Towards cyber-physical systems robust to communication delays: A differential game approach

TL;DR

This paper develops a differential game framework to design controllers for cyber-physical systems that maintain stability despite communication delays, addressing a critical challenge in interconnected robotic systems.

Contribution

It introduces a novel differential game approach that models communication delays as adversarial inputs, leading to robust control strategies for nonlinear time-delay systems.

Findings

Controllers designed via the differential game outperform Lyapunov-Krasovskii methods in simulations.

The approach effectively mitigates oscillations caused by communication delays.

Numerical experiments validate the robustness of the proposed controllers.

Abstract

Collaboration between interconnected cyber-physical systems is becoming increasingly pervasive. Time-delays in communication channels between such systems are known to induce catastrophic failure modes, like high frequency oscillations in robotic manipulators in bilateral teleoperation or string instability in platoons of autonomous vehicles. This paper considers nonlinear time-delay systems representing coupled robotic agents, and proposes controllers that are robust to time-varying communication delays. We introduce approximations that allow the delays to be considered as implicit control inputs themselves, and formulate the problem as a zero-sum differential game between the stabilizing controllers and the delays acting adversarially. The ensuing optimal control law is finally compared to known results from Lyapunov-Krasovskii based approaches via numerical experiments.