Abstract
Modified Wiener-Hopf equation in identification problems
Highlights
THE PROBLEM OF THE NON-STATIONARY OBJECT IDENTIFICATIONOptimality conditionsIt is proposed to consider the construction of the basic design of non-stationary control systems optimization algorithms, whose state measurement is performed against a background of interference [1, 2, 3]
The concept developed in the process of optimization algorithms construction can be used to solve a wide range of problems - from the identification system construction and the solution of filtering non-stationary processes tasks to the construction of parametric control algorithms for non-stationary objects
We show that the optimal operator where α◦(t) - the operator optimization parameters
Summary
It is proposed to consider the construction of the basic design of non-stationary control systems optimization algorithms, whose state measurement is performed against a background of interference [1, 2, 3]. Before finding the general minimum condition for a functional of the form (2.5), we note that a sufficiently large number of control objects models can be described with the help of systems of linear differential equations with incomplete information on parameters and the state vector. For such models, it is fair (1.6). For the Gaussian processes and linear operators condition (1.6) is a necessary and sufficient condition for the minimum of the functional (1.5) and has the form of the Wiener-Hopf equation. The optimal operator where R the space of linear operators, α◦(t) - the values of the operator optimization parameter
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