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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...
A modelbased algorithm for blood glucose control in type I diabetic patients
 IEEE Trans. Biomed. Eng
, 1999
"... Abstract—A modelbased predictive control algorithm is developed to maintain normoglycemia in the Type I diabetic patient using a closedloop insulin infusion pump. Utilizing compartmental modeling techniques, a fundamental model of the diabetic patient is constructed. The resulting nineteenthorder ..."
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Cited by 12 (1 self)
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Abstract—A modelbased predictive control algorithm is developed to maintain normoglycemia in the Type I diabetic patient using a closedloop insulin infusion pump. Utilizing compartmental modeling techniques, a fundamental model of the diabetic patient is constructed. The resulting nineteenthorder nonlinear pharmacokinetic–pharmacodynamic representation is used in controller synthesis. Linear identification of an input–output model from noisy patient data is performed by filtering the impulseresponse coefficients via projection onto the Laguerre basis. A linear model predictive controller is developed using the identified step response model. Controller performance for unmeasured disturbance rejection (50 g oral glucose tolerance test) is examined. Glucose setpoint tracking performance is improved by designing a second controller which substitutes a more detailed internal model including stateestimation and a Kalman filter for the input–output representation. The stateestimating controller maintains glucose within 15 mg/dl of the setpoint in the presence of measurement noise. Under noisefree conditions, the modelbased predictive controller using state estimation outperforms an internal model controller from literature (49.4 % reduction in undershoot and 45.7 % reduction in settling time). These results demonstrate the potential use of predictive algorithms for blood glucose control in an insulin infusion pump. Index Terms—Compartmental modeling, diabetes, glucose, infusion pumps, insulin, Kalman filter, model identification, model predictive control, state estimation. I.
A Framework for Robustness Analysis of Constrained Finite Receding Horizon Control
 IEEE Transactions on Automatic Control
, 1998
"... A framework for robustness analysis of input constrained finite receding horizon control is presented. Under the assumption of quadratic upper bounds on the finite horizon costs, we derive sufficient conditions for robust stability of the standard discretetime linearquadratic receding horizon cont ..."
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Cited by 1 (0 self)
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A framework for robustness analysis of input constrained finite receding horizon control is presented. Under the assumption of quadratic upper bounds on the finite horizon costs, we derive sufficient conditions for robust stability of the standard discretetime linearquadratic receding horizon control formulation. This is achieved by recasting conditions for nominal and robust stability as an implication between quadratic forms, lending itself to Sprocedure tools which are used to convert robustness questions to tractable convex conditions. Robustness with respect to plant/model mismatch as well as for state measurement error is shown to reduce to the feasibility of linear matrix inequalities. Simple examples demonstrate the approach. Keywords: predictive control, optimal control, linear systems, robustness, Sprocedure, LMI. 1 Introduction Receding horizon, moving horizon and model predictive control are names for a state feedback control technique where the control action is dete...
AN INFINITE HORIZON PREDICTIVE CONTROL ALGORITHM BASED ON MULTIVARIABLE INPUTOUTPUT MODELS
"... In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear inputoutput models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty ..."
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In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear inputoutput models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated offline. Considering constraints needs solving online a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.
Sheraton New Orleans Hotel Workshop on Identification and Adaptive Control
, 1998
"... Model predictive control (MPC) is currently the most widely implemented advanced process control technology for petroleum refineries and chemical plants. Based on the present state of the art in theory and practice, MPC works well for processes operating over a narrow range of conditions. However, p ..."
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Model predictive control (MPC) is currently the most widely implemented advanced process control technology for petroleum refineries and chemical plants. Based on the present state of the art in theory and practice, MPC works well for processes operating over a narrow range of conditions. However, processes frequently have to operate over a wide range of conditions, for reasons such as varying feedstocks, fluctuating markets for products and raw materials, large process disturbances, and equipment wear. Unsatisfactory MPC performance over widely ranging operating conditions may result in process downtime, environmental and safety risks, and waste of resources, with substantial economic losses. Therefore, there is a need for flexible MPC systems that perform well over a wide range of process operating conditions. While the inner complexity of such (nextgeneration) MPC systems may be high (to realize the sought improvements in control performance), the complexity of the design, operation, and maintenance of such systems by process engineers and operators should be low. The development and implementation of flexible MPC systems will almost certainly be facilitated by the future availability of predictably ever more powerful computers and communication hardware. 1.