Tunable Reactive Synthesis for Lipschitz-Bounded Systems with Temporal Logic Specifications

TL;DR

This paper presents a method for synthesizing reactive controllers for cyber-physical systems with temporal logic specifications, using a hierarchical approach and SMT-based counterexample-guided optimization, applicable to Lipschitz-bounded dynamics.

Contribution

It introduces a tunable reactive synthesis framework leveraging Lipschitz bounds and SMT solving, enabling controller design under varying information levels about adversarial inputs.

Findings

Effective synthesis for Lipschitz-bounded systems demonstrated

Hierarchical control problem formulation enhances flexibility

Application shown in autonomous car scenario

Abstract

We address the problem of synthesizing reactive controllers for cyber-physical systems subject to Signal Temporal Logic (STL) specifications in the presence of adversarial inputs. Given a finite horizon, we define a reactive hierarchy of control problems that differ in the degree of information available to the system about the adversary's actions over the horizon. We show how to construct reactive controllers at various levels of the hierarchy, leveraging the existence of Lipschitz bounds on system dynamics and the quantitative semantics of STL. Our approach, a counterexample-guided inductive synthesis (CEGIS) scheme based on optimization and satisfiability modulo theories (SMT) solving, builds a strategy tree representing the interaction between the system and its environment. In every iteration of the CEGIS loop, we use a mix of optimization and SMT to maximally discard controllers falsified by a given counterexample. Our approach can be applied to any system with local Lipschitz-bounded dynamics, including linear, piecewise-linear and differentially-flat systems. Finally we show an application in the autonomous car domain.