Multiple‐model adaptive robust dynamic surface control with estimator resetting

Abstract

A multiple-model adaptive robust dynamic surface control with estimator resetting is investigated for a class of semi-strict feedback nonlinear systems in this paper. The transient performance is mainly considered. The multiple models are composed of fixed models, one adaptive model, and one identification model that can be obtained when the persistent exciting condition is satisfied. The transient performance of the final tracking system can be improved significantly by designing proper switching mechanism during the parameter tuning procedure. The semi-globally uniformly ultimately bounded stability of the closed-loop system can be easily achieved because of the framework of adaptive robust dynamic surface control. Numerical examples are provided to demonstrate the effectiveness of the proposed multiple-model controller.Noting Equation (14), the nonlinear uncertainty d.x; t/ is unknown. The signal is generated by the following dynamic equation in implementation: P 0 D k.t/ 0 ; 0 .0/ D x.0/ ! 0 .0/ ! T .0/Â

Multiple model adaptive control for switched linear systems: A two‐layer switching strategy

“…The controller of the closest identification model is connected to the plant or the estimation parameter of the closest identification model is reset to the estimator. Extensive simulations and practical applications have also confirmed that MMAC is a feasible method to improve the transient behavior . Specially, in the works of Narendra and Balakrishnan and Narendra and Xiang, MMAC was applied to general linear systems in both continuous‐time and discrete‐time cases, where the identification models are composed of fixed models, adaptive models, and their different combinations.…”

Adaptive dynamic surface asymptotic tracking for a class of uncertain nonlinear systems

“…Assumptions 1 and 2 are standard conditions required in many adaptive state feedback DSC schemes, which can be commonly found in the existing literature. [14][15][16][17][18][19][20][21][22][23]60…”

“…In the work of Chen et al, an adaptive robust DSC with composite adaptation laws was designed for uncertain nonlinear systems in semistrict‐feedback form, where the persistent excitation (PE) condition has to be satisfied to ensure the convergence of parameter estimates. Furthermore, result based on multiple models and switching was exploited to improve the transient response of a adaptive DSC system, but the PE condition still exists. With the help of the composite learning, an adaptive DSC scheme was proposed to guarantee parameter convergence without the PE condition .…”

Transient performance improvement in indirect model reference adaptive control using perturbation‐based extremum seeking identifier

“…whereẑ ¼ s n Λ p s ð Þŷ p and the other parameters are the same as in Equation 10. We define the x I ≜y p −ŷ p as the estimation error, and then we normalize it as…”

“…6,7 There is a great deal of efforts to handle this imperfection of MRAC. High order tuning, 8 multiple model adaptive control, 9,10 resetting control, 11,12 adaptive control with closed-loop reference model, 13,14 adaptive dual control, 15,16 L 1 adaptive control, 17 combined or composite direct and indirect MRAC, 18,19 and H ∞ optimal method 6 are various methods that have been used to improve the transient response of MRAC. The aim of all mentioned methods is improving transient performance of adaptive systems besides maintaining ideal asymptotic properties.…”