Neural network solution for suboptimal control of non-holonomic chained form system

Abstract

In this paper, we develop fixed-final time nearly optimal control laws for a class of non-holonomic chained form systems by using neural networks to approximately solve a Hamilton—Jacobi—Bellman equation. A certain time-folding method is applied to recover uniform complete controllability for the chained form system. This method requires an innovative design of a certain dynamic control component. Using this time-folding method, the chained form system is mapped into a controllable linear system for which controllers can systematically be designed to ensure exponential or asymptotic stability as well as nearly optimal performance. The result is a neural network feedback controller that has time-varying coefficients found by a priori offline tuning. The results of this paper are demonstrated in an example.