Abstraction-Based Control Synthesis

ion-based control synthesis is a three-step process to solve a control problem for continuous-state system (difference equation or differential equation), by first abstracting this system into a finite transition system, solving the control problem on the abstraction, and finally refining the obtained controller to apply it to the continuous system. This chapter first provides an overview of the three steps of abstraction-based approaches and on the key role played by reachability analysis in the first step to create the finite abstraction. This approach is then illustrated on a docking problem for a marine vessel corresponding to a reach-avoid specification (reach the docking area in finite time while avoiding obstacles). This example highlights how the forward reachability analysis methods presented in this book can be used within such abstraction-based approaches to solve backward reachability problems.