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A mathematical programming approach to the analysis and control of hybrid systems


M. Morari

Stanford, California, Stanford University

[Based on work jointly with Mato Baotic, Alberto Bemporad, Francesco Borrelli, Francesco Cuzzola, Andrea Gentilini, Tobias Geyer, Domenico Mignone, Fabio Torrisi and Giancarlo Ferrari Trecate] Hybrid systems have emerged as a powerful modeling paradigm for a wide variety of practical systems and problems. For example, supply chains can be modeled as hybrid systems and their operation can be studied from that point of view. A chemical plant with the associated emergency shut-down control system can be viewed as a hybrid system and the proper operation of the control system can be analyzed effectively with the tools from that domain. We have introduced (Automatica 35, 407-427, 1999) the Mixed-Logic Dynamical (MLD) system form to describe hybrid systems. The major advantage of this form is that all problems of analysis and synthesis can be formulated as mixed-integer linear or quadratic programs, for which good commercial software exists. In this overview talk we motivate the approach, summarize the progress in a wide range of areas (controllability/observability assessment, optimal controller design, filter design, fault detection, modeling language & compiler) and present some application examples. The experimental application in the context of the automatic control of anesthesia will be described in detail. ______________________________________________________________________________


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