Barrier Lyapunov function-based adaptive asymptotic tracking of nonlinear systems with unknown virtual control coefficients

Automatica ◽  
2020 ◽  
Vol 121 ◽  
pp. 109181
Author(s):  
Yuan-Xin Li
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Barrier Lyapunov Function ◽  
Virtual Control ◽  
Asymptotic Tracking ◽  
Control Coefficients

Tracking Control for Switched Nonlinear Systems Subject to Time-Varying Output Constraints

2012 ◽  
Author(s):  
Ben Niu ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Tracking Control ◽  
Closed Loop ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Feedback Form ◽  
Barrier Lyapunov Function ◽  
Output Constraints ◽  
Asymptotic Tracking

In this paper, we address the tracking control problem for switched nonlinear systems in strict-feedback form with time-varying output constraints. To prevent the output from violating the time-varying constraints, we employ a Barrier Lyapunov Function, which relies explicitly on time. Based on the simultaneous domination assumption, we design a controller for the switched system, which guarantees that asymptotic tracking is achieved without transgression of the constraints and all closed-loop signals remain bounded under arbitrary switchings. The effectiveness of the proposed results is illustrated using a numerical example.

scholarly journals Decentralized Control for Large-Scale Interconnected Nonlinear Systems Based on Barrier Lyapunov Function

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Tao Guo
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Tracking Control ◽  
Large Scale ◽  
Closed Loop ◽  
Barrier Lyapunov Function ◽  
Control Scheme ◽  
Asymptotic Tracking ◽  
Interconnected Nonlinear Systems ◽  
First Time

We present a novel decentralized tracking control scheme for a class of large-scale nonlinear systems with partial state constraints. For the first time, backstepping design with the newly proposed BLF is incorporated to effectively deal with the control problem of nonlinear systems with interconnected constraints. To prevent the states of each subsystem from violating the constraints, we employ a special barrier Lyapunov function (BLF), which grows to infinity whenever its argument approaches some finite limits. By ensuring boundedness of the barrier Lyapunov function in the closed loop, we ensure that those limits are not transgressed. Asymptotic tracking is achieved without violation of the constraints, and all closed-loop signals remain bounded. In the end, an illustrative example is presented to demonstrate the performance of the proposed control.

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.

Finite-Time-Disturbance-Observer-Based Tracking Control of DC Motors With Velocity Constraint

2015 ◽  
Author(s):  
Z. L. Dong ◽  
J. Y. Yao ◽  
Z. B. Xu ◽  
D. W. Ma
Keyword(s):  
Lyapunov Function ◽  
Finite Time ◽  
Disturbance Observer ◽  
Design Procedure ◽  
Tracking Performance ◽  
Backstepping Design ◽  
Barrier Lyapunov Function ◽  
Dc Motors ◽  
Asymptotic Tracking ◽  
Velocity Constraint

The integration design of high tracking performance and velocity constraint for dc motors is present in this paper. When designing advanced controllers for dc motors, it would be best to take the constraint of output velocity into consideration due to performance and/or physical limitations. A barrier Lyapunov function, which grows to infinity when its arguments approach some pre-set limits, is utilized to prevent constraint violation. By ensuring the stabilization of the barrier Lyapunov function, and imposing a hard-bound on associated error signals through the steps of the backstepping design procedure, the system output velocity constraint is guaranteed to be not transgressed. However, potential disturbances, including unmodelled dynamic effects, parametric uncertainties and external disturbances may destroy above theoretical results and degrade the tracking performance. In this paper, a finite time disturbance observer is employed and integrated with the barrier Lyapunov function based backstepping design to achieve the asymptotic tracking without the violation of the velocity constraint meanwhile overcoming the disturbances. Extensive simulation results are provided to illustrate the performance of the proposed control strategy.

scholarly journals Adaptive Control of a Class of Switched Nonlinear System with Partial State Constraints Using a Barrier Lyapunov Function

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Enchang Cui ◽  
Yuanwei Jing ◽  
Xiaoting Gao
Keyword(s):  
Lyapunov Function ◽  
Adaptive Controller ◽  
State Constraint ◽  
Adaptive Tracking Control ◽  
Barrier Lyapunov Function ◽  
Arbitrary Switching ◽  
Switched Nonlinear System ◽  
Asymptotic Tracking ◽  
Partial State ◽  
And Control

This paper discusses partial state constraint adaptive tracking control problem of switched nonlinear systems with uncertain parameters. In order to ensure boundedness of the outputs and prevent the states from violating the constraints, a barrier Lyapunov function (BLF) is employed. Based on backstepping method, an adaptive controller for the switched system is designed. Furthermore, the state-constrained asymptotic tracking under arbitrary switching is performed. The closed-loop signals keep bounded when the initial states and control parameters are given. Finally, examples and simulation results are reported to illustrate the effectiveness of the proposed controller.

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