Adaptive Backstepping Control of Nonlinear Uncertain Systems With Quantized States

• Published in: IEEE transactions on automatic control Vol. 64; no. 11; pp. 4756 - 4763
• Main Authors: Zhou, Jing, Wen, Changyun, Wang, Wei, Yang, Fan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithms; Adaptive control; Backstepping; bounded quantizer; Computer simulation; Control algorithms; Control theory; Design parameters; Hysteresis; Measurement; Nonlinear control; Nonlinear systems; Quantization (signal); Stability analysis; state quantization; Uncertain systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2019.2906931

This paper investigates the stabilization problem for uncertain nonlinear systems with quantized states. All states in the system are quantized by a static bounded quantizer, including uniform quantizer, hysteresis-uniform quantizer, and logarithmic-uniform quantizer as examples. An adaptive backstepping-based control algorithm, which can handle discontinuity, resulted from the state quantization and a new approach to stability analysis are developed by constructing a new compensation scheme for the effects of the state quantization. Besides showing the global ultimate boundedness of the system, the stabilization error performance is also established and can be improved by appropriately adjusting design parameters. Simulation results illustrate the effectiveness of our proposed scheme.