Generalized Hamiltonian systems (Q2758324)

Generalized Hamiltonian (or pseudo-Hamiltonian) systems in the text differ from classical Hamiltonian systems in having external forces (controls) that control the system through the derivative of the adjoint vector. NEWLINENEWLINENEWLINEThe paper starts with a brief introduction to Hamiltonian mechanics, presenting concepts like symplectic manifolds, Poisson manifolds and Hamiltonian fields. Pseudo-Poisson and \(\omega\)-manifolds are presented, being generalizations of Poisson and symplectic manifolds, respectively. The \(N\)-group is a Lie subgroup of \(\text{GL}(n,\mathbb{R})\). Together with its algebra it plays a role analogous to that of the symplectic group and its algebra in classical Hamiltonian systems. Conditions for structure invariance under pseudo-Hamiltonian flows are presented. As an example, application to stabilization of an excitation control system is discussed. In the final section, stabilization and \(H_{\infty } \) control for dissipative Hamiltonian systems are discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00022].