Observed-based adaptive fuzzy control for robotic manipulators  with output and input  quantization

The most existing control studies of robotic manipulators are restricted to nonlinear systems without quantized signals. To eliminate this restriction, for a class of robotic systems with output and input quantization, a novel observer-based adaptive fuzzy control scheme is raised in this paper. In view of the quantized output and input signals, a novel quantized state observer with n-dimensional states is devised to evaluate the unmeasurable states. In the backstepping process, the incorporation of quantized output signals leads to discontinuity in the virtual controllers. To avoid this problem, the solution is divided into three steps: First of all, auxiliary intermediate controllers are designed using the command-filtered backstepping technique. Secondly, by substituting quantized states for unquantized ones in the auxiliary intermediate controllers, the actual torque controller is derived. Thirdly, Lemma 5 is presented to deal with the effects of quantization errors. Furthermore, the stability of robot systems with n-dimensional states can be ensured.