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 +===== A language and simulator for hybrid systems =====
 +//G. Fábián//
  
 +Many of today'​s industrial systems exhibit mixed discrete-event/​continuous-time behaviour. Typical
 +examples are batch processes from the process industry, digitally controlled plants, automobiles and aircraft.
 +Models play an important role in the design process of such systems, providing means to evaluate design decisions
 +at an early stage. Models written in a specification formalism present only the relevant system aspects. Such
 +models contribute significantly to the understanding of the functionality of the systems. Hybrid systems are used
 +increasingly in safety-critical applications,​ and therefore, their reliability is becoming more and more
 +important. For verification purposes, formal semantic models and frameworks are used.
 +
 +The Chi language is a hybrid specification formalism, suitable for the description of discrete-event,​
 +continuous-time and hybrid systems. It is a concurrent language, where the discrete-event part is based on
 +Communicating Sequential Processes and the continuous-time part is based on Differential Algebraic Equations
 +(DAEs). Models written in the Chi language can be executed by the Chi simulator.
 +
 +The contribution of the present work is twofold. First, the hybrid Chi language semantics is specified. This is an
 +extension to the discrete-event semantics that had already been developed in a previous work. Second, the existing
 +discrete-event simulator has been extended to execute hybrid models. To make a specification language suitable for
 +the design and analysis of complex systems, it needs to have a precise semantics. Specifically,​ a hybrid language
 +semantics has to preserve the pure continuous-time and the pure discrete-event functionality while integrating the
 +two smoothly. In the case of the Chi language, it is also important that models can be executed efficiently,​ using
 +existing numerical algorithms.
 +
 +Differential and algebraic variables with corresponding operators are defined in the Chi language. This
 +distinction emphasizes the physical role of the variables, and in this way supports the development of physically
 +correct models. Steady-state initialization is supported directly by the language. Currently, index 0 and 1
 +systems of DAEs can be solved directly. Higher index systems can be modelled by using substitute equations.
 +
 +The semantics of model composition is an important issue in hybrid languages. Model composition is well defined
 +for pure discrete models by CSP. This thesis treats the continuous aspects of model composition. Continuous
 +variables of sub-models are connected by the so-called channels in the Chi language. After studying existing
 +hybrid languages, algebraic equations have been chosen to be the meaning of connections between continuous
 +variables. This, together with using only local variables in processes, have contributed significantly to more
 +clear and robust models. Furthermore,​ state-event conditions are evaluated only in consistent states leading to
 +more predictable model behaviour.
 +
 +The mathematical model of continuous state calculation is specified together with the hybrid language semantics;
 +the latter in the form of a computational model. According to this model, discrete phases are divided into
 +sub-phases, each ending with a consistent initial state calculation. Within each sub-phase, processes work with
 +local variables only and interaction between sub-models is restricted to explicit communication. This simplifies
 +reasoning about model behaviour.
 +
 +The Chi simulator has been extended to execute hybrid models. It integrates a nonlinear equation solver to solve
 +the initial state problem and a DAE solver to solve the DAEs during the continuous phases. The local continuous
 +variables of processes are dynamically mapped onto a global variable set that the solvers work with, to increase
 +performance. The Chi simulator allows sophisticated logging of continuous variables, such that their trajectory
 +can be visualized by third party software. The user may also request a detailed trace file to be generated.
 +
 +In the future, formal methods and techniques should be developed, based on the operational semantics defined in
 +this thesis, to carry out formal analysis of hybrid Chi models. A possible extension to the Chi language is to
 +include dimension information in the data types. In the present work, it is proposed to perform physical
 +correctness checking based on this information. To extend the range of the physical systems that can be modelled
 +in Chi, it is necessary to be able to specify the so-called instantaneous equations. The performance of the Chi
 +simulator can further be enhanced by optimizing the equations, based on symbolic analysis and manipulation.
 +
 +//​Ph.D.thesis//,​ Eindhoven University of Technology, 1999.
 +
 +{{phdfabia.pdf|pdf}}
vanbeek/phdfabian.txt · Last modified: Wednesday, 19 March 2008 : 15:56:32 (external edit)