Controller design for nonlinear systems subject to both input saturation and asymmetry time‐varying state constraints: A novel network‐based approach

• Published in: International journal of adaptive control and signal processing Vol. 36; no. 12; pp. 3124 - 3141
• Main Authors: Li, Na, Zhu, Shan‐Liang, He, Wen‐Jing, Han, Yu‐Qun
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.12.2022
• Subjects: Adaptive control; Asymmetry; Continuity (mathematics); Control systems design; input saturation; Liapunov functions; multi‐dimensional Taylor network; Nonlinear systems; Saturation; state constraints; State variable; Tracking control
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3503

Summary In this article, the issues of asymmetric input saturation and asymmetric time‐varying state constraints are integrated into nonlinear systems for the first time, and a new adaptive tracking control strategy is proposed based on the multi‐dimensional Taylor network (MTN) method. Firstly, by introducing a continuous auxiliary function, the input saturation is transformed into a smooth model with bounded error. Secondly, MTNs are employed to estimate nonlinear functions, asymmetric barrier Lyapunov functions (ABLFs) are constructed to make all state variables meet asymmetric constraints, and then a novel control scheme with simple structure is developed via backstepping. Thirdly, according to the Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are bounded, and all state variables do not violate the constraints. Finally, three examples show the effectiveness of the proposed scheme.