Synthesis of Controllers for Continuous Blackbox Systems

Feed-forward controllers compute control outputs to adapt to changes in environmental parameters in a cyber-physical system. When synthesizing control functions it can be difficult to give an analytical description of the controlled plant or to decide the expected control output ahead of time. These systems must, however, adhere to strict safety requirements, which makes it hard to write correct controllers. In this paper, we propose a novel blackbox synthesis approach to construct a continuous control function while dynamically sampling a limited number of test cases. The controller is guaranteed to be correct for a given Lipschitz bound. It can be adapted to work for increasingly conservative estimates of the bound based on observed behavior, iteratively providing increasing confidence in its correctness. Our algorithm employs a linear interpolation model, based on a Delaunay triangulation, to identify candidate control functions. It then generates additional test cases to either confirm a candidate or to improve the model. We evaluate our approach on random benchmarks and CPS examples to show its effectiveness.