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The Carleman Approximation Approach to Solve a Stochastic Nonlinear Control Problem

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2 Author(s)
Mavelli, G. ; Ist. di Analisi dei Sist. ed Inf. A. Ruberti, Nat. Res. Council, Rome, Italy ; Palumbo, P.

This note investigates the optimal linear quadratic control problem in the discrete-time framework, for stochastic systems affected by disturbances generated by a nonlinear stochastic exosystem. The application of the maximum principle to nonlinear optimal control problems does not admit, in general, implementable solutions. Therefore, it is worthwhile to look for finite-dimensional approximation schemes. The approach followed in this note is based on the ??-degree Carleman approximation of a stochastic nonlinear system applied to the exosystem and provides a real-time algorithm to design an implementable control law. Simulations support theoretical results and show the improvements when the approximation index ?? is increased.

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Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 4 )