Exponential nonlinear observer based on the differential state-dependent Riccati equation
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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.
KeywordsDetectability direct method of Lyapunov exponential stability nonlinear observer region of attraction state-dependent Riccati equation (SDRE) technique
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- A. Azemi, E. Yaz. Comparative study of several nonlinear stochastic estimators. In Proceedings of the 38th IEEE Conference on Decision and Control, IEEE, Phoenix, USA, vol. 5, pp. 4549–4554, 1999.Google Scholar
- A. Gelb. Applied Optimal Estimation, Cambridge, UK: The MIT Press, 2001.Google Scholar
- A. H. Jazwinski. Stochastic Processes and Filtering Theory, New York, USA: Academic Press, 1972.Google Scholar
- C. P. Mracek, J. R. Cloutier, C. A. D’souza. A new technique for nonlinear estimation. In Proceedings of the 1996 IEEE International Conference on Control Applications, IEEE, Dearborn, USA, pp. 338–343, 1996.Google Scholar
- J. R. Cloutier, D. T. Stansbery. The capabilities and art of state-dependent Riccati equation-based design. In Proceedings of American Control Conference, IEEE, Anchorage, USA, vol. 1, pp. 86–91, 2002.Google Scholar
- J. R. Cloutier, C. N. D’souza, C. P. Mracek. Nonlinear regulation and nonlinear H-infinity control via the state-dependent Riccati equation technique. Part 1, theory; Part 2, Examples. In Proceedings of the 1st International Conference on Nonlinear Problems in Aviation and Aerospace, Daytona Beach, USA, pp. 117–141, 1996.Google Scholar
- Z. Qu, J. R. Cloutier, C. P. Mracek. A new sub-optimal nonlinear control design technique-SDARE. In Proceedings of the 13th IFAC World Congress, San Francisco, USA, pp. 365–370, 1996.Google Scholar
- D. Haessig, B. Friedland. State dependent differential Riccati equation for nonlinear estimation and control. In Proceedings of the 15th IFAC Triennial World Congress, Barcelona, Spain, 2002. [Online], Available: http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2002/data/content/02294/2294.pdf, January 11, 2011.
- T. Cimen, A. O. Merttopcuoglu. Asymptotically optimal nonlinear filtering: Theory and examples with application to target state estimation. In Proceedings of the 17th IFAC World Congress, Seoul, Korea, 2008. [Online], Available: http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2008/data/papers/3636.pdf, January 11, 2011.
- V. Pappano, B. Friedland. Analytical solution for a separate state and parameter SDRE observer for a CSI-fed induction motor. In Proceedings of the 1998 IEEE International Conference on Control Applications, IEEE, Trieste, Italy, vol. 2, pp. 1286–1291, 1998.Google Scholar
- I. Y. Bar-Itzhack, R. R. Harman, D. Choukroun. State-dependent pseudo-linear filters for spacecraft attitude and rate estimation. In Proceedings of AIAA Guidance, Navigation and Control Conference and Exhibit, Monterey, USA, pp. 259–269, 2002.Google Scholar
- B. M. Lewis. Optimal Control and Shape Design: Theory and Applications, Ph. D. dissertation, Department of Mathematics, North Carolina State University, Raleigh, 2003.Google Scholar
- C. M. Ewing. An analysis of the state-dependent Riccati equation nonlinear estimation technique. In Proceedings of the AIAA Guidance, Navigation and Control Conference, Denver, USA, 2000.Google Scholar
- N. F. Palumbo, T. D. Jackson. Integrated missile guidance and control system: A state-dependent Riccati differential equation approach. In Proceedings of the 1999 IEEE International Conference on Control Applications, IEEE, Hawaii, USA, vol. 1, pp. 243–248, 1999.Google Scholar
- H. Beikzadeh, H. D. Taghirad. Robust H ∞ filtering for nonlinear uncertain systems using state-dependent Riccati equation technique. In Proceedings of the 48th IEEE Conference on Decision and Control, IEEE, Shanghai, PRC, pp. 4438–4445, 2009.Google Scholar
- J. R. Cloutier. State dependent Riccati equation techniques: An overview. In Proceedings of the American Control Conference, IEEE, Albuquerque, New Mexico, vol. 2, pp. 932–936, 1997.Google Scholar