Closed-Loop Optimal Experiment Design: Solution via Moment Extension
We consider optimal experiment design for parametric prediction error system identification of linear time-invariant multiple-input multiple-output systems in closed-loop when the true system is in the model set. The optimization is performed jointly over the controller and the spectrum of the exter...
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Published in | IEEE transactions on automatic control Vol. 60; no. 7; pp. 1731 - 1744 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York
IEEE
01.07.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers |
Subjects | |
Online Access | Get full text |
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Summary: | We consider optimal experiment design for parametric prediction error system identification of linear time-invariant multiple-input multiple-output systems in closed-loop when the true system is in the model set. The optimization is performed jointly over the controller and the spectrum of the external excitation, which can be reparametrized as a joint spectral density matrix. The optimal solution consists of first computing a finite set of generalized moments of this spectrum as the solution of a semi-definite program. A second step then consists of constructing a spectrum that matches this finite set of optimal moments and satisfies some constraints due to the particular closed-loop nature of the optimization problem. This problem can be seen as a moment extension problem under constraints. Here we first show that the so-called central extension always satisfies these constraints, leading to a constructive procedure for the optimal controller and excitation spectrum. We then show that one can construct a broader set of parametrized optimal solutions that also satisfy the constraints; the additional degrees of freedom can then be used to achieve additional objectives. |
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ISSN: | 0018-9286 1558-2523 |
DOI: | 10.1109/TAC.2015.2400662 |