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1.	Hjalmarsson, Håkan, et al. (author) Closed loop experiment design for linear time invariant dynamical systems via LMIs 2008 In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 44:3, s. 623-636 Journal article (peer-reviewed)abstract All stationary experimental conditions corresponding to a discrete-time linear time-invariant causal internally stable closed loop with real rational system and feedback controller are characterized using the Youla-Kucera parametrization. Finite dimensional parametrizations of the input spectrum and the Youla-Kucera parameter allow a wide range of closed loop experiment design problems, based on the asymptotic (in the sample size) covariance matrix for the estimated parameters, to be recast as computationally tractable convex optimization problems such as semi-definite programs. In particular, for Box-Jenkins models, a finite dimensional parametrization is provided which is able to generate all possible asymptotic covariance matrices. As a special case, the very common situation of a fixed controller during the identification experiment can be handled and optimal reference signal spectra can be computed subject to closed loop signal constraints. Finally, a brief numerical comparison with closed loop experiment design based on a high model order variance expression is presented.

Hjalmarsson, Håkan, et al. (author)
Closed loop experiment design for linear time invariant dynamical systems via LMIs
2008
In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 44:3, s. 623-636
Journal article (peer-reviewed)abstract
- All stationary experimental conditions corresponding to a discrete-time linear time-invariant causal internally stable closed loop with real rational system and feedback controller are characterized using the Youla-Kucera parametrization. Finite dimensional parametrizations of the input spectrum and the Youla-Kucera parameter allow a wide range of closed loop experiment design problems, based on the asymptotic (in the sample size) covariance matrix for the estimated parameters, to be recast as computationally tractable convex optimization problems such as semi-definite programs. In particular, for Box-Jenkins models, a finite dimensional parametrization is provided which is able to generate all possible asymptotic covariance matrices. As a special case, the very common situation of a fixed controller during the identification experiment can be handled and optimal reference signal spectra can be computed subject to closed loop signal constraints. Finally, a brief numerical comparison with closed loop experiment design based on a high model order variance expression is presented.

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