Volume 9 Number 4
August 2012
Article Contents
Hossein Beikzadeh and Hamid D. Taghirad. Exponential Nonlinear Observer Based on the Differential State-dependent Riccati Equation. International Journal of Automation and Computing, vol. 9, no. 4, pp. 358-368, 2012. doi: 10.1007/s11633-012-0656-y
Cite as: Hossein Beikzadeh and Hamid D. Taghirad. Exponential Nonlinear Observer Based on the Differential State-dependent Riccati Equation. International Journal of Automation and Computing, vol. 9, no. 4, pp. 358-368, 2012. doi: 10.1007/s11633-012-0656-y

Exponential Nonlinear Observer Based on the Differential State-dependent Riccati Equation

Author Biography:
  • Hossein Beikzadeh received his B.Sc. and M.Sc. degrees in electrical engineering from K.N. Toosi University of Technology, Iran in 2006 and 2009, respectively. He is currently a Ph.D. candidate in the Department of Electrical and Computer Engineering University of Alberta, Canada. His research interests include nonlinear systems analysis, nonlinear observer design, robust control, and sampled-data control. E-mail: beikzade@ece.ualberta.ca

  • Corresponding author: Hossein Beikzadeh
  • Received: 2010-09-13
  • This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation (SDRE) filter with guaranteed exponential stability. Although impressive results have rapidly emerged from the use of SDRE designs for observers and filters, the underlying theory is yet scant and there remain many unanswered questions such as stability and convergence. In this paper, Lyapunov stability analysis is utilized in order to obtain the required conditions for exponential stability of the estimation error dynamics. We prove that under specific conditions, the proposed observer is at least locally exponentially stable. Moreover, a new definition of a detectable state-dependent factorization is introduced, and a close relation between the uniform detectability of the nonlinear system and the boundedness property of the state-dependent differential Riccati equation is established. Furthermore, through a simulation study of a second order nonlinear model, which satisfies the stability conditions, the promising performance of the proposed observer is demonstrated. Finally, in order to examine the effectiveness of the proposed method, it is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines. The simulation results verify how effectively this modification can increase the region of attraction and the observer error decay rate.
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Exponential Nonlinear Observer Based on the Differential State-dependent Riccati Equation

  • Corresponding author: Hossein Beikzadeh

Abstract: This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation (SDRE) filter with guaranteed exponential stability. Although impressive results have rapidly emerged from the use of SDRE designs for observers and filters, the underlying theory is yet scant and there remain many unanswered questions such as stability and convergence. In this paper, Lyapunov stability analysis is utilized in order to obtain the required conditions for exponential stability of the estimation error dynamics. We prove that under specific conditions, the proposed observer is at least locally exponentially stable. Moreover, a new definition of a detectable state-dependent factorization is introduced, and a close relation between the uniform detectability of the nonlinear system and the boundedness property of the state-dependent differential Riccati equation is established. Furthermore, through a simulation study of a second order nonlinear model, which satisfies the stability conditions, the promising performance of the proposed observer is demonstrated. Finally, in order to examine the effectiveness of the proposed method, it is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines. The simulation results verify how effectively this modification can increase the region of attraction and the observer error decay rate.

Hossein Beikzadeh and Hamid D. Taghirad. Exponential Nonlinear Observer Based on the Differential State-dependent Riccati Equation. International Journal of Automation and Computing, vol. 9, no. 4, pp. 358-368, 2012. doi: 10.1007/s11633-012-0656-y
Citation: Hossein Beikzadeh and Hamid D. Taghirad. Exponential Nonlinear Observer Based on the Differential State-dependent Riccati Equation. International Journal of Automation and Computing, vol. 9, no. 4, pp. 358-368, 2012. doi: 10.1007/s11633-012-0656-y
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