A Geometric Method for Generating Discrete Trace Transition System of a Polyhedral Invariant Hybrid Automaton

Sobhi Baniardalani,Javad Askari

doi:10.4236/ica.2012.32022

Sobhi Baniardalani, Javad Askari

Open Access

https://doi.org/10.4236/ica.2012.32022

Copy DOI

Abstract

Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode transition graph of a hybrid system. This method can be used for a general class of industrial hybrid plants which are defined by Polyhedral Invariant Hybrid Automata (PIHA). In these automata there are no resetting maps, while invariant sets are defined by linear inequalities. Therefore, based on the continuity property of the state trajectories in a PIHA, the problem is reduced to finding possible transitions between all two adjacent discrete modes. In the presented method, the possibility and the direction of such transitions are detected only by computing the angle between the vector field and the normal vector of the switching surfaces. Thus, unlike the most other reachability methods, there is no need to solve differential equations and to do mapping computations. In addition, the proposed method, with some modifications can be applied for extracting Stochastic or Timed Discrete Trace Transition Systems.

Highlights

Hybrid dynamical system (HDS) which contains both discrete and continuous dynamics, has attracted considerable attention in recent years [1,2,3]
Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph
In this paper an effective method is proposed for generating discrete mode transition graph of a hybrid system

Summary

Introduction

Hybrid dynamical system (HDS) which contains both discrete and continuous dynamics, has attracted considerable attention in recent years [1,2,3]. In these approaches the continuous state space is divided into a set of disjoint partitions so that the union of all partitions covers the entire state space These methods need complex computations for determining the transitions between elements of the partitions. Based on the properties of PIHA, especially its continuity property, in this paper a fast geometric method is introduced for detecting DTTS of PIHA with lower complexity As it will be illustrated, in a PIHA, invariant sets are linear inequalities; guard sets can be visualized as hyper-plans that partition the continuous state space into discrete states. These discrete states, which specify different dynamics of DCCS, are called locations.

Basic Definitions

Obtaining DTTS

Further Discussions

An Illustrative Example

Hierarchical DTTS

Conclusions