Detection of Transient Instabilities in Multi-Agent Systems and Swarms

In this paper, we introduce the novel concept of transient instabilities in multi-agent systems and swarms, i.e., a small disturbance leads to increasing-amplitude oscillations throughout the swarm, which results in a large number of inter-agent collisions. This instability is dominant in the transient phase of the system and it does not appear in the steady-state behavior of the system, as each agent uses Lyapunov-stable feedback control laws. We present a rigorous definition of transient instability in swarms, and discuss its key properties. We also present a sufficient condition to check if a swarm will be transient stable. Using both theoretical techniques and numerical results, we show that a simple Proportional-Integral-Derivative (PID) feedback-tracking control law is not suitable for these applications. We also present a robust control law for Euler-Lagrangian systems that maintains transient stability across static swarms or time-varying reconfiguration in swarms. Both theoretical results and numerical simulations are presented to demonstrate the effectiveness of our proposed approach.