1. Symbolic models for nonlinear time-delay systems using approximate bisimulations
- Author
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Giordano Pola, Maria Domenica Di Benedetto, Pierdomenico Pepe, and Paulo Tabuada
- Subjects
Lyapunov function ,Time-delay systems ,0209 industrial biotechnology ,General Computer Science ,Computer science ,Symbolic language ,Dynamical Systems (math.DS) ,02 engineering and technology ,Dynamical system ,symbols.namesake ,020901 industrial engineering & automation ,Approximate bisimulation ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Mathematics - Dynamical Systems ,Electrical and Electronic Engineering ,Mathematics - Optimization and Control ,Finite set ,Symbolic models ,Bisimulation ,Mechanical Engineering ,Sense (electronics) ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Nonlinear system ,93A30 ,Optimization and Control (math.OC) ,Control and Systems Engineering ,symbols ,020201 artificial intelligence & image processing ,Delay time - Abstract
Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to economics. However, the inherent complexity of such systems poses serious difficulties to control design, when control objectives depart from the standard ones investigated in the current literature, e.g. stabilization, regulation, and etc. In this paper we propose one approach to control design, which is based on the construction of symbolic models, where each symbolic state and each symbolic label correspond to an aggregate of continuous states and to an aggregate of input signals in the original system. The use of symbolic models offers a systematic methodology for control design in which constraints coming from software and hardware, interacting with the physical world, can be integrated. The main contribution of this paper is in showing that incrementally input-to-state stable time-delay systems do admit symbolic models that are approximately bisimilar to the original system, with a precision that can be rendered as small as desired. An algorithm is also presented which computes the proposed symbolic models. When the state and input spaces of time-delay systems are bounded, which is the case in many realistic situations, the proposed algorithm is shown to terminate in a finite number of steps., 12 pages
- Published
- 2010