SYSTEMS OF LINEAR CONTROLLED DIFFERENTIAL EQUATIONS WITH VARIABLE DIMENSION
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 1
Abstract
The article investigates the linear control system of variable dimension. The optimal control problem for several objects with a consistent in time mode of their operation is considered. The initial state of each object depends on the final state of the previous one and this unites them into a single system of variable dimension. It is assumed that each object is described by a system of ordinary differential equations in the interval of its operation. In this case, the lengths of the intervals are either given or unknown. The system of equations may have unequal dimensions, while the dimension of the control function and the restriction on its value can also vary. This system reduces to an impulse linear system containing controls and, therefore, the properties of the system solutions are repelled and the solutions themselves are found. Besides that, we consider the Mayer problem and obtain necessary and sufficient conditions for optimality. The obtained results are illustrated by examples.
Authors and Affiliations
O. D. Kichmarenko, A. A. Plotnikov
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