Novel average-valued condition for multi-agent systems via a quantized adaptive control protocol

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Abstract

A novel average-valued condition for consensus of multi-agent systems (MASs) is developed via a quantized adaptive control protocol, a framework that simultaneously addresses multiple self-delays, time-varying coupling, and logarithmic quantizers. A adaptive controller is designed, where each follower applies a quantized error signal and a shared adaptive gain that is updated by the quantized sum of all followers’ squared errors with a fixed adaptation rate. By constructing a Lyapunov functional and applying a generalized Halanay inequality that exploits the time-average property of the coupling strength, we prove that the adaptive gain is nondecreasing, remains bounded, and converges to a finite limit. A gain threshold, depending explicitly on the average coupling strength and the delay-related Lipschitz constants, is established: If the gain exceeds this threshold, exponential consensus is achieved; otherwise, asymptotic consensus still holds. Numerical simulations on a leader-follower network with Lorenz-type node dynamics and two self-delays validate the theoretical results, including the effect of different adaptation rates, quantization densities, and delay configurations.

Keywords

multi-agent system / consensus / time-varying coupling / logarithmic quantizer / adaptive control / time-delay

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