The extended linear complementarity problem and the modeling and analysis of hybrid systems
نویسندگان
چکیده
First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We briefly discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More specifically, we consider a traffic-light-controlled intersection, which can be considered as a hybrid system. We construct a model that describes the evolution of the queue lengths in the various lanes (as continuous variables) as a function of time and we show that this leads to an ELCP. Furthermore, it can be shown that some problems in the analysis of another class of hybrid systems, the “complementary-slackness systems”, also lead to an ELCP.
منابع مشابه
An interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function
In this paper, an interior-point algorithm for $P_{ast}(kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for large-update methods, which coinc...
متن کاملThe Extended Linear Complementarity Problemand the Modeling and Analysis of HybridSystemsBart De Schutter ? and Bart De Moor ? ?
First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We brieey discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More speciically, we consider a traac-light-controlled in...
متن کاملGeneralized linear complementarity problems and the analysis of continuously variable systems and discrete event systems
We present an overview of our research on the use of generalized linear complementarity problems (LCPs) for analysis of continuously variable systems and discrete event systems. We indicate how the Generalized LCP can be used to analyze piecewise-linear resistive electrical circuits. Next we discuss how the Extended LCP can be used to solve some fundamental problems that arise in max-algebraic ...
متن کاملThe extended linear complementarity problem and its applications in the analysis and control of discrete event systems and hybrid systems
In this paper we first present a mathematical programming problem, the Extended Linear Complementarity Problem (ELCP). Next we discuss how the ELCP can be used to solve some basic problems in the system theory for a class of discrete event systems that can be modeled using the max-plus algebra, which has maximization and addition as basic operations. Finally we show that the ELCP also appears i...
متن کاملThe Extended Linear Complementary Problem and the Modeling and Analysis of Hybrid Systems
First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We briefly discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More specifically, we consider a traffic-light-controlle...
متن کامل