Gradient-Free Cooperative Source Seeking with Input Saturation and Limited Communication

This paper addresses a multi-agent cooperative source seeking problem, with a particular focus on scenarios involving input saturation and limited communication. The objective is to guide the average position of a number of agents to the optimal point of a specified unknown scalar field function while maintaining the desired formation based on the field values measured by the agents. The difficulty of the above task arises due to the strong nonlinearity introduced by the saturation function and the limited communication among agents. To address this challenge, we propose a gradient-free formation-based collaborative source seeking algorithm, featuring both centralized and distributed implementations. In addition, we construct a proper composite Lyapunov function to establish the stability of the closed-loop system leveraging the nonlinear small-gain theorem. The proposed method estimates the gradient of an unknown scalar field through collaborative formation, eliminating the need for prior knowledge of the field function. Finally, the effectiveness of the proposed method is illustrated by a numerical simulation.