The paper is concerned with solving periodic boundary problem of semilinear systems,which will be differentiably embedded into an one-parameter family of operators.The solution of the systems is then found by continui...The paper is concerned with solving periodic boundary problem of semilinear systems,which will be differentiably embedded into an one-parameter family of operators.The solution of the systems is then found by continuing the solution curve of operator homotopy.When the Newton-Kantorovich's procedure is applied to the corresponding operator equations,an efficient algorithm is derived.Finally,the theoretical results are in excellent agreement with the numerical examples.展开更多
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stoc...This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.展开更多
Low gain feedback refers to certain families of stabilizing state feedback gains that areparameterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initiallyproposed to achieve sem...Low gain feedback refers to certain families of stabilizing state feedback gains that areparameterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initiallyproposed to achieve semi-global stabilization of linear systems subject to input saturation. It wasthen combined with high gain feedback in different ways for solving various control problems. Theresulting feedback laws are referred to as low-and-high gain feedback. Since the introduction of lowgain feedback in the context of semi-global stabilization of linear systems subject to input saturation,there has been effort to develop alternative methods for low gain design, to characterize key featuresof low gain feedback, and to explore new applications of the low gain and low-and-high gain feedback.This paper reviews the developments in low gain and low-and-high gain feedback designs.展开更多
文摘The paper is concerned with solving periodic boundary problem of semilinear systems,which will be differentiably embedded into an one-parameter family of operators.The solution of the systems is then found by continuing the solution curve of operator homotopy.When the Newton-Kantorovich's procedure is applied to the corresponding operator equations,an efficient algorithm is derived.Finally,the theoretical results are in excellent agreement with the numerical examples.
基金Project supported by the National Natural Science Foundation of China (No.10325101, No.101310310)the Science Foundation of the Ministry of Education of China (No. 20030246004).
文摘This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.
文摘Low gain feedback refers to certain families of stabilizing state feedback gains that areparameterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initiallyproposed to achieve semi-global stabilization of linear systems subject to input saturation. It wasthen combined with high gain feedback in different ways for solving various control problems. Theresulting feedback laws are referred to as low-and-high gain feedback. Since the introduction of lowgain feedback in the context of semi-global stabilization of linear systems subject to input saturation,there has been effort to develop alternative methods for low gain design, to characterize key featuresof low gain feedback, and to explore new applications of the low gain and low-and-high gain feedback.This paper reviews the developments in low gain and low-and-high gain feedback designs.
