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Nonparametric instrumental variables for identification of block-oriented systems

Mzyk G.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 3

521--537

A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.

Hybrid synchronization of n-scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback

Suresh R., Sundarapandian V.

Archives of Control Sciences

2012

Vol. 22, no. 3

343-365

This paper investigates the backstepping control design with novel feedback input approach for controlling chaotic systems to guarantee the complete synchronization as well as the anti-synchronization of chaotic systems, viz. n-scroll Chua (K. Wallace et.al. 2001) and Lur’e chaotic systems. Our theorems on hybrid synchronization for n-scroll Chua and Lur’e (J.Suyken et.al. 1997) chaotic systems is established using Lyapunov stability theory. Based on the Lyapunov function, the backstepping control is determined to tune the controller gain based on the precalculated feedback control inputs. The backstepping scheme is recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. Since the Lyapunov exponents are not required for these calculations, the backstepping control method is effective and convenient to synchronize the chaotic systems. Mainly this technique gives the flexibility to construct a control law. Numerical simulations are also given to illustrate and validate the hybrid synchronization results derived in this paper.