Lyapunov function computation for nonlinear systems through dynamical embedding – A case study*

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.

Download Full-text

Control of nonlinear systems with full state constraint using a Barrier Lyapunov Function

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference ◽

10.1109/cdc.2009.5400484 ◽

2009 ◽

Cited By ~ 35

Author(s):

Keng Peng Tee ◽

Shuzhi Sam Ge

Keyword(s):

Nonlinear Systems ◽

Lyapunov Function ◽

State Constraint ◽

Barrier Lyapunov Function ◽

Full State

Download Full-text

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

Journal of Vibration and Control ◽

10.1177/1077546320985980 ◽

2021 ◽

pp. 107754632098598

Author(s):

Marwen Kermani ◽

Anis Sakly

Keyword(s):

Nonlinear Systems ◽

Lyapunov Function ◽

Feedback Stabilization ◽

State Feedback Control ◽

Multiple Time ◽

Time Varying ◽

Switched Nonlinear Systems ◽

Common Lyapunov Function ◽

Suggested Approach ◽

Aggregation Techniques

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

Download Full-text

Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Symmetry ◽

10.3390/sym13050854 ◽

2021 ◽

Vol 13 (5) ◽

pp. 854

Author(s):

Raquel S. Rodríguez ◽

Gilberto Gonzalez Avalos ◽

Noe Barrera Gallegos ◽

Gerardo Ayala-Jaimes ◽

Aaron Padilla Garcia

Keyword(s):

Nonlinear System ◽

Nonlinear Systems ◽

Nonlinear Dynamic ◽

Bond Graph ◽

Physical Domain ◽

Graph Models ◽

Simple Task ◽

Analysis And Synthesis ◽

Simulation Results

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

Download Full-text