Adaptive quantized control for uncertain nonlinear systems with unknown control directions

Abstract

This study reports adaptive quantized control for a class of uncertain strict-feedback nonlinear systems with unknown control directions. Combining backstepping technique and Lyapunov stability theory, a systematic analysis method is designed. Based on the disintegration of the hysteresis quantizer, a Nussbaum-based scheme can be developed to get over the obstacle of the quantized input signal and unknown control directions. Moreover, the number of adaptive laws is small, thereby reducing the computational burden. Then we testify the boundedness of all signals in the closed-loop system. Besides, the tracking error can converge to an arbitrarily small domain of origin. Finally, a simulation example is provided to verify the feasibility of the control scheme.

Adaptive prescribed performance asymptotic tracking control for nonlinear systems with time‐varying parameters

“…[1][2][3][4] After decades of development, the backstepping method has gradually matured. With the combination of adaptive control and backstepping method, more and more nonlinear problems can be solved, [5][6][7][8] especially for strict-feedback nonlinear systems. The advantage of adaptive backstepping control is that the controller and the adaptive laws can be designed at the same time, which can improve the performance of the systems.…”

“…Based on the above observation, this study designs an adaptive asymptotic tracking controller for nonlinear systems with prescribed performance and time‐varying parameters. The followings are the main contributions of this study: Unlike the nonlinear systems with time‐invariant parameters in References 6 and 7, this study investigates the adaptive tracking control problem of nonlinear systems with time‐varying parameters. Inspired by the congelation of variables method in Reference 30, the adaptive laws are designed to approximate the averages of the time‐varying parameters.…”

“…Unlike the nonlinear systems with time‐invariant parameters in References 6 and 7, this study investigates the adaptive tracking control problem of nonlinear systems with time‐varying parameters. Inspired by the congelation of variables method in Reference 30, the adaptive laws are designed to approximate the averages of the time‐varying parameters.…”

Adaptive control for a class of high‐order nonlinear parameterized systems with multiple unknown control directions by switching linear controllers

“…12,13 Thus, different approaches have been proposed over the last few years. [14][15][16][17][18][19][20][21][22][23][24][25][26][27] It is well-recognized that Nussbaum-based methods require additional complexity in the control design. 28 However, these controllers are composed of nonlinear functions of system state.…”

“…Therefore, the adaptive control with unknown control directions becomes very complicated and challenging, and is an unfading research interest in the adaptive control community 12,13 . Thus, different approaches have been proposed over the last few years 14‐27 . It is well‐recognized that Nussbaum‐based methods require additional complexity in the control design 28 .…”