PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

摘要

A solution is provided in this paper for the adaptive approximate consensus problem of nonlinear multi-agent systems with unknown and non-identical control directions assuming an underlying graph topology having a spanning tree. This is achieved with the introduction of a novel variable transformation called PI consensus error transformation. The new variables include the position error of each agent from some reference trajectory chosen by him, which represents the agent's selection for the desired swarm trajectory, along with an integral term of the weighted total displacement of the agent's position from all neighbor positions. It is proven that if these new variables are bounded and regulated to zero, then asymptotic approximate consensus among all agents is ensured. Using classical Nussbaum gain based techniques, distributed controllers are designed to regulate the PI consensus error variables to zero and ultimately solve the approximate agreement problem. The proposed approach also allows for a specific calculation of the final consensus trajectory based on the controller parameter selection and the associated graph topology. It is shown that all agent positions converge towards a neighborhood of the weighted average of all agents reference trajectories. Simulation results verify our theoretical derivations. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.