Fixed-final-time-constrained optimal control, of Nonlinear systems using neural network HJB approach

In this paper, fixed-final time-constrained optimal control laws using neural networks (NNS) to solve Hamilton-jacobi-Bellman (HJB) equations for general affine in the constrained nonlinear systems are proposed. An NN is used to approximate the time-varying cost function using the method of least squares on a predefined region. The result is an NN nearly-constrained feedback controller that has time-varying coefficients found by a priori offline tuning. Convergence results are shown. The results of this paper are demonstrated in two examples, including a nonholonomic system.