American Institute of Mathematical Sciences

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

A pseudospectral observer for nonlinear systems

Qi Gong 1, , I. Michael Ross 2, and  Wei Kang 3,

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.
Keywords: Numerical observer, optimization, pseudospectral, nonlinear estimation..
Mathematics Subject Classification: Primary: 93E10, 93C10; Secondary: 93E1.
Citation: Qi Gong, I. Michael Ross, Wei Kang. A pseudospectral observer for nonlinear systems. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 589-611. doi: 10.3934/dcdsb.2007.8.589
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