October  2007, 8(3): 589-611. doi: 10.3934/dcdsb.2007.8.589

A pseudospectral observer for nonlinear systems

1. 

Department of Electrical & Computer Engineering, University of Texas at San Antonio, San Antonio, TX 78249, United States

2. 

Department of Mechanical and Astronautical Engineering, Naval Postgraduate School, Monterey, CA, 93943, United States

3. 

Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943

Received  August 2006 Revised  February 2007 Published  July 2007

In this paper, we present an observer design method for nonlinear systems based on pseudospectral discretizations and a moving horizon strategy. The observer has a low computational burden, a fast convergence rate and the ability to handle measurement noise. In addition to ordinary differential equations, our observer is applicable to nonlinear systems governed by deferential-algebraic equations (DAE), which are considered very difficult to deal with by other designs such as Kalman filters. The performance of the proposed observer is demonstrated by several numerical experiments on a time-varying chaotic nonlinear system with unknown parameters and a nonlinear circuit with a singularity-induced bifurcation.
Citation: Qi Gong, I. Michael Ross, Wei Kang. A pseudospectral observer for nonlinear systems. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 589-611. doi: 10.3934/dcdsb.2007.8.589
[1]

Diène Ngom, A. Iggidir, Aboudramane Guiro, Abderrahim Ouahbi. An observer for a nonlinear age-structured model of a harvested fish population. Mathematical Biosciences & Engineering, 2008, 5 (2) : 337-354. doi: 10.3934/mbe.2008.5.337

[2]

Xinmin Xiang. The long-time behaviour for nonlinear Schrödinger equation and its rational pseudospectral approximation. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 469-488. doi: 10.3934/dcdsb.2005.5.469

[3]

Hamid Reza Marzban, Hamid Reza Tabrizidooz. Solution of nonlinear delay optimal control problems using a composite pseudospectral collocation method. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1379-1389. doi: 10.3934/cpaa.2010.9.1379

[4]

G. Machado, L. Trabucho. Analytical and numerical solutions for a class of optimization problems in elasticity. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1013-1032. doi: 10.3934/dcdsb.2004.4.1013

[5]

Jianjun Liu, Min Zeng, Yifan Ge, Changzhi Wu, Xiangyu Wang. Improved Cuckoo Search algorithm for numerical function optimization. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-13. doi: 10.3934/jimo.2018142

[6]

Gianni Gilioli, Sara Pasquali, Fabrizio Ruggeri. Nonlinear functional response parameter estimation in a stochastic predator-prey model. Mathematical Biosciences & Engineering, 2012, 9 (1) : 75-96. doi: 10.3934/mbe.2012.9.75

[7]

Azmy S. Ackleh, H.T. Banks, Keng Deng, Shuhua Hu. Parameter Estimation in a Coupled System of Nonlinear Size-Structured Populations. Mathematical Biosciences & Engineering, 2005, 2 (2) : 289-315. doi: 10.3934/mbe.2005.2.289

[8]

Gong Chen, Peter J. Olver. Numerical simulation of nonlinear dispersive quantization. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 991-1008. doi: 10.3934/dcds.2014.34.991

[9]

Song Wang, Xia Lou. An optimization approach to the estimation of effective drug diffusivity: From a planar disc into a finite external volume. Journal of Industrial & Management Optimization, 2009, 5 (1) : 127-140. doi: 10.3934/jimo.2009.5.127

[10]

Pierre Fabrie, Elodie Jaumouillé, Iraj Mortazavi, Olivier Piller. Numerical approximation of an optimization problem to reduce leakage in water distribution systems. Mathematical Control & Related Fields, 2012, 2 (2) : 101-120. doi: 10.3934/mcrf.2012.2.101

[11]

Rolf Rannacher. A short course on numerical simulation of viscous flow: Discretization, optimization and stability analysis. Discrete & Continuous Dynamical Systems - S, 2012, 5 (6) : 1147-1194. doi: 10.3934/dcdss.2012.5.1147

[12]

Ji Li, Tie Zhou. Numerical optimization algorithms for wavefront phase retrieval from multiple measurements. Inverse Problems & Imaging, 2017, 11 (4) : 721-743. doi: 10.3934/ipi.2017034

[13]

Roya Soltani, Seyed Jafar Sadjadi, Mona Rahnama. Artificial intelligence combined with nonlinear optimization techniques and their application for yield curve optimization. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1701-1721. doi: 10.3934/jimo.2017014

[14]

Yanzhao Cao, Song Chen, A. J. Meir. Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1253-1273. doi: 10.3934/dcdsb.2013.18.1253

[15]

R.G. Duran, J.I. Etcheverry, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 497-506. doi: 10.3934/dcds.1998.4.497

[16]

Thierry Colin, Boniface Nkonga. Multiscale numerical method for nonlinear Maxwell equations. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 631-658. doi: 10.3934/dcdsb.2005.5.631

[17]

Wansheng Wang, Chengjian Zhang. Analytical and numerical dissipativity for nonlinear generalized pantograph equations. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1245-1260. doi: 10.3934/dcds.2011.29.1245

[18]

Chunrong Chen, T. C. Edwin Cheng, Shengji Li, Xiaoqi Yang. Nonlinear augmented Lagrangian for nonconvex multiobjective optimization. Journal of Industrial & Management Optimization, 2011, 7 (1) : 157-174. doi: 10.3934/jimo.2011.7.157

[19]

Jie Sun. On methods for solving nonlinear semidefinite optimization problems. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 1-14. doi: 10.3934/naco.2011.1.1

[20]

Igor Griva, Roman A. Polyak. Proximal point nonlinear rescaling method for convex optimization. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 283-299. doi: 10.3934/naco.2011.1.283

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]