Control in linear systems with “expenditure” criteria. On the eigenvalue multiplicity case.
"Математика. Компьютер. Образование". Cб. трудов XII международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2005. Vol. 2, 466pp. Pp. 554-567.
The controlled motion which is represented by the linear ODE system is considered. Here matrix of the system is a constant with real valued coefficients. The initial value is given. The control is supposed to belong to the class of piecewise constant functions of t along the interval [0, T]. The admissible controls satisfy the condition that all the terms of solution corresponding to some selected eigenvalues of the matrix of the system should be equal to zero at the moment t=T . The problem under consideration is to construct an admissible control which minimizes “The Expenditure”.