A class of generalized parametric implicit quasi-variational inequalities is studied. Thereupon a new existence theorem of the solutions is proved and sensitivity of solutions for this kind of problems is analyzed.
A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landi...A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming(QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities(LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.展开更多
In this paper a new GLKKM theorem in L-convex spaces is established. As applications, a new variational inequality, section theorem, maximal element theorem and fixed point theorem are obtained in L-convex spaces.
We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another ...We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case.展开更多
The definitions of S-KKM property and Γ-invariable property for multi-valued map- ping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uni...The definitions of S-KKM property and Γ-invariable property for multi-valued map- ping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uniform space are obtained, and a quasi-variational inequality theorem for acyclic map on Hausdorff Φ-space is proved. Our results improve and generalize the corresponding results in recent literatures.展开更多
This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone map...This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space.The authors showthat the iterative sequence converges strongly to a common element of the two sets,which solves somevariational inequality.Subsequently,the authors consider the problem of finding a common fixed pointof a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding acommon element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.The results obtained in this paper extend and improve the correspondingresults announced by Nakajo,Takahashi,and Toyoda.展开更多
文摘A class of generalized parametric implicit quasi-variational inequalities is studied. Thereupon a new existence theorem of the solutions is proved and sensitivity of solutions for this kind of problems is analyzed.
基金Project(61473304)supported by the National Natural Science Foundation of ChinaProject(2015AA042202)supported by Hi-tech Research and Development Program of China
文摘A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming(QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities(LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.
基金the Natural Science Research Foundation of Guizhou Provincial Education Department(No.2008072)the Natural Science Foundation of Science and Technology Bureau of Bijie Area (No.2008-06)
文摘In this paper a new GLKKM theorem in L-convex spaces is established. As applications, a new variational inequality, section theorem, maximal element theorem and fixed point theorem are obtained in L-convex spaces.
基金supported by National Natural Science Foundation of China(Grant No11301560)
文摘We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2.We apply an anticipative Girsanov transformation to transform the system into another one,driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion.We derive a maximum principle and the associated stochastic variational inequality,which both are generalizations of the classical case.
基金the National Natural Science Foundation of China (No.10361005)
文摘The definitions of S-KKM property and Γ-invariable property for multi-valued map- ping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uniform space are obtained, and a quasi-variational inequality theorem for acyclic map on Hausdorff Φ-space is proved. Our results improve and generalize the corresponding results in recent literatures.
基金supported by the National Natural Science Foundation of China under Grant No. 10771050
文摘This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space.The authors showthat the iterative sequence converges strongly to a common element of the two sets,which solves somevariational inequality.Subsequently,the authors consider the problem of finding a common fixed pointof a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding acommon element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.The results obtained in this paper extend and improve the correspondingresults announced by Nakajo,Takahashi,and Toyoda.
