Adaptive control of uncertain nonlinear systems with quantized input signal

This paper proposes new adaptive controllers for uncertain nonlinear systems in the presence of input quantization. The control signal is quantized by a class of sector-bounded quantizers including the uniform quantizer, the logarithmic quantizer and the hysteresis quantizer. To clearly illustrate our approaches, we will start with a class of single-loop nonlinear systems and then extend the results to multi-loop interconnected nonlinear systems. By using backstepping technique, a new adaptive control algorithm is developed by constructing a new compensation method for the effects of the input quantization. A hyperbolic tangent function is introduced in the controller with a new transformation of the control signal. When considering multi-loop interconnected systems with interactions, a totally decentralized adaptive control scheme is developed with a new compensation method incorporated for the unknown nonlinear interactions and quantization error. Each local controller, designed simply based on the model of each subsystem by using the adaptive backstepping technique, only employs local information to generate control signals. Unlike some existing control schemes for systems with input quantization, the developed controllers do not require the global Lipschitz condition for the nonlinear functions and also the quantization parameters can be unknown. Besides showing global stability, tracking error performance is also established and can be adjusted by tuning certain design parameters. Simulation results illustrate the effectiveness of our proposed schemes.