Fixed-Final-Time-Constrained Optimal Control of Nonlinear Systems Using Neural Network HJB Approach

• Published in: IEEE transactions on neural networks Vol. 18; no. 6; pp. 1725 - 1737
• Main Authors: Tao Cheng, Lewis, F.L., Abu-Khalaf, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2007; Institute of Electrical and Electronics Engineers
• Subjects: Adaptive control; Applied sciences; Approximation; Artificial intelligence; Computer science; control theory; systems; Connectionism. Neural networks; Constrained input systems; Constraint optimization; Control systems; Convergence; Cost function; Dynamical systems; Exact sciences and technology; finite-horizon optimal control; Hamilton-Jacobi-Bellman (HJB); Least squares approximation; Mathematical analysis; neural network (NN) control; Neural networks; Nonlinear dynamics; Nonlinear equations; Nonlinear systems; Optimal control; Tuning; Hamilton-Jacobi-Bellman (HJB); finite-horizon optimal control; Constrained input systems; neural network (NN) control; finite-horizon optimal a control; Non linear control; Neural network; Constrained optimization; Control constraint; Finite horizon; Time varying system; Minimum time; Hamilton Jacobi equation; Least squares method; Optimal control; Distributed control; Occupation time; neural network 5NN control; Optimal control (mathematics)
• ISSN: 1045-9227; 1941-0093
• DOI: 10.1109/TNN.2007.905848

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.