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Uniform topology onEQ-algebras

Jiang YangXiao Long XinPeng Fei He — 2017

Open Mathematics

In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.

Nonlinear dynamic systems and optimal control problems on time scales

Yunfei PengXiaoling XiangYang Jiang — 2011

ESAIM: Control, Optimisation and Calculus of Variations

This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing -strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration...

Nonlinear dynamic systems and optimal control problems on time scales

Yunfei PengXiaoling XiangYang Jiang — 2011

ESAIM: Control, Optimisation and Calculus of Variations

This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear dynamic systems on time scales. Introducing the reasonable weak solution of nonlinear dynamic systems, the existence of the weak solution for the nonlinear dynamic systems on time scales and its properties are presented. Discussing -strong-weak lower semicontinuity of integral functional, we give sufficient conditions for the existence of optimal controls. Using integration...

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