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Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil

Benaoued Meriem, Bouagada Djillali

Journal of Applied Analysis

2022

Vol. 28, nr 2

251--261

The present research paper deals with the effectiveness of the control of an infinite-dimensional degenerate Cauchy problem with variable operator coefficients, skew-Hermitian pencil and bounded input condition. This study explores the minimum energy control problem. The investigation follows a set of methods to examine the procedure for developing a new result to solve the problem. Indeed, by the use of decomposition transformation of the considered system and the application of the Gramian operator, the formula of the process for controlling the system with minimum energy is obtained. Afterwards, a procedure to compute the optimal input for minimizing the performance index is then proposed. In a nutshell, the obtained results indicate that optimal control for minimizing the performance index ensures the solution of the minimum energy control of an infinite-dimensional degenerate Cauchy problem.

Minimum energy control of fractional positive continuous-time linear systems with bounded inputs

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2014

Vol. 24, no. 2

335--340

A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.