Super-Ellipse Formation Tracking of Uncertain Vehicles: A Simplified Reinforcement Learning Energy Optimization Method

This article deals with the optimal super-ellipse formation tracking control problem for multiple unmanned vehicles (MUVs), where each vehicle contains nonlinear uncertainties of unmodeled basic resistance, and the objective of energy optimization includes the super-ellipse orbit tracking energy and formation motion energy on the normal and tangent directions along the super-ellipse orbits, respectively. The communication topology is the directed leader-following structure. To avoid using the inputs of neighboring MUVs and the global communication information, a novel augmented formation input is designed and integrated into the formation motion subsystem. To deal with the uncertain nonlinearity, the uncertain virtual leader information, and the limited information of neighboring MUVs in the Hamilton-Jacobi–Bellman equations, a simplified reinforcement learning (RL) energy optimization method is designed based on identifier neural networks (NNs) and optimized backstepping technique. Theoretical stability analysis of system errors are given in detail. Simulation results show that the super-ellipse formation tracking energy consumption is significantly saved and the algorithm run time is decreased through comparison.