CAJ | 학술논문

研究一个带有时滞机器人模型解的性质,其中机器人的动力学行为由一组含有时滞的微分方程描述.通过引入Hilbert状态空间将其写成一个发展方程,利用半群理论得到抽象发展方程的适定性.通过对系统算子的谱作细致分析,得到谱的渐近表达式,并证明系统的本征函数并不构成空间的基.但我们证明了对时间大于5倍时滞时,方程的解按照本征向量的展开式.
연구일개대유시체궤기인모형해적성질,기중궤기인적동역학행위유일조함유시체적미분방정묘술.통과인입Hilbert상태공간장기사성일개발전방정,이용반군이론득도추상발전방정적괄정성.통과대계통산자적보작세치분석,득도보적점근표체식,병증명계통적본정함수병불구성공간적기.단아문증명료대시간대우5배시체시,방정적해안조본정향량적전개식.
This paper is devoted to research of solution properties of a robot model with time delay, which is described by a retarded functional differential equations. At first the equations are transformed into an evolutionary equation in the Hilbert state space, and the well-posed-hess of the system is obtained by using the theory of C_0 semigroup. Then, by a detail spectral analysis, the asymptotic expression of all eigenvalues of the system operator is given, and it is shown that the eigenfunctions of the system operator fail to form a Schauder basis for the state space. However, it is proven that the solution of system can be explicitly expressed via its eigenvectors when t>5τ, where τ is the delay time.