Abstract
The solutions of most nonlinear optimal control problems are given in the form of open-loop optimal control which is computed from a given fixed initial condition. Optimal feedback control can in principle be obtained by solving the corresponding Hamilton-Jacobi-Bellman dynamic programming equation, though in general this is a difficult task. We propose a practical and effective alternative for constructing an approximate optimal feedback controller in the form of a feedforward neural network, and we justify this choice by several reasons. The controller is capable of approximately minimizing an arbitrary performance index for a nonlinear dynamical system for initial conditions arising from a nontrivial bounded subset of the state space. A direct training algorithm is proposed and several illustrative examples are given.
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Communicated by M. Simaan
This research was carried out with the support of a grant from the Australian Research Council.
We thank the anonymous reviewers for their helpful comments.
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Edwards, N.J., Goh, C.J. Direct training method for a continuous-time nonlinear optimal feedback controller. J Optim Theory Appl 84, 509–528 (1995). https://doi.org/10.1007/BF02191983
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DOI: https://doi.org/10.1007/BF02191983