The Concept of Deadlock and Livelock in Hybrid Control Systems

This short paper qualitatively introduces the definition of the concepts of Deadlock and Livelock for a general class of Hybrid Control Systems (HCS). Such a characterization hinges on three important aspects: firstly, the concept of composition of HCS; secondly, the general concept of specifications and their composition for HCS; finally, the dynamical structure and behaviors of HCS. The first aspect is introduced in a novel manner, including ideas from the literature of discrete transition systems and accounting for concepts such as that of dynamical feedback interconnection. The second point includes general properties that are of interest from a systems and control theory perspective. The third part categorizes the diverse and possibly pathological behaviors that are distinctive of HCS. A first look at the problem of Deadlock and Livelock Verification concludes the manuscript.

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