Computation of Lyapunov functions for smooth nonlinear systems using convex optimization

10.1016/s0005-1098(00)00088-1 ◽

2000 ◽

Vol 36 (11) ◽

pp. 1617-1626 ◽

Author(s):

Tor A. Johansen

Keyword(s):

Nonlinear Systems ◽

Convex Optimization ◽

Lyapunov Functions

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Synthesis of variable gain controllers for a class of uncertain nonlinear systems via piecewise Lyapunov functions

2009 European Control Conference (ECC) ◽

10.23919/ecc.2009.7074555 ◽

2009 ◽

Author(s):

Hidetoshi Oya ◽

Kojiro Hagino

Keyword(s):

Nonlinear Systems ◽

Lyapunov Functions ◽

Uncertain Nonlinear Systems ◽

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Model reduction of a class of nonlinear systems: a convex-optimization approach

IMA Journal of Mathematical Control and Information ◽

10.1093/imamci/dnt023 ◽

2013 ◽

Vol 31 (4) ◽

pp. 519-531 ◽

Author(s):

S. Ibrir ◽

M. Bettayeb

Keyword(s):

Nonlinear Systems ◽

Convex Optimization ◽

Model Reduction ◽

Optimization Approach

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Stability analysis of discontinuous nonlinear systems via piecewise linear Lyapunov functions

Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148) ◽

10.1109/acc.2001.945751 ◽

2001 ◽

Author(s):

Y. Ohta ◽

T. Wada ◽

D.D. Siljak

Keyword(s):

Stability Analysis ◽

Nonlinear Systems ◽

Lyapunov Functions ◽

Piecewise Linear ◽

Linear Lyapunov Functions

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Economic MPC of nonlinear systems with nonmonotonic Lyapunov functions and its application to HVAC control

International Journal of Robust and Nonlinear Control ◽

10.1002/rnc.4033 ◽

2018 ◽

Vol 28 (6) ◽

pp. 2513-2527 ◽

Author(s):

Zheming Wang ◽

Guoqiang Hu

Keyword(s):

Nonlinear Systems ◽

Lyapunov Functions ◽

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Design of a Controller of Switched Nonlinear Systems Based on Multiple Lyapunov Functions

Advances and Applications in Nonlinear Control Systems - Studies in Computational Intelligence ◽

10.1007/978-3-319-30169-3_27 ◽

2016 ◽

pp. 611-626

Author(s):

Khalil Jouili ◽

Arwa Abdelkarim ◽

Naceur Benhadj Braiek

Keyword(s):

Nonlinear Systems ◽

Lyapunov Functions ◽

Switched Nonlinear Systems ◽

Multiple Lyapunov Functions

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Fuzzy-Model-Based Output Feedback Controller Design for Discrete-Time Non-Affine Nonlinear Systems via Piecewise Lyapunov Functions

2018 Eighth International Conference on Information Science and Technology (ICIST) ◽

10.1109/icist.2018.8426064 ◽

2018 ◽

Author(s):

Wenqiang Ji ◽

Meng Wang ◽

Jianbin Qiu

Keyword(s):

Nonlinear Systems ◽

Discrete Time ◽

Output Feedback ◽

Lyapunov Functions ◽

Controller Design ◽

Fuzzy Model ◽

Feedback Controller ◽

Output Feedback Controller ◽

Model Based ◽

Affine Nonlinear Systems

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Reduced-order observers for nonlinear systems via contraction analysis and convex optimization

2021 American Control Conference (ACC) ◽

10.23919/acc50511.2021.9483279 ◽

2021 ◽

Author(s):

Bowen Yi ◽

Ruigang Wang ◽

Ian R. Manchester

Keyword(s):

Nonlinear Systems ◽

Convex Optimization ◽

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Lin-Sontag and common Lyapunov functions for stabilising control of a switched nonlinear systems

International Journal of Industrial and Systems Engineering ◽

10.1504/ijise.2018.095529 ◽

2018 ◽

Vol 30 (3) ◽

pp. 316

Author(s):

Abdessamad Abdelhedi ◽

Wided Saadi ◽

Driss Boutat ◽

Lassaad Sbita

Keyword(s):

Nonlinear Systems ◽

Lyapunov Functions ◽

Switched Nonlinear Systems ◽

Common Lyapunov Functions

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Stability Analysis for A Class of Nonlinear Systems via State-dependent Lyapunov Functions

2019 Chinese Control Conference (CCC) ◽

10.23919/chicc.2019.8865504 ◽

2019 ◽

Author(s):

JianLiang Chen ◽

XiaoHui Chen ◽

Yong-Yan Cao

Keyword(s):

Stability Analysis ◽

Nonlinear Systems ◽

Lyapunov Functions ◽

State Dependent

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Extended Finite Time Inverse Optimal Control of Nonlinear Systems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.403-408.1499 ◽

2011 ◽

Vol 403-408 ◽

pp. 1499-1502

Author(s):

Xin Jun Ren ◽

Yan Jun Shen

Keyword(s):

Optimal Control ◽

Nonlinear Systems ◽

Finite Time ◽

Lyapunov Functions ◽

Control Law ◽

Inverse Optimal Control ◽

Closed Loop System ◽

Affine Nonlinear Systems ◽

Definition Of ◽

In this paper, we use the definition of control Lyapunov functions to study finite time inverse optimal control for affine nonlinear systems. Based on control Lyapunov functions, a finite time universal control formula is presented, which can ensure the closed-loop system is finite time stable. From this, less conservative conditions for the finite time inverse optimal control are derived. We design a finite time inverse optimal control law, which minimizes the cost functional. A numerical example verifies the validity of the proposed method.

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