Abstractions of Constrained Linear Systems

ions of Constrained Linear Systems Herbert G. Tanner University of Pennsylvania George J. Pappas University of Pennsylvania, [email protected] Follow this and additional works at: http://repository.upenn.edu/ese_papers Copyright 2003 IEEE. Reprinted from Proceedings of the American Control Conference 2003, Volume 4, pages 3381-3386. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. This paper is posted at ScholarlyCommons. http://repository.upenn.edu/ese_papers/102 For more information, please contact [email protected]. Recommended Citation Herbert G. Tanner and George J. Pappas, "Abstractions of Constrained Linear Systems", . June 2003. Abstractions of Constrained Linear Systemsions of Constrained Linear Systems Abstract Simulation relations are powerful abstraction techniques in computer science that reduce the complexity of analysis and design of labeled transition systems. In this paper, we define and characterize simulation relations for discrete-time linear systems in the presence of state and input constraints. Given a discrete-time linear system and the associated constraints, we consider a control-abstract embedding into a transition system. We then establish necessary and sufficient conditions for one constrained linear system to simulate the transitions of the other. Checking the simulation conditions is formulated as a linear programming problem which can be efficiently solved for systems of large dimensions. We provide an example where our approach is applied to the hybrid model of the Electronic Throttle Control (ETC) System.Simulation relations are powerful abstraction techniques in computer science that reduce the complexity of analysis and design of labeled transition systems. In this paper, we define and characterize simulation relations for discrete-time linear systems in the presence of state and input constraints. Given a discrete-time linear system and the associated constraints, we consider a control-abstract embedding into a transition system. We then establish necessary and sufficient conditions for one constrained linear system to simulate the transitions of the other. Checking the simulation conditions is formulated as a linear programming problem which can be efficiently solved for systems of large dimensions. We provide an example where our approach is applied to the hybrid model of the Electronic Throttle Control (ETC) System. Comments Copyright 2003 IEEE. Reprinted from Proceedings of the American Control Conference 2003, Volume 4, pages 3381-3386. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/102 Abstractions of Constrained Linear Systemsions of Constrained Linear Systems Herbert G. Tanner and George J. Pappas Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia, PA 19104-6228 Abstract-Simulation relations are powerful abstraction techIn this paper we derive necessary and sufficient condiniques in computer science that reduce the complexity of analysis and design of labeled transition systems. In this paper, we define and characterize simulation relations for discretetime linear systems in the presence of state and input constraints. Given a discrete-time linear system and the associated constraints, we consider a control-abstract embedding into a transition system. We then establish necessary and sufficient conditions for one constrained linear system to simulate the transitions of the other. Checking the simulation conditions is formulated as a linear programming problem which can be efficiently solved for systems of large dimensions. We provide an example where our approach is applied to the hybrid model of the Electronic Throttle Control (ETC) System.Simulation relations are powerful abstraction techIn this paper we derive necessary and sufficient condiniques in computer science that reduce the complexity of analysis and design of labeled transition systems. In this paper, we define and characterize simulation relations for discretetime linear systems in the presence of state and input constraints. Given a discrete-time linear system and the associated constraints, we consider a control-abstract embedding into a transition system. We then establish necessary and sufficient conditions for one constrained linear system to simulate the transitions of the other. Checking the simulation conditions is formulated as a linear programming problem which can be efficiently solved for systems of large dimensions. We provide an example where our approach is applied to the hybrid model of the Electronic Throttle Control (ETC) System.