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Adaptive stabilization of uncertain nonholonomic systems by state and output feedback. (English) Zbl 1038.93079

This paper addresses constructive adaptive state feedback control strategies for stabilizing a class of uncertain non-holonomic chained systems without imposing any restrictions on the system order or the growth of drift nonlinearities. Control laws are developed that use state scaling and backstepping. An innovative adaptive switching approach is proposed to prevent possible escape to infinity in finite time of system states and to guarantee boundedness of all signals in the system. A nonlinear observer-based output feedback design is proposed when only partial system states are measurable. A filtered observer rather than the customary linear observer is used to handle technical problems associated with the presence of unavailable states in the regressor matrix. The authors prove that all system states converge globally to the origin and that the estimated parameters remain bounded. Simulation results with a bilinear model of a mobile robot demonstrate the effectiveness of the authors’ approach.

MSC:

93D21 Adaptive or robust stabilization
70F25 Nonholonomic systems related to the dynamics of a system of particles
93C85 Automated systems (robots, etc.) in control theory
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