ON ONE ABSTRACT CONTROL SYSTEM WITH MEMORY IN FEEDBACK

Many real control systems of different nature have the property of memory – when future states cannot be predicted without taking into account how the system arrived at the current state. In mathematical description, this effect can indicate itself both in the equations of state and in expressions for feedback control. A characteristic feature of memory is the presence of integral operators of the Volterra type in the system equations. In this paper, some properties of integro-differential equations describing one class of abstract control systems with memory in feedback are investigated. The existence and uniqueness of a solution to the system equations are proved, and the impossibility of blowing up the solution in a finite time in the linear case is shown. A class of feedback kernels is identified that allows a transition to a memoryless model due to the introduction of additional controls.