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arXiv · 2006.04260

Formal synthesis of closed-form sampled-data controllers for nonlinear continuous-time systems under STL specifications

Cees F. Verdier·Niklas Kochdumper·Matthias Althoff·Manuel Mazo Jr
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Abstract

We propose a counterexample-guided inductive synthesis framework for the formal synthesis of closed-form sampled-data controllers for nonlinear systems to meet STL specifications over finite-time trajectories. Rather than stating the STL specification for a single initial condition, we consider an (infinite and bounded) set of initial conditions. Candidate solutions are proposed using genetic programming, which evolves controllers based on a finite number of simulations. Subsequently, the best candidate is verified using reachability analysis; if the candidate solution does not satisfy the specification, an initial condition violating the specification is extracted as a counterexample. Based on this counterexample, candidate solutions are refined until eventually a solution is found (or a user-specified number of iterations is met). The resulting sampled-data controller is expressed as a closed-form expression, enabling both interpretability and the implementation in embedded hardware with limited memory and computation power. The effectiveness of our approach is demonstrated for multiple systems.

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Cees F. Verdier, Niklas Kochdumper, Matthias Althoff, Manuel Mazo Jr. 2020-06-07. Formal synthesis of closed-form sampled-data controllers for nonlinear continuous-time systems under STL specifications. https://arxiv.org/abs/2006.04260

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