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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...
Global Stabilization of Linear DiscreteTime Systems with Bounded Feedback
 Systems & Control Letters
, 1997
"... This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabi ..."
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Cited by 9 (3 self)
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This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections ("single hidden layer neural networks") of simple saturation functions. 1 Introduction This paper is concerned with the global stabilization to the origin x = 0 of the state x(t) of a linear discretetime system \Sigma : x(t + 1) = Ax(t) + Bu(t) ; (1.1) when the control values u(t) are constrained to lie in a bounded subset U of R m which contains zero in its interior. (As usual, A 2 R n\Thetan and B 2 R n\Thetam .) The study of ...
Model Predictive Control: Multivariable Control Technique of Choice in the 1990s?
 In Advances in Modelbased Predictive Control
, 1990
"... The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived ..."
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Cited by 8 (0 self)
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The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived powerful stability results for linear and nonlinear systems with and without constraints, for the nominal case and in the presence of model uncertainty. Some of these results are reviewed. Optimistic speculations about the future of MPC conclude the paper. 1 Introduction The objective of this paper is to review some major trends in model predictive control (MPC) research with emphasis on recent developments in North America. We will focus on the spirit rather than the details, i.e. we do not attempt to provide a complete list of all the relevant papers published during the last few years. 1 We will try to contrast the motivations driving the research in the different camps. There is...
A Frequency Domain Approach To AntiWindup Compensator Design
 1 r1,y1 (W=I) 1 r2,y2 (W=I) 1 Plant input signal v1 (W=I) 1 Plant input signal v2 (W=I) 1 r1,y1 (W optimal) 1 r2,y2 (W optimal) 1 Plant input signal v1 (W optimal) 1 Plant input signal v2 (W optimal
, 1993
"... The effect of input saturation in linear time invariant control systems is addressed. We utilize a controller in polynomial form, with a three degrees of freedom structure. This makes it possible to add a saturation compensator (an antiwindup filter) separately, after tuning of the controller prop ..."
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Cited by 2 (2 self)
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The effect of input saturation in linear time invariant control systems is addressed. We utilize a controller in polynomial form, with a three degrees of freedom structure. This makes it possible to add a saturation compensator (an antiwindup filter) separately, after tuning of the controller properties for unsaturated signals. Our aim is that the effect of a saturation event should decay as quickly as possible after desaturation, while the tendency for repeated resaturations, due to nonlinear oscillations, should be supressed. This is achieved by modifying the relevant loop gain by a safety margin. The modified loop gain is then adjusted, so that it touches the describing function of the saturation nonlinearity. The construction of the safety margin takes the magnitude of exogenous signals into account. The method requires only simple calculations. It can be automated, using a onedimensional numerical search. Furthermore, the effect of D/Aquantization in digital feedback syste...