Discrete-Time Adaptive Controller for Unfixed and Unknown Control Direction

An adaptive controller is proposed for unknown nonlinear discrete-time systems when the control direction is unknown and unfixed. Two fuzzy rules emulated networks are utilized to establish a system dynamic model which provides the control-gain and the control direction. The control law is developed according to the control direction including the following advantages: first, the relation between input and output of controlled plant cannot be generally Lipschitz with the zero-change of control effort; and second, the control direction is unfixed for both positive and negative values. Theoretical expressions are manifested to guarantee the convergence of model and tracking performance. The practical-validation is conducted by two experimental systems: first, dc motor current control for the case of fixed control direction and Lipschitz condition, and second, robotic system with opened architecture for the case of unfixed control direction and non-Lipschitz condition at constant input.