On Synthesizing Robust Discrete Controllers under Modeling Uncertainty
Ufuk Topcu, Necmiye Ozay, Jun Liu, and Richard M. Murray
Submitted, 2012 International Conf on Hybrid Systems: Computation and Control (HSCC)
We investigate the robustness of reactive control protocols synthesized to guarantee system’s correctness with respect to given temporal logic specifications. We consider uncertainties in open finite transition systems due to unmodeled transitions. The resulting robust synthesis problem is formulated as a temporal logic game. In particular, if the specification is in the so-called generalized reactivity  fragment of linear temporal logic, so is the augmented specification in the resulting robust synthesis problem. Hence, the robust synthesis problem belongs to the same complexity class with the nominal synthesis problem, and is amenable to polynomial time solvers. Additionally, we discuss reasoning about the effects of different levels of uncertainties on robust synthesizability and demonstrate the results on a simple robot motion planning scenario.
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