A back propagation through time-like min–max optimal control algorithm for nonlinear systems

Authors

  • Vladimir Milić,

    Corresponding author
    • Department of Robotics and Automation of Manufacturing Systems, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb HR-10000, Croatia
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  • Josip Kasać,

    1. Department of Robotics and Automation of Manufacturing Systems, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb HR-10000, Croatia
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  • Dubravko Majetić

    1. Department of Robotics and Automation of Manufacturing Systems, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb HR-10000, Croatia
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Correspondence to: Vladimir Milić, Department of Robotics and Automation of Manufacturing Systems, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, Zagreb HR-10000, Croatia.

E-mail: vladimir.milic@fsb.hr

SUMMARY

This paper presents a conjugate gradient-based algorithm for feedback min–max optimal control of nonlinear systems. The algorithm has a backward-in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one-layer NN. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation, to provide an effective, numerically robust algorithm for solving optimal min–max control problems. The proposed algorithm is evaluated on a robotic system with two DOFs. Copyright © 2012 John Wiley & Sons, Ltd.

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