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Complicacies of calculating algorithms in control optimization of dynamic objects


V. G. Kurbanov

Efficiency of DO control methods is normally associated with possibility of realization of these methods by means of computers in the form of algorithms for control functions. According to chosen quality of control criteria, algorithms of calculation of control functions can have different calculating difficulty. Thus, for instance, non-search algorithms based on methods with square criteria of quality provide computers with numeral integration vector-matrix equations and have simple logical part. Search algorithms based on methods of mathematical programming, on the contrary, have more complicated logical part. Non-search algorithms provide quality of control for stationary conditions with no account taken of non-linearities and limitations for state and control vectors, and search algorithms provide quality of control for non-stationary conditions and with account taken of limitations. Evidently, search algorithms are able to provide higher quality of control but it is difficult to perform them on computers. Complicacy of implementation of algorithms is conditional on strict request to the time of their performing on computers, which is usual for the real-time systems. In other words, algorithms are to be performed on computers for strictly defined time which is called quantization of control influence (action) time. If we understand DO control quality as maximal or root-mean-square value of accuracy, under given values of control and disturbing influence, and considering non-linearity, limitations for state and control vectors, it is obvious that the same property can be provided by various methods and corresponding to them algorithms. Then, the most effective is going to appear a method which algorithm has the least complicacy. The essence of this method is that characteristic feature of uncon-ventional calculating algorithms is that they can be represented in two parts. The part, where calculating procedures, calculating complicacy of which is known, are performed successively. And the logical part, which uses calculation results of the first part for making one or several logical steps for calculating of logical function vector. Logical function attributes in a capacity of initial conditions (or feedback) are given firstly for carrying out following iteration. The process lasts till values of attributes a logical functions vector satisfy given conditions. Thus, it is necessary to be able to identify complicacies of calculating of control influences for the comparative assessment of the effectiveness of control methods.
June 24, 2020
May 29, 2020

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