Synthesis of Reactive Control Protocols for Differentially Flat Systems

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Jun Liu, Ufuk Topcu, Necmiye Ozay, and Richard M. Murray
2012 Conference on Decision and Control (CDC)

We propose a procedure for the synthesis of con- trol protocols for systems governed by nonlinear differential equations and constrained by temporal logic specifications. This procedure relies on a particular finite-state abstraction of the un- derlying continuous dynamics and a discrete representation of the external environmental signals. A two-player game formulation provides computationally efficient means to construct a discrete strategy based on the finite-state model. We focus on systems with differentially flat outputs, which, in a straightforward manner, allows the construction of continuous control signals from the discrete transitions dictated by the discrete strategy. The resulting continuous-time output trajectories are provably guaranteed to robustly satisfy the original specifications.