Presented by:
Reza Raoufi
Hamid Khaloozadeh

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Abstract


A robust/adaptive stochastic observer is presented for stochastic nonlinear dynamics having excessive uncertainties. It was shown through a new theorem that the proposed nonlinear robust sliding mode observer has very accurate state estimate error characteristic. The observer uses the sliding mode technique for the robustness and a deterministic adaptive law to guarantees a globally asymptotically convergence observation error. Finally, an example is given to illustrate the application and very favorable convergence properties of the proposed observer.


Introduction

Observing the state hence the name "observer", is an important problem in the theory of systems. For linear systems, it has been extensively improved, and has proven extremely useful, especially for control applications such as observer-based-control design. For nonlinear systems, the theory of observers is not nearly as complete as it is for linear systems. The use of variable structure techniques in state reconstruction of nonlinear systems based on feedback linearization and extended linearization have been presented (Bestel and Zetiz, 1983; Krener, 1985; Isidori, 1985; Baumann and Rugh, 1986).A comparison of some of these techniques came to the conclusion that variable structure observers exhibit the best performance in this particular case study (Walcott and et al., 1987).
Therefore, robust techniques of state observation like sliding-mode observers have received ever increasing attention for linear and nonlinear systems (Koshkouei and Zinober, 1995; Sira and Spurgeon, 1994; Sira and et al., 1994; Utkin, 1992). The major feature of Robust sliding mode observer is the capability of reconstruction the states of a linear or nonlinear variable structure system with uncertainty having unknown bounded disturbances and measurement uncertainties (Slotine and Hedrick, 1986; Yaz and Azemi, 1994; Barbot and et al., 1996).It should be pointed out all the designed observers introduced above requires the knowledge of a bounding function on the uncertainties which should not be intensive and too excessive. A method for designing an adaptive observer for nonlinear deterministic systems has been presented (Yaz and Azemi, 1993) and other adaptive approaches in the context of variable-structure have been considered (Corless and Leitmann, 1983; Chen, 1989; Yoo and Chung, 1992).
In this work, nonlinear systems with excessive and strong uncertainties and unmodeled dynamics in presence of noise are considered. Designing a robust stochastic observer based on a new adaptive update law, Ito calculus and stochastic lyapunov stability (Florchinger, 1995; Gard, 1988; Mao1994) have been proposed. Finally, a simulation example will illustrate the efficacy and much more accurate observation of the new propose filter in comparison with the standard nonlinear estimation method of extended Kalman filter (EKF).



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