Identification and Control of A Nonlinear Discrete-Time System Based on Its Linearization : A Unified Framework  

Oleh:

Narendra, K. S. ; Chen, Lingji

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: IEEE Transactions on Neural Networks vol. 15 no. 3 (May 2004), page 663-673.
Topik: FRAMEWORK; identification; control; non linear; discrete - time system; linearization; unified framework

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: II36.10 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

This paper presents a unified theoretical framework for the identification and control of a nonlinear discrete - time dynamical system, in which the non linear system is represented explicitly as a sum of its linearized component and the residual non linear component referred to as a "higher order function." This representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system, and reveals the role played by the linearized system in a more transparent form. Under the assumption that the linearized system is controllable and observable, it is shown that : 1) the non linear system is also controllable and observable in a local domain ; 2) a feedback law exists to stabilize the non linear system locally ; and 3) the non linear system can exactly track a constant or a periodic sequence locally, if its linearized system can do so. With some additional assumptions, the non linear system is shown to have a well - defined relative degree (delay) and zero - dynamics. If the zero - dynamics of the linearized system is asymptotically stable, so is that of the nonlinear one, and in such a case, a control law exists for the non linear system to asymptotically track an arbitrary reference signal exactly, in a neighborhood of the equilibrium state. The tracking can be achieved by using the state vector for feedback, or by using only the input and the output, in which case the non linear autoregressive moving - average (NARMA) model is established and utilized. These results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete -time dynamical systems.

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