Abstract
The optimal control of bilinear systems with aftereffect is considered. A class of systems is identified for which the optimal control is constructed by solving linear differential equations. Recursive formulas are derived for this solution. As an example, we analyse a bilinear model with aftereffect of the process of bacterial growth in a microbiological controlled environment. A system is usually called bilinear if the evolution equations are linear in the phase coordinates for fixed controls and in the controls for fixed coordinates /1, 2/. Systems of this kind are used for modelling a variety of control processes, including processes in biological systems /3–5/, etc.
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