Abstraction-Free Control Synthesis to Satisfy Temporal Logic Constraints under Sensor Faults and Attacks

TL;DR

This paper presents an abstraction-free control synthesis method for complex tasks specified by Gaussian distribution temporal logic, ensuring task satisfaction under sensor faults and attacks without finite system abstraction.

Contribution

It introduces a novel fault-tolerant control barrier function approach that guarantees task satisfaction despite malicious sensor faults and attacks, without relying on system abstraction.

Findings

Guarantees almost sure satisfaction of GDTL specifications under faults and attacks.

Develops linear constraints for control inputs using fault-tolerant CBFs.

Demonstrates effectiveness through a mobile robot coordination case study.

Abstract

We study the problem of synthesizing a controller to satisfy a complex task in the presence of sensor faults and attacks. We model the task using Gaussian distribution temporal logic (GDTL), and propose a solution approach that does not rely on computing any finite abstraction to model the system. We decompose the GDTL specification into a sequence of reach-avoid sub-tasks. We develop a class of fault-tolerant finite time convergence control barrier functions (CBFs) to guarantee that a dynamical system reaches a set within finite time almost surely in the presence of malicious attacks. We use the fault-tolerant finite time convergence CBFs to guarantee the satisfaction of `reach' property. We ensure `avoid' part in each sub-task using fault-tolerant zeroing CBFs. These fault-tolerant CBFs formulate a set of linear constraints on the control input for each sub-task. We prove that if the error incurred by system state estimation is bounded by a certain threshold, then our synthesized controller fulfills each reach-avoid sub-task almost surely for any possible sensor fault and attack, and thus the GDTL specification is satisfied with probability one. We demonstrate our proposed approach using a numerical study on the coordination of two wheeled mobile robots.