Symbolic Self-triggered Control of Continuous-time Non-deterministic Systems without Stability Assumptions for 2-LTL Specifications

TL;DR

This paper introduces a symbolic self-triggered control method for non-deterministic continuous-time nonlinear systems that satisfies 2-LTL specifications and optimizes energy use without relying on stability assumptions.

Contribution

It presents a novel synthesis procedure that combines state and input quantization with game-theoretic strategies for complex system specifications.

Findings

Successfully applied to a nonholonomic robot navigation example.

Achieves specification satisfaction without stability assumptions.

Reduces energy consumption through self-triggered control.

Abstract

We propose a symbolic self-triggered controller synthesis procedure for non-deterministic continuous-time nonlinear systems without stability assumptions. The goal is to compute a controller that satisfies two objectives. The first objective is represented as a specification in a fragment of LTL, which we call 2-LTL. The second one is an energy objective, in the sense that control inputs are issued only when necessary, which saves energy. To this end, we first quantise the state and input spaces, and then translate the controller synthesis problem to the computation of a winning strategy in a mean-payoff parity game. We illustrate the feasibility of our method on the example of a navigating nonholonomic robot.