Lazy Symbolic Controller for Continuous-Time Systems Based on Safe Set Boundary Exploration

In this paper, we present an abstraction-based approach to robust safety controller synthesis for continuous-time nonlinear systems. To reduce the computational complexity associated with symbolic control approaches, we develop a lazy controller synthesis algorithm, which iteratively explores states on the boundary of controllable domain while avoiding exploration of internal states, supposing that they are safely controllable a priory. A closed- loop safety controller for the original problem is then defined as follows: we use the abstract controller to push the system from a boundary state back towards the interior, while for inner states, any admissible input is valid. We then compare the proposed approach with the classical safety synthesis algorithm and illustrate the advantages, in terms of run-time and memory efficiency, on an adaptive cruise control problem.