| 1. |
- Glad, Torkel, 1947-
(author)
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On the Gain Margin of Nonlinear and Optimal Regulators
- 1984
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In: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 29:7, s. 615-620
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Journal article (peer-reviewed)abstract
- The robustness of nonlinear regulators for nonlinear systems with respect to variations in gain is investigated. It is shown that there exist regulators that produce asymptotically stable closed-loop systems, but do not tolerate any variation in gain without instability. However, if the linearized closed-loop system is also asymptotically stable, then there is always some gain margin. For a wide class of optimal regulators, it is shown that the gain margin is infinite with respect to increases in gain and that decreases down to 0.5 can be tolerated. The robustness properties of linear quadratic control laws are thus generalized.
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| 2. |
- Kailath, Thomas, et al.
(author)
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Recursive Input-Output and State Space Solutions for Continuous-Time Linear Estimation Problems
- 1983
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In: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 28:9, s. 897-906
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Journal article (peer-reviewed)abstract
- A general linear least-squares estimation problem is considered. It is shown how the optimal filters for filtering and smoothing can be recursively and efficiently calculated under certain structural assumptions about the covariance functions involved. This structure is related to an index known as the displacement rank, which is a measure of non-Toeplitzness of a covariance kernel. When a state space type structure is added, it is shown how the Chandrasekhar equations for determining the gain of the Kalman-Bucy filter can be derived directly from the covariance function information; thus we are able to imbed this class of state-space problems into a general input-output framework.
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| 3. |
- Ljung, Lennart, 1946-, et al.
(author)
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Asymptotic Properties of Black-Box Identification of Transfer Functions
- 1985
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In: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 30:6, s. 514-530
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Journal article (peer-reviewed)abstract
- The problem of estimating the transfer function of a linear, stochastic system is considered. The transfer function is parametrized as a black box and no given order is chosen a priori. This means that the model orders may increase to infinity when the number of observed data tends to infinity. The consistency and convergence properties of the resulting transfer function estimates are investigated. Asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase. It is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise-to-signal ratio at that frequency mulliplied by the model-order-to-number-of-data-points ratio.
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| 4. |
- Ljung, Lennart, 1946-
(author)
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Asymptotic Variance Expressions for Identified Black-Box Transfer Function Models
- 1985
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In: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; 30:9, s. 834-844
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Journal article (peer-reviewed)abstract
- Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due to variance for a number of typical model uses. Some consequences for input design are also drawn.
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| 5. |
- Wahlberg, Bo, 1959-, et al.
(author)
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Design Variables For Bias Distribution In Transfer Function Eestimation
- 1986
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In: IEEE Transactions on Automatic Control. - : IEEE Control Systems Society. - 0018-9286 .- 1558-2523. ; AC-31:2, s. 134-144
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Journal article (peer-reviewed)abstract
- Estimation of transfer functions of linear systems is one of the most common system identification problems. Several different design variables, chosen by the user for the identification procedure, affect the properties of the resulting estimate. The way in which the choices of prefilters, noise models, sampling interval, and prediction horizon (the use of k-step ahead prediction methods) influence the estimate is discussed. An important aspect is that the true system is not assumed to be exactly represented within the chosen model set. The estimate will thus be biased. It is shown how the distribution of bias in the frequency domain is governed by a weighting function, which emphasizes different frequency bands. The weighting function, in turn, is a result of the previously listed design variables. It is shown that the common least-squares method has a tendency to emphasize high frequencies and that this can be counteracted by prefiltering. It is also shown that, asymptotically, it is only the prediction horizon itself, and not how it is split up into sampling interval times number of predicted sampling instants, that affects this weighting function.
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| 6. |
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| 7. |
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| 8. |
- Wittenmark, Björn
(author)
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Sampling of a system with a time delay
- 1985
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In: IEEE Transactions on Automatic Control. - 0018-9286. ; 30:5, s. 507-510
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Journal article (peer-reviewed)abstract
- This note deals with the problem of sampling a continuous-time system which contains a time delay. It is shown that the infinite-dimensional continuons-time system can be represented by a finite-dimensional sampled data system. It is shown that there are simple expressions for the sampled data state-space representations.
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