Application of continuous dynamic programming equations to determine optimal control laws of automated systems

<ns0:p>The growing shortage of energy resources necessitates the search for effective technical means of reducing the energy intensity of technological systems and industrial installations, including in the agro-industrial complex, processing and utility industries. One of these solutions is the application of optimal control laws that allow saving energy and material resources.Among the methods of optimization of automatic systems, under certain conditions, the Bellman dynamic programming method in continuous form may be convenient for constructing closed-loop optimal control systems, which makes it possible to determine the optimal control law as a function of the initial coordinates of the control object. In this work, an electric drive loaded with a viscous friction torque is considered as a control object, which can be both the main load moment of some units and, much more often, a linear component of the motor resistance torque, which does not perform useful work, but causes energy consumption to overcome it.The purpose of this work is to justify the use of continuous Bellman dynamic programming equations to find optimal, according to the criterion of minimum energy losses, control laws for electromechanical objects using the example of electric drives operating under the action of a viscous friction moment.This justification is based on finding the conditions for the existence of analytical solutions to dynamic programming equations, obtaining and solving a system of differential equations of an electromechanical object in partial derivatives and solving these equations to find the optimal control law for the object as a function of its initial coordinates.</ns0:p>