Problem of Optimal Management of Resources of Industrial Production with Given Statistical Data of Disturbance Parameter
A problem of optimum control with static quality function and with integral reachability criterion of a job for consuming control resources when perturbation distribution is known a priori has been formulated. It has been demonstrated that with the introd
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Problem of Optimal Management of Resources of Industrial Production with Given Statistical Data of Disturbance Parameters Ali Gasan Nagiev, Firuza Allahkuli Aliyeva and Hasan Ali Nagiyev
Abstract A problem of optimum control with static quality function and with integral reachability criterion of a job for consuming control resources when perturbation distribution is known a priori has been formulated. It has been demonstrated that with the introduction of a certain structure providing feedback the problem can be reduced to a problem of stabilizing a relation of weight coefficients for optimality and reachability criteria during a process with a terminating time. Synthesis of stabilizing Lagrangian function in feedback network is made. Results of numerical analysis are given. Keywords Stochastic systems · Optimization of planning Restriction on control resources
· A feedback system ·
83.1 Introduction A number of problems from practice of production planning and other spheres of controlling static states of objects at perturbation are distinguished for the presence of integral constraint in the from of equality on the consumption being planned for control resources. The necessity of attaining a predetermined value of sectionally continuous control function integral within the fixed time creates certain analogies to familiar problems of terminal control [1, 2, 4, 8, 11]. However, these analogies are only formal. Firstly, the terminal part in this problem represent not the final state of an object at any prescribed moment of time but some deviation of the integral A.G. Nagiev · F.A. Aliyeva Sumgayit State University, Block 43, Sumgayit, Azerbaijan H.A. Nagiyev (B) Institute of Control Systems of ANAS The Institute of Mathematics and Mechanics of ANAS, 9 F.Agayev Str., 370141 Baku, Azerbaijan e-mail: [email protected] © Springer Science+Business Media Singapore 2017 J. Xu et al. (eds.), Proceedings of the Tenth International Conference on Management Science and Engineering Management, Advances in Intelligent Systems and Computing 502, DOI 10.1007/978-981-10-1837-4_83
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from control function in the course of preset period of planning. And, moreover, in the given case it is necessary to optimize static states of an object defined not by a dynamic model but by some static dependence of an exit and entry of a system, and control. Problems with integral restrictions on control must be related to the problems which have not bean thoroughly tackled and considered so far. Only a research [5] that published recently can be taken as an example as the research directly concerned with this domain of problems. This paper raises the issue about the finding of optimal trajectory of movement of a dynamical system with a terminal restriction which is set in the form of an integral of control. Through introduction of a penalty function the authors manage to make a transition from unconditional optimization with a proof of the necessary conditions of optimality. However, in this paper the authors have for
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