Neural Network Based Distributed Consensus Control for Heterogeneous Multi-agent Systems

This paper is concerned with leader-following consensus problems for a class of heterogeneous linear multi-agent systems. The consensus problem is decomposed to a collection of local tracking problems with local cost functions defined based on the tracking errors. Each follower will adjust its control input to minimize its own cost function. Since the local tracking error of a follower will be influenced by its own control policy as well as its neighbors' actions, the optimal control policy of each follower cannot be solved independently. Based on game theory, a set of stable optimal policies of the whole network falls at the Nash equilibrium. To find the Nash solutions for all followers, we design a distributed algorithm that calculate the control policies through an iterative process. A convergence analysis is given to show that the generated control policies converge to the Nash equilibrium. To implement our algorithm, a neural network based controller framework is proposed, in which neural networks are employed to estimate the system dynamics and to generate the desired controls. A simulation example is presented to demonstrate the effectiveness of the proposed method.