Barrier Lyapunov Functions for the control of output-constrained nonlinear systems

Automatica ◽  
2009 ◽  
Vol 45 (4) ◽  
pp. 918-927 ◽  
Author(s):  
Keng Peng Tee ◽  
Shuzhi Sam Ge ◽  
Eng Hock Tay
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Constrained Nonlinear Systems ◽  
Barrier Lyapunov Functions

scholarly journals Stability for a Class of State Constrained Impulsive Nonlinear Systems: Barrier Lyapunov Functions Method

2021 ◽  
Author(s):  
Liangliang Li ◽  
Zhengwen Tu ◽  
Guanghui Zhou
Keyword(s):  
Nonlinear Systems ◽  
Hybrid Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Inductive Method ◽  
Linear Matrix ◽  
Ellipsoid Method ◽  
Lyapunov Functions Method ◽  
Barrier Lyapunov Functions

Abstract This paper studies the problem for a class of state constrained impulsive nonlinear systems. Firstly, we establish two sufficient conditions for the stability of invariant sets of state constrained hybrid systems. Secondly, we construct the symmetric and asymmetric barrier Lyapunov functions, respectively. A feedback method is presented to solve the stabilization problem of constrained hybrid systems. Introduce the auxiliary matrix, combining with inductive method and linear matrix inequality theory, some sufficient conditions are obtained to ensure stability for state constrained hybrid dynamical networks by the attractive ellipsoid method approach. Finally, one example with simulations is given to validate the effectiveness of the proposed criteria.

Robust state-constrained control design for nonlinear systems with uncertainties using a new barrier Lyapunov function

2017 ◽  
Vol 40 (12) ◽  
pp. 3489-3497 ◽  
Author(s):  
Jianguo Guo ◽  
Zhenxin Feng ◽  
Jun Zhou
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Control Algorithm ◽  
Closed Loop ◽  
Constrained Control ◽  
Time Varying ◽  
Initial State ◽  
External Disturbances ◽  
Attitude Tracking ◽  
Barrier Lyapunov Functions

In this paper, a robust state-constrained control algorithm is proposed by introducing time-varying barrier Lyapunov functions (BLF) for nonlinear systems with uncertainties. Novel time-varying symmetric/asymmetric forms of error barrier functions are investigated in order to relax the requirements of the initial state compared with existing BLF-based literatures. By integrating the proposed time-varying BLF method with the backstepping technique, constraint satisfaction is achieved and signals in closed-loop are uniform asymptotically stable. In addition, the extended state observer technique is utilized to prevent the constraint violation during the transient phase and strengthen the robustness of the control system in the presence of uncertainties. Numerical simulations are implemented to illustrate the attitude tracking performance obtained from the proposed method for a homing missile with angle of attack constraint, parametric uncertainties and external disturbances.

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.

Sign in / Sign up

Export Citation Format

Share Document