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This article describes the construction of stochastic, data-based discrete abstractions for uncertain random processes continuous in time and space. Motivated by the fact that modeling processes often introduce errors which interfere with the implementation of control strategies, here the abstraction process proceeds in reverse: the methodology does not abstract models; rather it models abstractions. Specifically, it first formalizes a template for a family of stochastic abstractions, and then fits the parameters of that template to match the dynamics of the underlying process and ground the abstraction. The article also shows how the parameter-fitting approach can be implemented based on a probabilistic model validation approach which draws from randomized algorithms, and results in a discrete abstract model which is approximately simulated by the actual process physics, at a desired confidence level. In this way, the models afford the implementation of symbolic control plans with probabilistic guarantees at a desired level of fidelity. [ABSTRACT FROM AUTHOR]

There have been efforts to simplify analysis of a complex system by relating it to a simpler system through certain system relations. In this paper, we consider continuous-time systems related by a graph simulation relation and focus on preservation of input-output-to-state stability (IOSS) and its integral variant, integral IOSS (iIOSS). We establish that, under mild continuity and boundedness assumptions on some appropriately defined set-valued functions, the (i)IOSS property for the simulating system can lead to the (i)IOSS property for the original simulated system. The results thus demonstrate the possibility of inferring the (i)IOSS of a system by analyzing a potentially simpler system. [ABSTRACT FROM AUTHOR]

Abstract: Compositional analysis techniques such as assume-guarantee reasoning are frequently used in computer science to validate the design of complex process models. Since many engineering systems are built modularly from interconnections of components, the resulting mathematical models can be arbitrarily complex, which makes their analysis equally challenging. This paper presents a framework of how to apply compositional and assume-guarantee reasoning to linear time-invariant (LTI) systems. A key tool are simulation relations which are used to relate systems models with their specifications as well as to determine abstractions of given system behaviors. First, complex systems defined by standard feedback interconnections are considered. Parallel composition of LTI systems, the second type of interconnections, introduces algebraic constraints but allows for decomposition of a global specification. [ABSTRACT FROM AUTHOR]

Abstract: Quotienting by simulation equivalences is a well-established technique for reducing the size of nondeterministic Büchi automata. We adapt this technique to alternating Büchi automata. To this end we suggest two new quotients, namely minimax and semi-elective quotients, prove that they preserve the recognized languages, and show that computing them is not more difficult than computing quotients for nondeterministic Büchi automata. Our approach is game-theoretic; the proofs rely on a specifically tailored join operation for strategies in simulation games which is interesting in its own right. We explain the merits of our quotienting procedures with respect to converting alternating Büchi automata into nondeterministic ones. [Copyright &y& Elsevier]