Optimal control of the behavior of solutions of an initial boundary value problem simulating rotation of a solid with an elastic rod

• Published in: Automatic control and computer sciences Vol. 49; no. 7; pp. 597 - 607
• Main Authors: Kubyshkin, E. P., Tryakhov, M. S.
• Format: Journal Article
• Language: English
• Published: New York Allerton Press 01.12.2015
• Subjects: Computer Science; Control Structures and Microprogramming; discrete-continuum mechanical system; optimal control; time control problem; initial boundary problem
• ISSN: 0146-4116; 1558-108X
• DOI: 10.3103/S0146411615070135

The paper discusses an initial boundary value problem simulating the rotation of a discretecontinuum mechanical system, which consists of a solid and rigidly connected elastic rod. For the initial boundary problem, the concept of the solution is determined and its existence, uniqueness, and continuous dependence on the initial conditions and parameters of the boundary problem are determined. The following control problems are solved: the problem of conversion of the solution from the initial phase state to the final one at a given time with the minimum of the norm of the control function in space L ∞ (0, T ) and the problem of the response rate under limitation of the norm of the control function in the specified space. The maximum principle is formulated, and an algorithm for optimal control of the simulation is proposed. The problem of moments is used as the investigation method.