Bounded robust control of nonlinear systems using neural network–based HJB solution

• Published in: Neural computing & applications Vol. 20; no. 1; pp. 91 - 103
• Main Authors: Adhyaru, Dipak M., Kar, I. N., Gopal, M.
• Format: Journal Article
• Language: English
• Published: London Springer-Verlag 01-02-2011
• Subjects: Artificial Intelligence; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Data Mining and Knowledge Discovery; Image Processing and Computer Vision; Original Article; Probability and Statistics in Computer Science; Robust control; Bounded control; Lyapunov stability; HJB equation; System uncertainty
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-010-0441-1

In this paper, a Hamilton–Jacobi–Bellman (HJB) equation–based optimal control algorithm for robust controller design is proposed for nonlinear systems. The HJB equation is formulated using a suitable nonquadratic term in the performance functional to tackle constraints on the control input. Utilizing the direct method of Lyapunov stability, the controller is shown to be optimal with respect to a cost functional, which includes penalty on the control effort and the maximum bound on system uncertainty. The bounded controller requires the knowledge of the upper bound of system uncertainty. In the proposed algorithm, neural network is used to approximate the solution of HJB equation using least squares method. Proposed algorithm has been applied on the nonlinear system with matched and unmatched type system uncertainties and uncertainties in the input matrix. Necessary theoretical and simulation results are presented to validate proposed algorithm.