Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems

Authors:
M. Abu-Khalaf;F. L. Lewis;Jie Huang
Affiliations:
Control & Estimation Group, MathWorks, Inc., Natick, MA;-;-
Venue:
IEEE Transactions on Neural Networks
Year:
2008

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Abstract

In this paper, neural networks are used along with two-player policy iterations to solve for the feedback strategies of a continuous-time zero-sum game that appears in L2-gain optimal control, suboptimal Hinfin control, of nonlinear systems affine in input with the control policy having saturation constraints. The result is a closed-form representation, on a prescribed compact set chosen a priori, of the feedback strategies and the value function that solves the associated Hamilton-Jacobi-Isaacs (HJI) equation. The closed-loop stability, L2-gain disturbance attenuation of the neural network saturated control feedback strategy, and uniform convergence results are proven. Finally, this approach is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem under actuator saturation, offering guaranteed stability and disturbance attenuation.