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Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems

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3 Author(s)
Abu-Khalaf, M. ; Control & Estimation Group, MathWorks, Inc., Natick, MA ; Lewis, F.L. ; Jie Huang

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.

Published in:

Neural Networks, IEEE Transactions on  (Volume:19 ,  Issue: 7 )