Control and Stabilization of a Class of Nonlinear Systems with Symmetry

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dc.contributor.advisorKrishnaprasad, P.S.en_US
dc.contributor.authorManikonda, Vikramen_US
dc.contributor.departmentISRen_US
dc.contributor.departmentCDCSSen_US
dc.date.accessioned2007-05-23T10:06:51Z
dc.date.available2007-05-23T10:06:51Z
dc.date.issued1998en_US
dc.description.abstractThe focus of this dissertation is to study issues related to controllability and stabilization of a class of underactuated mechanical systems with symmetry. In particular we look at systems whose configuration can be identified with a Lie group and the reduced equations are of the Lie-Poisson type. Examples of such systems include hovercraft, spacecraft and autonomous underwater vehicles. We present sufficient conditions for the controllability of affine nonlinear control systems where the drift vector field is a Lie-Poisson reduced Hamiltonian vector field. In this setting we show that depending on the existence of a radially unbounded Lyapunov type function, the drift vector field of the reduced system is weakly positively Poisson stable. The weak positive Poisson stability along with the Lie algebra rank condition is used to show controllability. These controllability results are then extended to the unreduced dynamics. Sufficient conditions for controllability are presented in both cases where the symmetry group is compact and noncompact. We also present a constructive approach to design feedback laws to stabilize relative equilibria of these systems. The approach is based on the observation that, under certain hypotheses the fixed points of the Lie-Poisson dynamics belong to an immersed equilibrium submanifold. The existence of such equilibrium manifolds, along with the center manifold theory is used to design stabilizing feedback laws.en_US
dc.format.extent735495 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/6003
dc.language.isoen_USen_US
dc.relation.ispartofseriesISR; PhD 1998-2en_US
dc.relation.ispartofseriesCDCSS; PhD 1998-2en_US
dc.subjectgeometric controlen_US
dc.subjectkinematicsen_US
dc.subjectlinear systemsen_US
dc.subjectnonlinear systemsen_US
dc.subjectroboticsen_US
dc.subjectstabilityen_US
dc.subjectsystems on Lie groupsen_US
dc.subjectsymmetry en_US
dc.subjectreductionen_US
dc.subjectPoisson structuresen_US
dc.subjectunderwater vehiclesen_US
dc.subjecthovercraften_US
dc.subjectunderactuated systemsen_US
dc.subjectcontrollability in the presence of driften_US
dc.subjectIntelligent Control Systemsen_US
dc.titleControl and Stabilization of a Class of Nonlinear Systems with Symmetryen_US
dc.typeDissertationen_US

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