Optimal test signals as a solution of the generalized Bulgakov problem

摘要

The Bulgakov problem on the accumulation of perturbations at the output of an object when disturbances of bounded amplitude, along with useful signals, act at the input is generalized. The optimal test signal is determined as the worst input disturbance for which the output error is maximal, using estimates of operator norms and eigenfunctions of operators associated with a linear stationary dynamic system. Norms for input and output signals are taken to be modular Hilbert and Chebyshev norms in different combinations. Nine problems thus obtained are classified by the type of constraints for the amplitude, area, and energy of the test signal. The results are applicable in diagnostics, metrology, and identification.