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Stabilization and tracking control for an extended Heisenberg system with a drift. (English) Zbl 1129.93457

Summary: We present sliding mode control algorithms, that are designed to practically stabilize (which means that the system state is stabilized to an \(\varepsilon\) neighborhood of the origin) the perturbed multidimensional Heisenberg system (therefore, with a drift) with additional two multidimensional integrators in the control inputs path. This result is then used to solve a tracking problem for the class of system which unperturbed model fails Brockett’s necessary condition for the existence of a continuous, time independent feedback law.

MSC:

93C85 Automated systems (robots, etc.) in control theory
70F25 Nonholonomic systems related to the dynamics of a system of particles
70Q05 Control of mechanical systems
93B12 Variable structure systems
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