We present a novel approach to the computation of symbolic abstractions of incrementally stable switched systems. The main novelty consists in using mode sequences of given length as symbolic states for our abstractions. We show that the resulting symbolic models are approximately bisimilar to the original switched system and that an arbitrary precision can be achieved by considering sufficiently long mode sequences. The advantage of this approach over existing ones is double: firstly, the transition relation of the symbolic model admits a very compact representation under the form of a shift operator; secondly, our approach does not use lattices over the state-space and can potentially be used for higher dimensional systems. We provide a theoretical comparison with the lattice-based approach and present a simple criterion enabling to choose the most appropriate approach for a given switched system. Finally, we show an application to a model of road traffic for which we synthesize a schedule for the coordination of traffic lights under constraints of safety and fairness.
This paper deals with solution of inequality $\textbf{A}\otimes
\textbf{x}\preceq \textbf{b}$, where $\textbf{A}, \textbf{x}$ and $\textbf{b}$
are interval matrices with entries defined over idempotent semiring. It deals
also with the computation of a pair of intervals, ($\textbf{x},\textbf{y}$)
which satisfies the equation $\textbf{A} \otimes \textbf{x}=\textbf{B}\otimes
\textbf{y}$. It will be shown that this equation may be solved by considering
the interval version of the iterative scheme proposed by Cuninighame-Green and
Butkovic in 2003
Chronicle recognition is an efficient and robust method for fault diagnosis. The knowledge about the underlying system is gathered in a set of chronicles, then the occurrence of a fault is diagnosed by analyzing the flow of observations and matching this flow with a set of available chronicles. The chronicle approach is very efficient as it relies on the direct association of the symptom, which is in this case a complex temporal pattern, to a situation. Another advantage comes from the efficiency of recognition engines which make chronicles suitable for one-line operation. However, there is a real bottleneck for obtaining the chronicles. In this paper, we consider the problem of learning the chronicles. Because a given situation often results in several admissible event sequences, our contribution targets an extension to multiple event sequences of a chronicle discovery algorithm tailored for one single event sequence. The concepts and algorithms are illustrated with representative and easy to understand examples.
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