Structural synthesis of discrete adaptive tracking systems based on the combined maximum principle

Introduction. Discrepancy of the mathematical model structure to the observed process is one of the causes for loss in the control system operation. It determines the urgency of the problem of structural synthesis of the adaptive tracking systems which is considered in the extremum formulation. Materials and Methods. The combined maximum principle methodology is used to solve the synthesis problem in the quasideterministic approximation. In this case, the minimum condition of the objective functional which is the result of the convolution of the quality criterion and action integral is investigated. This allows building a state filter model with the structural adaptation as a solution to the inverse dynamic problem. Practical implementation of the results received through this approach in the digital tracking systems sets a problem of selecting a finite-dimensional approximation scheme for the obtained model which is associated with the determination of the synthesizing function approximation form and the use of the general solution to the homogeneous differential equation. Research Results. Embodiment of the digital tracking systems based on the finite-dimensional approximation with a new structure of the transfer matrix and covariance matrix of the disturbance intensity vector in discrete time is considered. Discussion and Conclusions. The mathematical modeling results show that a new method of the tracking systems synthesis in discrete time under regular perturbances improves accuracy of the estimators operation compared with the traditional approaches.

дискретное время, структурная адаптация, объединенный принцип максимума, синтез, фильтр Калмана, discrete time, structural adaptation, combined maximum principle, synthesis, Kalman filter

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