Publications

 Inspired by [He94], a language to describe hybrid systems, i.e. networks of communicating discrete and continuous processes, is proposed. A semantics of the language is given in Extended Duration Calculus [ZRH93], a real-time interval logic with a proof system that allows reasoning in mathematical analysis about continuous processes to be embedded into the logic. The semantics thus provides a secure link to hybrid system models based on a general theory of dynamical systems.

 The {\em stability} of a control system is of primary interest and always appears as a critical property in the performance specification. In this paper, we formalize the criteria of stability in hybrid systems and present a formal approach to design of a hybrid dynamic system while the sufficient condition for stability is enforced. The formalism adopted is the Extended Duration Calculus with infinite intervals.

 In this paper we formulate the design of digital dynamic systems using a programming notation, called Hybrid CSP. A continuous specification of such a system under some performance requirements is decomposed and digitized using Hybrid CSP, whose correctness is guaranteed by the control principles such as Shannon's Sampling Theorem. Therefore, a digital dynamic system can be specified and refined in a framework of formal development approach.

 A hybrid system is a system containing both of time-evolving components and event-driven components. A formal approach is explored in this paper, based on Extended Duration Calculus (EDC), for the development of hybrid systems. A typical example of hybrid system from modern control theory, a two-level adaptive control system is used for illustrating our approach. Its high level consists of an event-driven supervisor which reacts to the change of plant structure, and its time-evolving low level consists of adaptive controllers and other components. Firstly performance specifications and system specification of the case are formulated in EDC; then they are refined stepwisely into specifications of the supervisor and the low level components. Our approach emphasizes the interface between the two kinds of components in the hybrid system.

 Most results obtained in the research of hybrid control systems are related to the description and analysis of hybrid control systems. But it is doubtless that how to design a hybrid control system is of great significance in the research of hybrid control systems. This paper is devoted to discuss the design methodology of hybrid control systems. After an introduction of a new framework of hybrid control systems, a top-down design approach is proposed which is consistent to the framework. The approach consists of decomposition of system performance specifications, the design of discrete event driven decision maker and the design of digital control loops. Two examples, a gas burner and an inverse pendulum are systematically designed to show the goodness of the top-down design approach. Finally, a bottom-up analysis approach which is consistent to the new framework is proposed and then applied to these examples.

 The research on hybrid control systems attracts many scientists both in computer science and control theories and applications. The study should be carried out on a general framework abstracted from various hybrid control systems. This paper analyses the drawbacks of the present frameworks used by most researchers and proposes a new framework to overcome these shortcomes. The new framework consists of a discrete time box, a discrete event box and a digital-symbol interface. The new framework shows the crucial nature of the hybridity of time envolving variables and event driven variables in hybrid control systems. The new framework is easy to integrate the knowledges of computer science and control theories and applications. Two examples, a gas burner and an inverse pendulum are given to show the fitness of the new framework. The design and analysis aspects of hybrid control systems related to the new framework are also discussed.