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Nonlinear feedback, double bracket dissipation and port control of Lie-Poisson systems (2307.09235v1)
Published 18 Jul 2023 in math-ph, math.MP, and math.OC
Abstract: Methods from controlled Lagrangians, double bracket dissipation and interconnection and damping assignment -- passivity based control (IDA-PBC) are used to construct nonlinear feedback controls which (asymptotically) stabilize previously unstable equilibria of Lie-Poisson Hamiltonian systems. The results are applied to find an asymptotically stabilizing control for the rotor driven satellite, and a stabilizing control for Hall magnetohydrodynamic flow.