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Remarks on Set Invariance in Control of Constrained Discrete Time Systems

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Abstract:
The talk provides solution to two problems; (i)The solution to the problem of computing a robustly positively invariant outer approximation of the minimal robustly positively invariant set for a discrete-time, linear, time-invariant system is presented. It is assumed that the disturbance is additive and persistent, but bounded. (ii) Novel results that permit the computation of the set of states that can be robustly steered, using state feedback, to a given target set in a finite number of steps are presented. It is assumed that the system is discrete-time, nonlinear, time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. These results generalize previously published results that are not able to address state-input dependent disturbances. It is briefly discussed how polyhedral algebra, linear programming and computational geometry may be employed for set computations relevant to the analysis of linear and piecewise affine systems with additive state disturbances. Some simple examples are given to demonstrate that convexity of the robustly controllable sets cannot be guaranteed even if all relevant sets are convex and the system is linear. Keywords: Set invariance, constrained control, robust control, model predictive control, linear systems, piece-wise ane systems.

Type of Seminar:
Public Seminar
Speaker:
Sasa V. Rakovic
Imperial College London
Date/Time:
Oct 08, 2003   16:00
Location:

ETH Zentrum, ETL K 25
Contact Person:

Pascal Grieder
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Biographical Sketch:
Sasa V. Rakovic received the B.Sc. degree in Electrical Engineering from the Technical Faculty Cacac, University of Kragujevac (Serbia and Montenegro) and the M.Sc degree in Control Engineering from Imperial College London. He is currently employed as a research assistant in the Power and Control Research Group at Imperial College where he is registered for the degree of PhD. He closely works with Prof. David Q. Mayne. His research interests include optimization, optimization based design, and robust model predictive control.