Information-based complexity
Conditionally optimal algorithms and estimation of reduced order models
Journal of Complexity
On identification of stable systems and optimal approximation
Automatica (Journal of IFAC)
Worst case system identification in l1 ne-equation1: optimal algorithms and error bounds
Systems & Control Letters
Automatica (Journal of IFAC) - Special issue on trends in system identification
Worst-case control-relevant identification
Automatica (Journal of IFAC) - Special issue on trends in system identification
System identification with generalized orthonormal basis functions
Automatica (Journal of IFAC) - Special issue on trends in system identification
Selected topics in approximation and computation
Selected topics in approximation and computation
On approximation of stable linear dynamical systems using Laguerre and Kautz functions
Automatica (Journal of IFAC)
Induced L2 norm model reduction of polytopic uncertain linear systems
Automatica (Journal of IFAC)
Model quality evaluation in set membership identification
Automatica (Journal of IFAC)
On input design in l∞ conditional set membership identification
Automatica (Journal of IFAC)
Hi-index | 22.15 |
We consider optimality of identification of linear systems by reduced complexity models which belong to a subspace (of possibly low dimension) of a system space. Identification is based on the 'a priori' knowledge that an unknown system belongs to a certain class, and 'a posteriori' information given by its nonexact output measurements. Measurement errors are assumed unknown but norm bounded. The analysis is not restricted to specific norms in system and measurement spaces; generic norms are considered. We derive tight upper and lower bounds on the minimal local worst-case identification error, and define an algorithm whose error is within the derived bounds. The results are specified for product norms (which include l"p norms, 1@?p@?+~) in the system space. The bounds are expressed in terms of the model error which measures a quality of representing systems by a model subspace, and the diameter of information reflecting the size of a model uncertainty set. The model error is further splitted into truncated model error and residual error which controls ''tail'' properties of the unknown system. Examples of model and input selection in some special cases are given, and numerical experiments showing the behavior of the estimates reported.