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New Results in Optimal Control of Hybrid Systems and Quantized Systems

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Abstract:
Combinatorial optimization over continuous and integer variables is a useful tool for solving complex optimal control problems for hybrid dynamical systems formulated in discrete-time. Current approaches are based on mixed-integer linear/quadratic programming (MIP), which provides the solution after solving a sequence of relaxed standard linear or quadratic programs. An MIP formulation has the drawback of requiring that the discrete/logic part of the hybrid problem is converted into mixed-integer inequalities, therefore losing most of the original discrete structure of the problem during the conversion, and of relying upon the tightness and the convexity of its continuous relaxations. In this talk we present some preliminary results that attempt at overcoming such difficulties. For optimal control of hybrid systems, by combining MIP and constraint logic programming (CLP) techniques into a ``hybrid'' solver, we detail how to model the hybrid dynamics so that the optimal control problem can be solved by the hybrid MIP+CLP solver, and show on a case study that the achieved performance is superior to the one achieved by pure MIP solvers. For state-feedback optimal control laws of systems with quantized inputs, we present a multiparametric nonlinear integer solver for problems with optimization variables that belong to a finite set and with cost function and constraints depending in an arbitrary nonlinear fashion on the optimization variables and in a linear fashion on the parameters, problems for which approaches based on continuous relaxations are not applicable.

http://www.dii.unisi.it/~bemporad
Type of Seminar:
Public Seminar
Speaker:
Dr. Alberto Bemporad, Ass. Prof.
Dept. of Information Engineering, University of Siena, Italy
Date/Time:
Mar 24, 2003   11:00
Location:

ETH Zentrum, Physikstrasse 3, Building ETL, Room K25
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Alberto Bemporad received the master degree in Electrical Engineering in 1993 and the Ph.D. in Control Engineering in 1997 from the University of Florence, Italy. He spent the academic year 1996/97 at the Center for Robotics and Automation, Dept. Systems Science & Mathematics, Washington University, St. Louis, as a visiting researcher. In 1997-1999, he held a postdoctoral position at the Automatic Control Lab, ETH, Zurich, Switzerland, where he collaborated as a senior researcher in 2000-2002. He is currently assistant professor at the University of Siena, Italy. He has published papers in the area of hybrid systems, model predictive control, computational geometry, and robotics. He is coauthoring the new version of the Model Predictive Control Toolbox (The Mathworks, Inc.). He is an Associate Editor of the IEEE Transactions on Automatic Control, and Chair of the IEEE Control Systems Society Technical Committee on Hybrid Systems.