The least-squares identification of FIR systems subject to worst-case noise

Akçay, Hüseyin; Hjalmarson, Håkan

doi:10.1016/0167-6911(94)90065-5

Cited by 19 publications

(5 citation statements)

References 9 publications

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“…Moreover, its optimality property holds true whatever these values are [46]. Note that this optimality result of the least-squares estimate does not exclude that its identification error may behave badly (even diverge) in some asymptotic situations (see, e.g., [47]- [49]). Now the problem of evaluating is considered.…”

Section: Minimal Identification Error Evaluationmentioning

confidence: 88%

“…Now, in view of (33), the problem is to estimate the norm , i.e., the norm of the system with the finite impulse response using the measurement information (30). From well-known results in SM theory (see, e.g., [17]), for any , the optimal estimate of is given by the central estimate (34) where (35) (36) and is the feasible error set defined as (37) with (38) From (35) and (36), recalling (33), it follows: (39) Then, the central estimate of is given by (40) The following theorem solves the problem of evaluating (35) and (36) Proof: To find the expressions of (35) and (36), note that is given by (46) Introducing the vector defined as in (42), one gets (47) so that, taking the real and imaginary parts of (47), the result is Re Im (48) The image of in (37) through the linear operator is the ellipse in the complex plane represented in real and imaginary components as (49) Then, it follows that if otherwise.…”

Section: Unmodeled Dynamic Estimationmentioning

confidence: 99%

See 1 more Smart Citation

H/sub ∞/ identification and model quality evaluation

Giarré

Milanese²,

Taragna³

1997

IEEE Trans. Automat. Contr.

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Set membership H 1 identification is investigated using time-domain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors. The problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error, called radius of information, is solved. For classes of models affine in the parameters, the radius of information is obtained as function of the H1 norm of the unmodeled dynamics. A method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics, thus allowing the actual evaluation of the radius of information. The radius represents a measure of the "predictive ability" of the considered class of models, and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part. The effectiveness of the proposed procedure is tested on some numerical examples and compared with standard statistical criteria for model order selection.Index Terms-Identification for robust control, model order selection, set membership identification, uncertainty model identification.

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Section: Minimal Identification Error Evaluationmentioning

confidence: 88%

Section: Unmodeled Dynamic Estimationmentioning

confidence: 99%

H/sub ∞/ identification and model quality evaluation

Giarré

Milanese²,

Taragna³

1997

IEEE Trans. Automat. Contr.

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“…Closed-loop identification was discussed in [18], where worst-case identification was studied with closed-loop performance criteria. The classical least-squares estimation has also been employed in worst-case identification problems [1], [25], [29].…”

Section: A Related Early Workmentioning

confidence: 99%

“…In this paper, stable systems will consist of LTV causal bounded discrete-time systems on with convolution representations (1) where the kernel of satisfies , and . The norm of is defined by…”

Section: B Systemsmentioning

confidence: 99%

Persistent identification of time-varying systems

Wang

1997

IEEE Trans. Automat. Contr.

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In this paper, the problem of identification of timevarying systems is investigated in the framework of worst-case identification and information-based complexity. Measures of intrinsic errors, termed persistent identification errors, in such identification problems are introduced. For a selected model space of dimension n (finite impulse response models) and an observation window of length m, the persistent identification measures provide the worst-case posterior identification errors over all possible starting times of the observation windows when the input and identification algorithms are optimized. For linear time-invariant (LTI) plants with unmodeled dynamics belonging to certain types of prior unstructured uncertainty sets, upper and lower bounds of the persistent identification measures are explicitly computed. It is shown that when prior unmodeled dynamics are balls in the l 1 space, the lower and upper bounds coincide. In this case, any full-rank periodic probing signals are optimal, and the standard least-squares estimation is in fact an optimal identification algorithm. Motivated by closed-loop identification problems, the concept of nearly periodic signals is introduced. It is shown that such signals are asymptotically optimal for persistent identification and at the same time can be generated in a closed-loop configuration. For slowly varying systems, the persistent identification measures are shown to be continuous functions of the plant variation rates. Furthermore, periodic signals are asymptotically optimal in the sense that they achieve identification errors which approach the optimal persistent identification errors for LTI systems when the variation rates of the plants become small. This result verifies that the persistent identification measures are indeed benchmark values for the identification of time-varying systems.

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“…By Akcay and Khargonekar (1993) it is shown that this method robustly converges for estimating of the finite impulse response (FIR) models of systems. The result which demonstrates a divergence of LS ∞ Hidentification of the infinite impulse response (IIR) models under the bounded noise, was obtained by Akcay and Hjalmarson (1994). In other words it is impossible to use LS identification for IIR-models, as the problem is ill-posed irrespective of its matrix conditionality.…”

Section: Introductionmentioning

confidence: 99%