Robust adaptive stabilization of nonlinear systems with mismatched time delays. (September 2021) - Zhang, Zhengqiang; Li, Wenjie; Ge, Shuzhi Sam; Shang, Yuqi
Abstract: For a class of nonlinear systems with mismatched time delays and disturbances, robust adaptive stabilization control is studied. The control law is split into two terms. One is used to cope with the delayed states, and the other is to handle the disturbance. The improved robust adaptive laws with control gain function and time-varying σ -modification are constructed to estimate the unknown integrated parameters. It is proved that the designed adaptive controller can ensure the asymptotic convergence of the closed-loop system states. Another adaptive algorithm is also proposed to ensure the asymptotic stability of the closed delayed nonlinear system without external disturbance. Highlights: We introduce control gain function ρ ( ⋅ ) and embed it into the Lyapunov–'Krasovskii functional. Continuous memoryless control functions are designed. The theoretical result is applied to chemical reactor.