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Polyhedral Tools for Control

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Abstract:
Polyhedral operations play a central role in constrained control. Analysis and/or implementation of controllers for linear systems subject to linear constraints often requires the computation of three fundamental such operations: projection, parametric linear programming and vertex enumeration. There is as yet no approach for any of these three problems that is efficient in every case, and all three are active topics of research. This presentation draws links between these three operations. We show that an algorithm that can compute any of the three functions can in fact also be used to compute the other two. While some of these links are well-known and are commonly used, our work fills in the remaining equivalences. By exploiting the links between these operations, we have developed two new approaches to the calculation of a parametric linear program that offer speed and space savings for many problems. The proposed algorithms are compared through example to existing methods and a significant improvement is demonstrated.

Type of Seminar:
Public Seminar
Speaker:
Dr. Colin Jones
University of Cambridge, UK
Date/Time:
Nov 08, 2005   17:15
Location:

ETH Zentrum, Gloriastr. 35, Building ETZ, Room E6
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Colin Jones obtained a PhD in 2005 from the University of Cambridge, where his work on polyhedral computational methods for constrained control and fault tolerant aircraft control was supervised by Jan Maciejowski. Prior to that, he was at the University of British Columbia in Canada, where he took a BASc in Electrical Engineering and Mathematics, as well as an MASc, also in Electrical Engineering, for his work on the isolation of faults in hydraulic circuits under the supervision of Peter Lawrence. Colin has worked in a variety of industrial roles, ranging from predictive control of heating, ventilation and air conditioning for commercial buildings, to control of hydro-metallurgical processes, to ballistic missile interception. His current research interests are in the areas of robust and predictive control, computational geometry and control of industrial biological processes.