Improved Adaptive Fuzzy Control for Non-Strict Feedback Nonlinear Systems: a Dynamic Compensation System Approach

Highlights：

• By designing the inducible factor (IF), an improved BLF method is proposed. Compared with the traditional BLF, the improved BLF does not depend on the initial value of the system state. It is worth noting that the novel IF design is based on the variant Sigmoid function, which makes the adjustment of the improved BLF more flexible and intuitive.

• Based on the proposed new control framework, the DO design method is improved. The integration of DCS states into the DO design can cleverly avoid the coupling problem of disturbances and unknown nonlinear functions in the NSFS.

• By combining the DCS, the improved BLF and the DO, a novel adaptive fuzzy tracking control law is constructed, and all the signals in the closed-loop system are proved to be semiglobally uniformly ultimately bounded.

摘要

•An improved state-feedback control framework based on the dynamic compensation system (DCS) is proposed. Different from the traditional backstepping method, the estimated signal based on the adaptive fuzzy system is indirectly introduced into the virtual and actual control laws through the DCS, which has the advantage of avoiding the algebraic-loop problem in the non-strict feedback system control. Compared with the existing methods, the proposed design framework not only greatly simplifies the control law design, but also reduces the constraint on unknown functions. The significance of this framework is that it unifies the control law design of strict feedback systems and nonlinear non-strict feedback systems (NSFSs).•By designing the inducible factor (IF), an improved BLF method is proposed. Compared with the traditional BLF, the improved BLF does not depend on the initial value of the system state. It is worth noting that the novel IF design is based on the variant Sigmoid function, which makes the adjustment of the improved BLF more flexible and intuitive.•Based on the proposed new control framework, the DO design method is improved. The integration of DCS states into the DO design can cleverly avoid the coupling problem of disturbances and unknown nonlinear functions in the NSFS.•By combining the DCS, the improved BLF and the DO, a novel adaptive fuzzy tracking control law is constructed, and all the signals in the closed-loop system are proved to be semiglobally uniformly ultimately bounded.