From conservation to openess. -- Theory and applications of generalized controlled Hamiltonian systems (Q2708022)

The paper intends to treat classical Hamiltonian systems, Poisson bracket and symplectic geometry from the energy point of view and extends them to generalized Hamiltonian systems, which have internal dissipation and energy exchange with the environment. The authors propose the pseudo-Poisson manfold and the generalized symplectic manifold as the geometric frame of the generalized Hamiltonian control systems, and propose the generalized symplectic group and symplectic algebra as the algebraic structure of the generalized Hamiltonian systems. They obtain some important results that can provide a foundation for further investigation. As an example, the results are applied to the excitation control of power systems.