Non-Parametric Neuro-Adaptive Formation Control

We develop a learning-based algorithm for the distributed formation control of networked multi-agent systems governed by unknown, nonlinear dynamics. Most existing algorithms either assume certain parametric forms for the unknown dynamic terms or resort to unnecessarily large control inputs in order to provide theoretical guarantees. The proposed algorithm avoids these drawbacks by integrating neural network-based learning with adaptive control in a two-step procedure. In the first step of the algorithm, each agent learns a controller, represented as a neural network, using training data that correspond to a collection of formation tasks and agent parameters. These parameters and tasks are derived by varying the nominal agent parameters and a user-defined formation task to be achieved, respectively. In the second step of the algorithm, each agent incorporates the trained neural network into an online and adaptive control policy in such a way that the behavior of the multi-agent closed-loop system satisfies the user-defined formation task. Both the learning phase and the adaptive control policy are distributed, in the sense that each agent computes its own actions using only local information from its neighboring agents. The proposed algorithm does not use any a priori information on the agents’ unknown dynamic terms or any approximation schemes. We provide formal theoretical guarantees on the achievement of the formation task. Note to Practitioners—This paper is motivated by control of multi-agent systems, such as teams of robots, smart grids, or wireless sensor networks, with uncertain dynamic models. Existing works develop controllers that rely on unrealistic or impractical assumptions on these models. We propose an algorithm that integrates offline learning with neural networks and real-time feedback control to accomplish a multi-agent task. The task consists of the formation of a pre-defined geometric pattern by the multi-agent team. The learning module of the proposed algorithm aims to learn stabilizing controllers that accomplish the task from data that are obtained from offline runs of the system. However, the learned controller might result in poor performance owing to potential data inaccuracies and the fact that learning algorithms can only approximate the stabilizing controllers. Therefore, we complement the learned controller with a real-time feedback-control module that adapts on the fly to such discrepancies. In practise, the data can be collected from pre-recorded trajectories of the multi-agent system, but these trajectories do need to accomplish the task at hand. The real-time feedback-control is a closed-form function of the states of each agent and its neighbours and the trained neural networks and can be straightforwardly implemented. The experimental results show that the proposed algorithm achieves greater performance than algorithms that use only the trained neural networks or only the real-time feedback-control policy. Our future research will address the sensitivity of the algorithm to the quality and quantity of the employed data as well as to the learning performance of the neural networks.