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Extra resources for [Article] Sensitivity analysis for trend tests application to the risk of radiation exposure

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In the present paper, we provide an ultimate extension of the theorems for analytic continuous-time systems, showing that there are inputs that are universal with respect to all finite dimensional analytic systems, and, moreover, the set of such inputs is generic. A preliminary version of our result was presented at the 1994 IEEE Conference on Decision and Control [20] (see also [11]). Besides their intrinsic theoretical appeal, universal input theorems help provide a rationale for systems identification when using information provided by “random” or unknown inputs.

D. Sontag and Y. Wang 10. D. Sontag. Universal nonsingular controls. Systems & Control Letters, 19(3):221–224, 1992. 11. D. Sontag. Spaces of observables in nonlinear control. Proceedings of the International Congress of Mathematicians, 1:1532–1545, 1994. 12. D. Sontag. Control of systems without drift via generic loops. IEEE Trans. on Automat. , 40(7):1210–1219, 1995. 13. D. Sontag. Mathematical Control Theory: Deterministic Finite Dimensional Systems. Springer-Verlag, New York, 2nd edition, 1998.

1 Introduction One of the key concepts in control theory is that of a universal input for observability and parameter identification. Informally stated, an input u0 is universal (for a given system) provided that the following property holds: if two internal states x1 and x2 are in principle distinguishable by any possible input/output experiment, then x1 and x2 can be distinguished by forcing the system with this particular input u0 (and observing the corresponding output function). Universal input theorem(s) for distinguishability show that such inputs indeed do exist, and, furthermore, show that “generic” (in an appropriate technical sense) inputs have this property.

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