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The combinations of analog and digital equipment to form hybrid installations are of such variety that hybrid software routines are generally restricted to particular hardware configurations. The software developed in this thesis is applicable and operational on the EAI PACE-231R-V; DEC PDP-9 Hybrid Computer. The programs (in the form of subroutines and handlers) are structured, according to the characteristics of this computer, to handle the general situations of hybrid programming; such situations as the synchronization of the analog and digital computers, and the transfer of data and control information. The present level of software development has considerably simplified the use of the interface for hybrid problem applications. Successive stages of software development would incorporate this stage, in whole or in part; each stage being more comprehensive and sophisticated than its predecessor. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This dissertation presents a new framework, trace-automata, for verifying hybrid systems. In addition, a simple, general theory of abstraction is presented, based on the idea of approximations that are liberal or conservative with respect to an abstraction function. This theory gives rise to a sound technique whereby hybrid systems are verified by constructing discrete approximations of both the implementation and the specification, and verifying that the approximate implementation satisfies the approximate specification. Trace-automata are language accepting, infinite tape automata, extended to allow multiple tapes, and to allow tapes that consist of continuous traces over the reals, as well as tapes that consist of sequences of discrete symbols. Hybrid systems are represented by automata that read some continuous tapes and some discrete tapes. Trace-automata are used to represent both the implementation and the specification of the system to be verified. Verification corresponds to demonstrating that the language accepted by the implementation is contained in that accepted by the specification. Hybrid systems are verified by constructing and verifying discrete approximations. Abstraction functions map continuous traces to discrete sequences. A liberal approximation of the system implementation is verified against a conservative approximation of the system specification. From this verification, it can be concluded that the original hybrid model satisfies the original specification. The dissertation describes a general technique for constructing discrete, liberal approximations of trace-automata representing differential equations and inclusions. In addition, trace-automata themselves can encode abstraction functions, with the result that trace-automata language containment can also be used to establish that an approximation is liberal or conservative as the case may be. These techniques are illustrated with an example verification based upon the Philips Audio Control Protocol with two agents, each capable of both transmitting and receiving. The verification is novel in that it is based upon a detailed model of the analog electrical behaviour of the bus.

This dissertation presents a new framework, trace-automata, for verifying hybrid systems. In addition, a simple, general theory of abstraction is presented, based on the idea of approximations that are liberal or conservative with respect to an abstraction function. This theory gives rise to a sound technique whereby hybrid systems are verified by constructing discrete approximations of both the implementation and the specification, and verifying that the approximate implementation satisfies the approximate specification. Trace-automata are language accepting, infinite tape automata, extended to allow multiple tapes, and to allow tapes that consist of continuous traces over the reals, as well as tapes that consist of sequences of discrete symbols. Hybrid systems are represented by automata that read some continuous tapes and some discrete tapes. Trace-automata are used to represent both the implementation and the specification of the system to be verified. Verification corresponds to demonstrating that the language accepted by the implementation is contained in that accepted by the specification. Hybrid systems are verified by constructing and verifying discrete approximations. Abstraction functions map continuous traces to discrete sequences. A liberal approximation of the system implementation is verified against a conservative approximation of the system specification. From this verification, it can be concluded that the original hybrid model satisfies the original specification. The dissertation describes a general technique for constructing discrete, liberal approximations of trace-automata representing differential equations and inclusions. In addition, trace-automata themselves can encode abstraction functions, with the result that trace-automata language containment can also be used to establish that an approximation is liberal or conservative as the case may be. These techniques are illustrated with an example verification based upon the Philips Audio Control Protocol with two agents, each capable of both transmitting and receiving. The verification is novel in that it is based upon a detailed model of the analog electrical behaviour of the bus. / Science, Faculty of / Computer Science, Department of / Graduate

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Hybrid systems now form a classical computational paradigm unifying discrete and continuous system aspects. The modelling, analysis and verification of these systems are very difficult. One way to reduce the complexity of hybrid system models is to consider randomization. The need for stochastic models has actually multiple motivations. Usually, when building models complete information is not available and we have to consider stochastic versions. Moreover, non-determinism and uncertainty are inherent to complex systems. The stochastic approach can be thought of as a way of quantifying non-determinism (by assigning a probability to each possible execution branch) and managing uncertainty. This is built upon to the - now classical - approach in algorithmics that provides polynomial complexity algorithms via randomization. In this thesis we investigate the stochastic hybrid systems, focused on modelling and analysis. We propose a powerful unifying paradigm that combines analytical and formal methods. Its applications vary from air traffic control to communication networks and healthcare systems. The stochastic hybrid system paradigm has an explosive development. This is because of its very powerful expressivity and the great variety of possible applications. Each hybrid system model can be randomized in different ways, giving rise to many classes of stochastic hybrid systems. Moreover, randomization can change profoundly the mathematical properties of discrete and continuous aspects and also can influence their interaction. Beyond the profound foundational and semantics issues, there is the possibility to combine and cross-fertilize techniques from analytic mathematics (like optimization, control, adaptivity, stability, existence and uniqueness of trajectories, sensitivity analysis) and formal methods (like bisimulation, specification, reachability analysis, model checking). These constitute the major motivations of our research. We investigate new models of stochastic hybrid systems and their associated problems. The main difference from the existing approaches is that we do not follow one way (based only on continuous or discrete mathematics), but their cross-fertilization. For stochastic hybrid systems we introduce concepts that have been defined only for discrete transition systems. Then, techniques that have been used in discrete automata now come in a new analytical fashion. This is partly explained by the fact that popular verification methods (like theorem proving) can hardly work even on probabilistic extensions of discrete systems. When the continuous dimension is added, the idea to use continuous mathematics methods for verification purposes comes in a natural way. The concrete contribution of this thesis has four major milestones: 1. A new and a very general model for stochastic hybrid systems; 2. Stochastic reachability for stochastic hybrid systems is introduced together with an approximating method to compute reach set probabilities; 3. Bisimulation for stochastic hybrid systems is introduced and relationship with reachability analysis is investigated. 4. Considering the communication issue, we extend the modelling paradigm.

Thesis (M.S.)--University of Wisconsin--Madison, 1967. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.