Nonlinear observer design based on immersion and invariance method: an insight to chaotic systems

This paper presents some use of reduced order observers for two classes of chaotic systems. The first class includes rod-type plasma torch and Arneodo systems and the second class contains Lorenz and Chen systems. In this regard, a recently developed approach called immersion and invariance method is employed. During the estimation the first state of the system is assumed measured. Implementation of the proposed nonlinear observer is simple and does not need high gain to estimate unavailable state in comparison with conventional methods by rendering manifold observer design inspired form sliding mode theory. An important point of this design is to find appropriate mapping that give rise to exponential stability of observer dynamic. It is worth mentioning that the problem of designing a reduced order observer can be turned into the problem of finding a proper invariant manifold. Stability of the proposed scheme is proven via Lyapunov theorem whilst the simulation results confirm the significance of the proposed immersion and invariance observer.

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