Performance improvement for formation-keeping control using a neural network HJI approach

This article deals with the performance improvement issues for nonlinear formation-keeping control systems by using a neural network HamiltonJacobi-Isaacs (HJI) approach. The associated HJI equation is successively solved by approximating its value function with a neural network and the successive Galerkin approximation (SGA) method. The neural network is also used to approximate the control laws achieved by successive policy iterations rather than data-based training. As a case study, we present the application of this approach to the nonlinear optimal (nearly) and robust formation control of multiple autonomous underwater robotic vehicles (AURVs). A nonlinear change of coordinates and feedback is made such that the SGA algorithm developed for time-invariant nonlinear systems can be implemented to the formation control system under consideration in this article. The formation-keeping performance is significantly improved by solving the associated HJI equation with the SGA algorithm. The synthesized formation-keeping controller, which is expressed by a neural network, also has nearly optimal and robust properties in comparison with the original control law designed by taking advantage of Lyapunov’s direct method. Simulation results are presented to demonstrate the improved formation-keeping performance of a leader-follower formation of AURVs in nonholonomic chained form.