Lazy safety controller synthesis with multi-scale adaptive-sampling abstractions of nonlinear systems

In this paper, we present an abstraction-based approach to safety controller synthesis for continuous-time nonlinear systems. To reduce the computational burden associated with symbolic control approaches, we develop a lazy controller synthesis algorithm, which uses the incremental forward exploration of the symbolic dynamics, allowing us to restrict the controller synthesis computations to reachable states only. We propose using this algorithm with novel multi-scale abstractions, which also use adaptive time sampling. Transition duration is constrained by intervals that must contain the reachable set, which enables better control of the symbolic transitions as opposed to using transitions of predetermined duration. Implementation of the algorithm and controller refinement are discussed. We provide a simple example to illustrate these benefits of the approach.