The paper investigates the optimal control problem for a stochastic linear di®erential system, driven by a persistent disturbance generated by a nonlinear stochastic exogenous system. The assumption of incomplete information has been assumed, that is neither the state of the system, nor the state of the exosystem are directly measurable. The standard quadratic cost functional has been considered. The approach followed consists of applying the º-degree Carleman approximation scheme to the exosystem, which provides a stochastic bilinear system. Then, the optimal regulator is obtained (i.e. the solution to the minimum control problem among all the a±ne transformations of the measurements). Better performances of the regulator are expected using higher order system approximations.

A Carleman approximation scheme for a stochastic optimal control problem in the continuous-time framework

Mavelli G;Palumbo P
2008

Abstract

The paper investigates the optimal control problem for a stochastic linear di®erential system, driven by a persistent disturbance generated by a nonlinear stochastic exogenous system. The assumption of incomplete information has been assumed, that is neither the state of the system, nor the state of the exosystem are directly measurable. The standard quadratic cost functional has been considered. The approach followed consists of applying the º-degree Carleman approximation scheme to the exosystem, which provides a stochastic bilinear system. Then, the optimal regulator is obtained (i.e. the solution to the minimum control problem among all the a±ne transformations of the measurements). Better performances of the regulator are expected using higher order system approximations.
2008
Istituto di Analisi dei Sistemi ed Informatica ''Antonio Ruberti'' - IASI
978-3-902661-00-5
Stochastic control
Optimal control
Carleman approximation
Filtering theory
Bilinear systems.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/71224
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