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Smooth, time‐invariant regulation of nonholonomic systems via energy pumping‐and‐damping
Author(s) -
Yi Bowen,
Ortega Romeo,
Zhang Weidong
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5109
Subject(s) - control theory (sociology) , passivity , nonholonomic system , integrator , lebesgue measure , interconnection , kinematics , controller (irrigation) , mathematics , computer science , lebesgue integration , engineering , physics , mathematical analysis , control (management) , classical mechanics , robot , mobile robot , computer network , agronomy , electrical engineering , bandwidth (computing) , artificial intelligence , biology
Summary 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.