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Mekhatronika, Avtomatizatsiya, Upravlenie, 2018, vol. 19, no. 1, pp. 19—25
DOI: 10.17587/mau.19.19-25

Optimal Terminal Control by Linear Discrete Systems with Use of Matrices Pseudoinversion

V. T. Matvienko, matvienko.vt@gmail.com, National Taras Shevchenko University, Kyiv, 01033, Ukraine

Corresponding author: Matvienko Vladimir T., Ph. D., Associate Professor Faculty of Computer Science and Cybernetics, of National Taras Shevchenko University,
Kyiv, Ukraine, e-mail: matvienko.vt@gmail.com

Accepted on August 07, 2017

In this paper obtain the general solution of terminal control problem with a set of initial perturbations. Propose conditions of the general solution existence to discrete linear control systems. Also give the optimal solution of the terminal control problem minimizing the distance between the trajectory and fixed points. Constraints on the trajectory of the system are selected for certain points. Describe the set of all solutions to the control problem of trajectories ensemble with discrete time. The problem of optimal displacement of a discrete system from the initial state to the final one is solved. The problem of optimal displacement of a discrete system from the initial state to the final state with restriction to phase coordinates is solved. The trajectory of the system with optimal terminal control will pass next to the predefined points. The problem of control a set of trajectories for linear discrete systems is formulated and solved. The obtained control of the set trajectories is optimal. Necessary and sufficient conditions for solving this problem are obtained. Consideration is given to the mathematical problem on constructing general solutions of the problem concerning the terminal control for the set of initial perturbations. The existence conditions of the general solution of this problem for linear dynamic systems with the discrete argument is given. The obtained function of control is based on filtration of linearly independent rows and columns of the matrix. The optimal controls for linear dynamic discrete systems will solve of practical important problems.
Keywords: optimal, linear discrete systems, pseudoinversion, set of all solutions.

For citation:
Matvienko V. T. Optimal Terminal Control by Linear Discrete Systems with Use of Matrices Pseudoinversion, Mekhatronika, Avtomatizatsiya, Upravlenie, 2018, vol. 19, no 1, pp. 19—25.

DOI: 10.17587/mau.19.19-25

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