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Neural network solution for finite-horizon H-infinity constrained optimal control of nonlinear systems

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Abstract

In this paper, neural networks are used to approximately solve the finite-horizon constrained input H-infinity state feedback control problem. The method is based on solving a related Hamilton-Jacobi-Isaacs equation of the corresponding finite-horizon zero-sum game. The game value function is approximated by a neural network with time-varying weights. It is shown that the neural network approximation converges uniformly to the game-value function and the resulting almost optimal constrained feedback controller provides closed-loop stability and bounded L 2 gain. The result is an almost optimal H-infinity feedback controller with time-varying coefficients that is solved a priori off-line. The effectiveness of the method is shown on the Rotational/Translational Actuator benchmark nonlinear control problem.

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Authors and Affiliations

  1. Automation and Robotics Research Institute, University of Texas, Arlington, TX, 76118, USA

    Tao Cheng & Frank L. Lewis

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  1. Tao Cheng
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  2. Frank L. Lewis
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Additional information

This work was supported by the National Science Foundation (ECS-0501451) and Army Research Office (W91NF-05-1-0314).

Tao CHENG was born in P.R. China in 1976. He received his Bachelor’s degree in Electrical Engineering from Hubei Institute of Technology in 1998. He then joined Beijing Polytechnic University from which he received the Master’s of Science in Electrical Engineering in 2001. In 2006 he obtained Ph.D. degree in Automation and Robotics Research Institute from The University of Texas at Arlington. His research interest is in time-varying optimal nonlinear systems, nonholonomic vehicle systems.

Frank L. LEWIS was born in Wurzburg, Germany, subsequently studying in Chile and Gordonstoun School in Scotland. He obtained B.S. degree in Physics, Electrical Engineering and M.S. degree in Electrical Engineering at Rice University in 1971. In 1977 he received the Master of Science in Aeronautical Engineering from the University of West Florida. In 1981 he obtained the Ph.D. degree at The Georgia Institute of Technology in Atlanta, where he had been employed as a Professor from 1981 to 1990 and is currently an Adjunct Professor. Currently he is a Professor of Electrical Engineering at The University of Texas at Arlington.

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Cheng, T., Lewis, F.L. Neural network solution for finite-horizon H-infinity constrained optimal control of nonlinear systems. J. Control Theory Appl. 5, 1–11 (2007). https://doi.org/10.1007/s11768-006-6048-5

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  • DOI: https://doi.org/10.1007/s11768-006-6048-5

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