Intertemporal Optimization of Formation Control for Nonlinear Networks With Multiple Constraints: A Reach-Avoid Game Approach

This paper, by using viability theory, presents a novel coordinate-free and optimal formation control protocol for nonlinear network systems with control, communication, connection and collision avoidance constraints. Existing numerical tools of viability theory characterize the feasible region of states in which a solution exists with respect to two-player reach-avoid games for constrained complex systems. This work formulates the optimal formation control problem as a multi-player reach-avoid differential graphical game based on viability theory, ensuring the formation control law adapts to the fastest convergence rate for the switching local networks while satisfying all the constraints by employing local information. The network is assumed to be always unknown and switching, where the edges of its graph are allowed to be temporarily disconnected while the connectivity of graph is guaranteed. The value function is approximated by the adaptive graph neural network (GNN), where its parametric domains are characterized by viability theory. Besides, the convergence of the approximation errors of the value function for the differential graphical game is analyzed. The effectiveness of the proposed method is confirmed and illustrated via simulations.