By Fouad Giri, Er-Wei Bai
ISBN-10: 1849965129
ISBN-13: 9781849965125
Block-oriented Nonlinear approach Identification offers with a space of study that has been very energetic because the flip of the millennium. The ebook makes a pedagogical and cohesive presentation of the equipment built in that point. those include:
• iterative and over-parameterization techniques;
• stochastic and frequency approaches;
• support-vector-machine, subspace, and separable-least-squares methods;
• blind id method;
• bounded-error process; and
• decoupling inputs approach.
The id tools are provided by means of authors who've both invented them or contributed considerably to their improvement. all of the vital matters e.g., enter layout, continual excitation, and consistency research, are mentioned. the sensible relevance of block-oriented versions is illustrated via biomedical/physiological approach modeling. The booklet can be of significant curiosity to all those who find themselves desirous about nonlinear approach identity no matter what their job components. this is often fairly the case for educators in electric, mechanical, chemical and biomedical engineering and for practicing engineers in approach, aeronautic, aerospace, robotics and cars keep an eye on. Block-oriented Nonlinear procedure Identification serves as a reference for energetic researchers, rookies, business and schooling practitioners and graduate scholars alike.
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Additional resources for Block-oriented Nonlinear System Identification
Example text
Bn c , a1 d , . . , a p d )T have a special structure in terms of a, b, c and d. , hl ). Then, (bˆ 1 (N)cˆT (N), . . , bˆ n (N)cˆT (N), aˆ1 (N)dˆT (N), . . , aˆ p (N)dˆT (N))T − θ (N) 2 2 3 Two-stage Algorithm 31 = ˆ vec(b(N) cˆT (N)) − θ (N) vec(a(N) ˆ dˆT (N)) = b(N)cT (N) − Θbc (N) 2 F 2 2 + a(N)d T (N) − Θad (N) 2 F, where · F stands for the matrix Frobenius norm. Thus, the closest a(N), b(N), c(N) and d(N) to θ (N) in the 2-norm sense is given by (a(N), d(N)) = arg min x∈R p ,w∈Rq (b(N), c(N)) = arg min Θad (N) − xwT z∈Rn ,v∈Rm Θbc (N) − zvT 2 F and 2 F The solutions of b(N), c(N), a(N) and d(N) are provided by SVD decompositions of Θbc (N) and Θad (N) as given in Step 2 of the proposed Identification Algorithm.
A robust and recursive identification method for Hammerstein model. In: IFAC World Congress, San Francisco, pp. 447–452 (1996) 4. : A non-iterative method for identification using Hammerstein model. IEEE Trans. on Auto. Contr. 16, 464–468 (1971) 5. : A multi-stage least squares method for identifying Hammerstein model nonlinear systems. In: Proc. of CDC, Clearwater Florida, pp. 934–938 (1976) 6. : Consistency of the least squares identification method. IEEE Trans. on Auto. Contr. 21, 779–781 (1976) 7.
Bai ⎛ θ1 , . . , θm θm+1 , . . , θ2m .. . . . ⎛ ⎞ θnm+1 , . . , θnm+q θnm+q+1 , . . , θnm+2q .. . . . ⎞ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ Θbc (N) = ⎜ ⎟ and Θad (N) = ⎜ ⎟ ⎝ ⎝ ⎠ ⎠ θ(n−1)m+1 , . . , θnm θnm+(p−1)q+1, . . 4) denote the estimate of Θbc and Θad respectively. 1) under the Uniqueness Assumption. For a given data set {u(k), y(k)}Nk=1 , Step 1: Calculate the least squares estimate θ (N) = θls (N) = (ΦNT ΦN )−1 ΦNT YN . , q) are n, m, p, q-dimensional orthonormal vectors respectively. Step 3: Let sμ denote the sign of the first non-zero element of μ1 and sξ denote the sign of the first non-zero element of ξ1 .
Block-oriented Nonlinear System Identification by Fouad Giri, Er-Wei Bai
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