Efficient control synthesis for augmented finite transition systems with an application to switching protocols

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Fei Sun, Necmiye Ozay, Eric M. Wolff, Jun Liu and Richard M. Murray
Submitted, 2014 American Control Conference (ACC)

ugmented finite transition systems generalize nondeterministic transition systems with additional liveness conditions. We propose efficient algorithms for synthesizing control protocols for augmented finite transition systems to satisfy high-level specifications expressed in a fragment of linear temporal logic (LTL). We then use these algorithms within a framework for switching protocol synthesis for discrete-time dynamical systems, where augmented finite transition systems are used for abstracting the underlying dynamics. We introduce a notion of minimality for abstractions of certain fidelity and show that such minimal abstractions can be exactly computed for switched affine systems. Additionally, based on this framework, we present a procedure for computing digitally implementable switching protocols for continuous-time systems. The effectiveness of the proposed framework is illustrated through two examples of temperature control for buildings.