This paper investigates the asymptotical stabilization of Hamiltonian control systems with time delay. First, Hamiltonian control systems with time delay are proposed. Second, a two-to-one （TTO） principle is introdu...This paper investigates the asymptotical stabilization of Hamiltonian control systems with time delay. First, Hamiltonian control systems with time delay are proposed. Second, a two-to-one （TTO） principle is introduced that two different Hamiltonian functions are simultaneously energy-shaping by one desired energy function. Third, a novel matching equation is built via the TTO principle for the Hamiltonian control systems with time delay, which generates an effective control law for the Hamiltonian control systems with time delay. Finally, a numerical example shows the effectiveness of proposed method.展开更多
The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case. We first extend symplectic group to a general N- group, GN, and prove that it has...The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case. We first extend symplectic group to a general N- group, GN, and prove that it has certain similar properties. A particular property of GN is that as a Lie group dim (GN)≥1. Certain properties of its Lie-algebra 9N are investigated. The results obtained are used to investigate the structure-preserving systems, which generalize the property of symplectic form preserving of Hamiltonian system to a covariant tensor field preserving of certain dynamic systems. The results provide a theoretical benchmark of applying symplectic algorithm to a considerably larger class of structure-preserving systems.展开更多
基金supported by the National Science Fund for Distinguished Youth Scholars of China (No. 61125301)
文摘This paper investigates the asymptotical stabilization of Hamiltonian control systems with time delay. First, Hamiltonian control systems with time delay are proposed. Second, a two-to-one （TTO） principle is introduced that two different Hamiltonian functions are simultaneously energy-shaping by one desired energy function. Third, a novel matching equation is built via the TTO principle for the Hamiltonian control systems with time delay, which generates an effective control law for the Hamiltonian control systems with time delay. Finally, a numerical example shows the effectiveness of proposed method.
基金National Natural Science Foundation of China (No.G59837270, G1998020308) and the National Key Project of China.
文摘The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case. We first extend symplectic group to a general N- group, GN, and prove that it has certain similar properties. A particular property of GN is that as a Lie group dim (GN)≥1. Certain properties of its Lie-algebra 9N are investigated. The results obtained are used to investigate the structure-preserving systems, which generalize the property of symplectic form preserving of Hamiltonian system to a covariant tensor field preserving of certain dynamic systems. The results provide a theoretical benchmark of applying symplectic algorithm to a considerably larger class of structure-preserving systems.
