A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under whi...A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.展开更多
This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful alge...This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.展开更多
Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability e...Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.展开更多
基金Project supported by the National Natural Science Foundation ofChina (No. 10332030), the Special Fund for Doctor Programs inInstitutions of Higher Learning of China (No. 20020335092), andthe Zhejiang Provincial Natural Science Foundation (No. 101046),China
文摘A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
基金supported by the National Natural Science Foundation under Grant Nos.60904029 and 60704002the State Key Laboratory under Grant No.RCS2008ZT002
文摘This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.
基金Project supported by the National Natural Science Foundation of China(No.11101070)the Grant MTM2011-29306-C02-00 of the MICINN,Spain+4 种基金the Project PI2010-04 of the Basque Governmentthe ERC Advanced Grant FP7-246775 NUMERIWAVESthe ESF Research Networking Programme OPT-PDEScientific Research Fund of Sichuan Provincial Education Department of China(No.10ZC110) the project Z1062 of Leshan Normal University of China
文摘Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.
