The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the...The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the exponential stability of the system. Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to haveshown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria forthe exponential stability on the linear stochastic uncertain closed-loop systems are given.展开更多
This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian c...This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties： randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved.展开更多
文摘The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the exponential stability of the system. Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to haveshown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria forthe exponential stability on the linear stochastic uncertain closed-loop systems are given.
基金Supported by National Natural Science Foundation of China(71171003,71210107026)Anhui Natural Science Foundation(10040606003)Anhui Natural Science Foundation of Universities(KJ2012B019,KJ2013B023)
文摘This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties： randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved.
