Observer-based adaptive fuzzy quantized control of uncertain nonlinear systems with unknown control directions

Abstract

This paper studies the output-feedback tracking control problem for a class of strict-feedback systems with input quantization and unknown control directions. A coordinate transformation is first introduced such that the unknown control coefficients are lumped together and the studied system is transformed into an equivalent system. Subsequently, a high-gain fuzzy state observer is designed to estimate unmeasurable states. Based on the high-gain fuzzy state observer, the adaptive backstepping design procedure is proposed for the new defined system. Then, by introducing a Nussbaum function and a smooth function, the obstacle caused by unknown control direction and input quantization is successfully circumvented, and a coarse quantization can be achieved. Moreover, the proposed adaptive controller can guarantee that the closed-loop system is bounded, and the tracking error converge to a predefined small residue set. The main advantages of our method are that: first, the restrictions on system control gains are relaxed. Second, the controller design does not depend on the quantization parameter. Finally, simulation results are provided to illustrate the effectiveness and benefits of the proposed results.