Abstract:
The paper considers non-local control and optimal control problems for a linear time-varying dynamic system described by an ordinary differential equation with undivided multipoint conditions and with an integral condition imposed on the components of the state vector in some part of the time interval of the system operation. For the problem of optimal control, it is assumed that the quality criterion is specified over the whole time interval of system operation and has the meaning of the norm of some normed space. Conditions for complete controllability of a dynamic system with imposed non-local conditions are formulated. Conditions are obtained under which a solution to the control problem with such nonlocal conditions exists, and this solution is constructed. A constructive approach to solving control problems and a method for constructing an optimal control function are proposed. Continuity and non-uniqueness of the control function are shown. A solution to a specific control problem is given as an illustration.
Keywords:dynamic system, undivided multipoint condition, integral condition, nonlocal control problem, optimal control, complete controllability
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