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Smooth, time‐invariant regulation of nonholonomic systems via energy pumping‐and‐damping

Abstract : In this article we propose an energy pumping-and-damping technique to regulate nonholonomic systems described by kinematic models. The controller design follows the widely popular interconnection and damping assignment passivity-based methodology, with the free matrices partially structured. Two asymptotic regulation objectives are considered: drive to zero the state or drive the systems total energy to a desired constant value. In both cases, the control laws are smooth, time-invariant, state-feedbacks. For the nonholonomic integrator we give an almost global solution for both problems, with the objectives ensured for all system initial conditions starting outside a set that has zero Lebesgue measure and is nowhere dense. For the general case of higher order nonholonomic systems in chained form, a local convergence result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-03387947
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Submitted on : Wednesday, October 20, 2021 - 10:14:22 AM
Last modification on : Tuesday, January 4, 2022 - 5:47:59 AM

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Bowen Yi, Romeo Ortega, Weidong Zhang. Smooth, time‐invariant regulation of nonholonomic systems via energy pumping‐and‐damping. International Journal of Robust and Nonlinear Control, Wiley, 2020, 30 (16), pp.6399-6413. ⟨10.1002/rnc.5109⟩. ⟨hal-03387947⟩

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