Abstraction-based control design (ABCD) is a methodology to algorithmically construct controllers for continuous time dynamical systems for temporal specifications. The ABCD algorithm constructs a finite and discrete-time abstraction of the dynamical system, computes a discrete controller for the finite system using reactive synthesis, and refines the discrete controller to a controller for the original dynamical system. These lecture notes lay out the basic theory for ABCD and describe a recent extension which performs the abstraction in a multi-layered, adaptive way.
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