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A robot system composed of two-link arm and three-joint is considered in this paper. An evolution equation corresponding to the robot system formulated by partial differential equations with initial and boundary conditions is established in an appropriate Hilbert space. The spectral properties of the main operator of the evolution equation is first discussed, and then its semigroup generation is presented based on the resulting spectral properties of. Finally, an asymptotical behavior of the robot system under a designed feedback control is shown in terms of semigroup approach. [Copyright &y& Elsevier]

A feedback control is designed for a torsional elastic robot arm to be exponentially stable and to arrive at any designated position. An eigenvalue problem is discussed, and a finite-dimensional approximation theorem is proposed and proved. Based on the numerical analysis and the approximation theorem we can simulate the system and show that the bending vibration, the torsional vibration, the rigid turning angle, and the bending moment of the robot arm can be controlled in a short period of time. [Copyright &y& Elsevier]

Abstract: In this paper, the application of penalty shifting method to the calculation of optimal linewise control of the dam-detouring osmotic system for concrete dams with heterogemous is studied. The approximation program is structured, and the convergence of the method on appropriate Hilbert spaces is proved. [Copyright &y& Elsevier]