Subspace-Based Identification for linear and nonlinear systems

Subspace-Based - 2005 American Control Conference June 8-10 2005 Portland OR USA ThB02.2 Subspace-Based Identication for Linear and Nonlinear

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Subspace-Based Identifcation For Linear and Nonlinear Systems Harish J. Palanthandalam-Madapusi, Seth Lacy, Jesse B. Hoagg and Dennis S. Bernstein 1. INTRODUCTION Mathematical models describe the dynamic behavior of a system as a function of time, and arise in all scientiFc disciplines. These mathematical models are used for simula- tion, operator training, analysis, monitoring, fault detection, prediction, optimization, control system designs and quality control. System identifcation is the process of constructing mathe- matical models of dynamical systems using measured data. The identiFed models can be used for output prediction, system analysis and diagnostics, system design, and control. IdentiFcation of linear models has been well studied and numerous frequency-domain and time-domain methods are available [21]. Among the available time-domain methods, subspace algorithms are an important class of algorithms for identifying linear state-space models. Subspace methods are naturally applicable to multi-input multi-output (MIMO) systems and identify the system in the state-space form. These methods are computationally tractable and robust since they use QR factorization and singular value decompositions. Another advantage of sub- space algorithms is that no a priori information about the system is needed, and thus they are widely applicable. Since the number of user choices is small, the software is user- friendly. All these factors make subspace identiFcation a valuable tool. Overviews of linear subspace identiFcation are presented in detail in [5, 34, 45]. Detailed examination of subspace- based identiFcation of bilinear and linear parameter-varying (LPV) systems is done in [36]. Subspace algorithms have also been applied to numerous industrial and real-life ap- plications ranging from glass tube manufacturing processes to bridge dynamics. A few application-based papers are [9], Sections 6.3 and 6.4 of [34] and [31]. Section 6.4 of [34] references several other interesting applications. In this paper, we introduce the basic ideas behind subspace algorithms to the uninitiated reader and provide an overview of linear, time-varying, nonlinear and closed-loop methods. The basic idea behind subspace is that the Kalman Flter state sequence can directly be estimated from the input/output observations. Once the state estimates are avail- able, the state space matrices are estimated using a linear least squares Ft. This is contrary to traditional identiFcation S. Lacy is with the Air ±orce Base, Albuquerque, New Mexico H. J. Palanth, J. B. Hoagg and D. S. Bernstein are with the department of Aerospace Engineering at the University of Michigan, Ann Arbor, MI 48109-2140. { hpalanth,hoagg,dsbaero } @umich.edu methods, where the model is identiFed Frst and then the states are generated using the identiFed model.
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This note was uploaded on 01/29/2011 for the course ENGR 52 taught by Professor Mcmillan during the Spring '10 term at Baylor Med.

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Subspace-Based - 2005 American Control Conference June 8-10 2005 Portland OR USA ThB02.2 Subspace-Based Identication for Linear and Nonlinear

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