Duality of optimal designs for model discrimination and parameter estimation

Invited Discussion Paper Constrained Optimization of Experimental Design

“…Example 3. In model testing experiments (see Atkinson and Fedorov, 1975;Fedorov and Khabarov, 1986) when there are two rival response models, the design problem consists of maximization of some discrepancy measure between these competing models. This case can be transformed to the case when a response function ~( x , 0) is compared with the totally null hypothesis q,(x, 0,) -0.…”

“…The comparison of Theorems 1,2, and 4 gives a hint how the latter can be generalized when one adds (8), or (12), or (14) to constraints (17). For this purpose the function $(x, 5) must be replaced by a corresponding function q(x, u, <) = $(x, () + uT4(x, 5).…”

“…, 1 + 1.Assume that all A: are known. Then Theorem 3 states that (l3),(14) are equivalent to(1 I),(12) with @(4) = (@(& 3.3,. . .…”

Input design for discrimination between classes of LTI models

“…This design method is an extension of the ideas proposed in, e.g., Bombois, den Dekker, Rojas, Hjalmarsson, and Van den Hof (2011) and Fedorov and Khabarov (1986).…”

“…And, in the field of fault detection and isolation there are frequently a finite number of operation modes corresponding to failures of different components. Experiment design for model discrimination has been addressed using a hypothesis test in Fedorov (1972) and shown to be closely related to parameter estimation problems in Fedorov and Khabarov (1986). In the context of dynamic systems, in Kerestecioǧlu and Zarrop (1994) a frequency-domain approach to input design problem is introduced for model discrimination in terms of cumulative sum and probability ratio tests.…”