A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condit...A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.展开更多
In this paper, we concern the approaching condition of sliding mode control （SMC） with a Lipschitz switching surface that may be nonsmooth. New criteria on the relation between phase trajectories and an arbitrary Li...In this paper, we concern the approaching condition of sliding mode control （SMC） with a Lipschitz switching surface that may be nonsmooth. New criteria on the relation between phase trajectories and an arbitrary Lipschitz continuous surface are examined firstly. Filippov＇s differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system with SMC. Compared with Filippov＇s criteria for only smooth surface, new criteria are proposed by utilizing the cone conditions that allow the surface to be nonsmooth. This result also yields a new approaching condition of SMC design. Based on the new approaching condition, we develop the sliding mode controller for a class of nonlinear single-input single-output （SISO） systems, of which the switching surface is designed Lips- chitz continuous for the nonsmooth sliding motion. Finally, we provide a numerical example to verify the new design method.展开更多
This paper is devoted to the problem of partial asymptotic null-controllability of control sys-tems governed by ordinary differential equations,subjected to possibly mixed state-input con-straints.Using Lyapunov funct...This paper is devoted to the problem of partial asymptotic null-controllability of control sys-tems governed by ordinary differential equations,subjected to possibly mixed state-input con-straints.Using Lyapunov functions within the framework of viability theory,feedback controls are designed in such a way a part of system’s state can be driven to the origin asymptotically,taking into account the mixed constraints.By using Michael selection theorem,the existence of such controls is proved,in the case of convex constraints,and their expressions are given as continu-ous selections of an appropriate constructed multifunction.Finally,two examples are processed numerically in order to illustrate the theoretical results.展开更多
文摘A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.
文摘In this paper, we concern the approaching condition of sliding mode control （SMC） with a Lipschitz switching surface that may be nonsmooth. New criteria on the relation between phase trajectories and an arbitrary Lipschitz continuous surface are examined firstly. Filippov＇s differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system with SMC. Compared with Filippov＇s criteria for only smooth surface, new criteria are proposed by utilizing the cone conditions that allow the surface to be nonsmooth. This result also yields a new approaching condition of SMC design. Based on the new approaching condition, we develop the sliding mode controller for a class of nonlinear single-input single-output （SISO） systems, of which the switching surface is designed Lips- chitz continuous for the nonsmooth sliding motion. Finally, we provide a numerical example to verify the new design method.
文摘This paper is devoted to the problem of partial asymptotic null-controllability of control sys-tems governed by ordinary differential equations,subjected to possibly mixed state-input con-straints.Using Lyapunov functions within the framework of viability theory,feedback controls are designed in such a way a part of system’s state can be driven to the origin asymptotically,taking into account the mixed constraints.By using Michael selection theorem,the existence of such controls is proved,in the case of convex constraints,and their expressions are given as continu-ous selections of an appropriate constructed multifunction.Finally,two examples are processed numerically in order to illustrate the theoretical results.
