An Optimal Tracking Approach to Formation Control of Nonlinear Multi-Agent Systems

Abstract

Formation control of network of multi-agent systems with heterogeneous nonlinear dynamics is formulated as an optimal tracking problem and a decentralized controller is developed using the framework of ‘adaptive critics’ to solve the optimal control problem. The reference signal is assumed available only in online implementation so its dynamics is unavailable for offline training of the neurocontroller. However, this issue is resolved by using a re-optimizatio n of the network output through retraining of the neurocontroller online. Finally, the developed controller is applied to the formation control of multispacecraft orbiting the Earth at different orbits and seeking consensus on their position to dock. I. Introduction HE formation control of network of multi-agent systems with heterogeneous nonlinear dynamics has many application and benefits compared to single agent systems; designing a decentralized controller for such a network of agents though is a challenging problem. Using a decentralized controller, each agent is supposed to have access to its neighbors only while the mission for the whole system is to achieve a desired formation. Solutions to the network of linear agents have been developed by several different authors. A method developed in Ref. 1, called behavior-based decentralized control, performs the multi-agent control for network of agents with ring-wise communication topology by considering two desired behaviors: formation keeping and goal seeking. The role of the communication topology in the formation’s stability is shown in Ref. 2 through the appearance of the eigenvalues of Laplacian matrix of the communication graph in the dynamics of the formation. In Ref. 3 also, the stability of the formation/consensus is shown to be related to the eigenvalues of the Laplacian matrix and for the double-integrator system, the authors of Ref. 3 have designed a controller based on the eigenvalues of this matrix. Minimization of some performance index to reach a consensus is the approach used in Ref. 4 and Ref. 5 for single integrator and double integrator dynamics, respectively. Many of the developed methods in the literature are