Algorithm for the synthesis of dual non-parametric control of "black box" type dynamic object with use state matrix diagonalization method

Abstract

The subject of the article is a variant of an efficient algorithm for synthesizing a dual discrete model and controller for tracking a given trajectory of a dynamic nonlinear, nonstationary black box object, using standard procedures for diagonalizing the state matrix, which makes it possible to simplify obtaining control values in numerical form and reduce the number of calculations. The current article presents one the possible solutions to the problem of regulator synthesis to ensure stable development of a given trajectory of motion of a nonlinear, non-stationary object of "black box" type using the concept of dual control. The task was set to simplify the previously proposed synthesis algorithm for the adaptive control of dynamic nonlinear, non-stationary objects using the example of first-order object of the "black box" type, using standard procedures for the diagonalization of the state matrix. An extended state matrix is the basis for obtaining a control model and predicting the behavior of a nonlinear non-stationary object, which in turn makes it possible to effectively use the concept of dual control. Methods used in the work are based on concept of dual control, nonlinear dynamic models, matrix theory, difference equations. Obtained results of this work consist of the development of a version of a dual nonparametric controller of nonstationary nonlinear processes, which has adaptive properties, does not require knowledge of the physics of functioning of the control object, is presented in the form of a simple algebraic formula that does not contain coefficients that require adjustment. Conclusion. Scientific novelty lies in the application of each interval matrix operator control for the diagonalization of the state submatrix. This operator is used for subsequent calculation of the control action. This approach enables the use of a standard diagonalization procedure using mathematical applications. The results are presented in the form of a final formula that does not require use of matrix operations during control, which makes it possible to simplify the synthesis of the controller using standard mathematical procedures.