Variable structure control of continuous time systems involving non-smooth nonlinearities.

摘要

When the control system falls in a class obeying non-Lipschitzian (or "non-smooth") dynamics, the conventional nonlinear theory cannot be readily applied. Non-smooth nonlinearities are input-output mappings of the form ;The characterization of a given nonlinearity as a member of this class primarily serves for two purposes: (i) Analysis of the closed loop system behavior and identification of stiction and limit cycles, (ii) Development of robust control methodologies to deter system trajectories getting stuck at the "system induced" stiction manifolds. Also studied within the characterization framework are the invertibility issues associated with the non-smooth nonlinearities by pre- and post-processing the nonlinearity input and output.;Based on this characterization, a rigorous definition of "stiction in an open region" in ;Two special but rather common cases corresponding to a linear system accompanied by a non-smooth nonlinearity at its input or output channel are considered separately and global boundedness, stabilizability to origin, non-zero set point regulation and arbitrary reference tracking topics are investigated when discontinuous controllers are employed. Advantages of full-state feedback and robust observer design issues to overcome difficulties introduced into control due to the existence of non-smooth nonlinearities are addressed and the benefits of not having to identify the actual nonlinearity to achieve robust performance within the framework of sliding mode controllers are clarified.