The function space to describe the dynamics of linear systems
For control systems engineers, this provides a theoretically consistent framework and improved noise handling, but the contribution is incremental as it refines an existing mathematical description.
The paper resolves contradictions in describing linear time-invariant system dynamics by shifting from Lebesgue square integrable functions to almost periodic functions in Hilbert space, and introduces a more effective noise reduction method. The method was applied to identify differential equations for an Airbus during automatic landing.
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to contradictions. It is shown that the transition to the Hilbert space of almost periodic functions leads to the elimination of the detected inconsistencies. Multiple signals and interference with discrete spectrum are systems of sets. The properties of these systems lead to a new more effective method to combat noise in this space. The method used to identify the differential equations for the airbus. Baseline data were obtained during automatic landing.