes. # Research suppored by the NSF grant DMI 9812857. 1 1 Introduction The central problem of nonlinear filtering is to study the conditional distribution of a signal process at any time instant given noisy observations on the signal available up until that time. If the signalobservation pair is Markov, the conditional distribution process, referred to hereafter as the optimal filter , is determined completely ...
Robust Control and Filtering of ForwardLooking Models
, 2000
"... This paper shows how to compute robust Ramsey (aka Stackelberg) plans for linear models with forward looking private agents. We formulate a Bellman equation for the robust plan. We describe robust filtering for when some of the forcing variables (like potential GDP or trend growth) are not observed, ..."
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Cited by 10 (0 self)
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This paper shows how to compute robust Ramsey (aka Stackelberg) plans for linear models with forward looking private agents. We formulate a Bellman equation for the robust plan. We describe robust filtering for when some of the forcing variables (like potential GDP or trend growth) are not observed, and how the decision problem interacts with the filtering problem. We use a ‘new synthesis’ macro model of Woodford as an example.