Global Robust Stabilizing Control for a Dynamic Neural Network System

• Published in: IEEE transactions on systems, man and cybernetics. Part A, Systems and humans Vol. 39; no. 2; pp. 426 - 436
• Main Authors: Ziqian Liu, Shih, S.C., Qunjing Wang
• Format: Journal Article
• Language: English
• Published: IEEE 01.03.2009
• Subjects: Control design; Control nonlinearities; Control systems; Cost function; Disturbances; Dynamic neural network system; Dynamical systems; Dynamics; Hamilton-Jacobi-Isaacs (HJI) equation; inverse optimality; Lyapunov method; Lyapunov stability; Mathematical models; Neural networks; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear dynamics; Nonlinear equations; nonlinear {\rm H}_{\infty} control; Nonlinearity; Robust control
• ISSN: 1083-4427; 1558-2426
• DOI: 10.1109/TSMCA.2008.2010749

This paper presents a new approach for the global robust stabilizing control of a class of dynamic neural network systems. This approach is developed via Lyapunov stability and inverse optimality, which circumvents the task of solving a Hamilton-Jacobi-Isaacs equation. The primary contribution of this paper is the development of a nonlinear H infin control design for a class of dynamic neural network systems, which are usually used in the modeling and control of nonlinear affine systems with unknown nonlinearities. The proposed H infin control design achieves global inverse optimality with respect to some meaningful cost functional, global disturbance attenuation, and global asymptotic stability provided that no disturbance occurs. Finally, four numerical examples are used to demonstrate the effectiveness of the proposed approach.