Bogomas W. On optimization of one class dynamical systems with state constraints

The object is mathematical models of optimization problem of the nonlinear dynamical systems of concentrated type with state constraints. The aim is research of state constraints regularization problem in the optimization problems of the dynamical systems and construction algorithm of search effective control such systems. Methods are basic methods of functional analysis, theory of partial ordered spaces, theory of vector optimization, theory of optimal control. The scheme of relaxation of optimization problem for the dynamical systems with state constraints is proposed. The sufficient conditions of the existence efficient solutions to such problem are obtained, the notion of efficient regularizator and weakly regularizator, the sufficient conditions of the existence are obtained and algorithm of their construction for concrete kind of constraints are proposed. The construction of efficient solutions and regularizators for vector optimization problem the adaptive scalarization is proposed. The mathematical model of optimization problem dynamical system is built as a "oscillation skating rink - module". The construction of that was patented by an autor. Attracting the offered algorithm of regurization of state constraints, efficient controls are built such by a numeral design. Scope - machine building, industrial producting, the learning process.