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Direct training method for a continuous-time nonlinear optimal feedback controller. (English) Zbl 0822.93033

Summary: 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 feedback neural network. The controller is capable of approximately minimizing an arbitrary performance index for a nonlinear dynamical system for initial conditions chosen in a bounded subset of the state space. A direct training algorithm is proposed and several illustrative examples are given.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
92B20 Neural networks for/in biological studies, artificial life and related topics
93C10 Nonlinear systems in control theory
49N35 Optimal feedback synthesis
93B52 Feedback control

Software:

MISER3
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Full Text: DOI

References:

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