The paper investigates the optimal linear quadratic control problem in the discrete-time framework, for stochastic systems affected by disturbances generated by a nonlinear stochastic exosystem. By applying the maximum principle to nonlinear optimal control problems, it does not admit, in general, implementable solutions. Therefore, it is worthwhile to look for finite-dimensional approximation schemes. The approach followed in this paper is based on the υ-degree Carleman approximation of a stochastic nonlinear system applied to the nonlinear 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 υ is increased.

Mavelli, G., Palumbo, P. (2007). A Carleman approximation scheme for a stochastic optimal nonlinear control problem. In Proceedings 9th European Control Conference, ECC 2007; Kos International Convention Center (KICC) Kos; Greece; 2-5 July 2007 (pp.3672-3678). IEEE Institute of Electrical and Electronics Engineers [10.23919/ecc.2007.7068738].

A Carleman approximation scheme for a stochastic optimal nonlinear control problem

Palumbo, P
2007

Abstract

The paper investigates the optimal linear quadratic control problem in the discrete-time framework, for stochastic systems affected by disturbances generated by a nonlinear stochastic exosystem. By applying the maximum principle to nonlinear optimal control problems, it does not admit, in general, implementable solutions. Therefore, it is worthwhile to look for finite-dimensional approximation schemes. The approach followed in this paper is based on the υ-degree Carleman approximation of a stochastic nonlinear system applied to the nonlinear 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 υ is increased.
paper
Optimal control; Nonlinear systems; Carleman approximation;
English
European Control Conference (ECC07) - 2 July 2007 through 5 July 2007
2007
Proceedings 9th European Control Conference, ECC 2007; Kos International Convention Center (KICC) Kos; Greece; 2-5 July 2007
978-395241738-6
2007
3672
3678
7068738
reserved
Mavelli, G., Palumbo, P. (2007). A Carleman approximation scheme for a stochastic optimal nonlinear control problem. In Proceedings 9th European Control Conference, ECC 2007; Kos International Convention Center (KICC) Kos; Greece; 2-5 July 2007 (pp.3672-3678). IEEE Institute of Electrical and Electronics Engineers [10.23919/ecc.2007.7068738].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/246591
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