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

Abstract

Abstract 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.