Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems

Automatica ◽  
2017 ◽  
Vol 76 ◽  
pp. 143-152 ◽  
Author(s):  
Yan-Jun Liu ◽  
Shaocheng Tong
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Full State ◽  
Constrained Nonlinear Systems ◽  
Barrier Lyapunov Functions

Semi-Global Adaptive Control Using Barrier Lyapunov Functions for a Class of Uncertain Nonlinear Systems

2012 ◽  
Vol 190-191 ◽  
pp. 1053-1056
Author(s):  
Peng Nian Chen ◽  
Ling Ling Sun
Keyword(s):  
Neural Networks ◽  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Closed Loop ◽  
Control Method ◽  
Uncertain Nonlinear Systems ◽  
Closed Loop System ◽  
Periodic Disturbances ◽  
Barrier Lyapunov Functions

This paper deals with the problem of adaptive control for a class of nonlinear systems. The system considered in the paper contains non-parameterized uncertainties and periodic disturbances. A semi-global adaptive control method is proposed using the barrier Lyapunov functions. The method does not need to assume that the solution of the closed loop system remains in the domain of approximation by neural networks and guarantees that the solution of the system converges to zero.

Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

2021 ◽  
pp. 014233122098563
Author(s):  
Fei Shen ◽  
Xinjun Wang ◽  
Xinghui Yin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Dead Zone ◽  
Small Neighborhood ◽  
Unmodeled Dynamics ◽  
Stochastic Nonlinear Systems ◽  
Dynamic Surface ◽  
Barrier Lyapunov Function ◽  
Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

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