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Robust Constrained Model Predictive Control using Linear Matrix Inequalities

Kothare, Mayuresh V. and Balakrishnan, Venkataramanan and Morari, Manfred (1995) Robust Constrained Model Predictive Control using Linear Matrix Inequalities. California Institute of Technology , Pasadena, CA. (Unpublished)

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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 state-feedback control law which minimizes a "worst-case" 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 "worst-case" 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 state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented.

Item Type:Report or Paper (Technical Report)
Additional Information:Partial financial support from the US National Science Foundation is gratefully acknowledged. We would like to thank Pascal Gahinet for providing the LMI-Lab software. Submitted to Automatica
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1995.011
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Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28091
Deposited By: Imported from CaltechCDSTR
Deposited On:20 Sep 2006
Last Modified:03 Oct 2019 03:29

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