FINITE-DIMENSIONAL APPROXIMATION OF THE SOLUTION OF THE CONTROL PROBLEM WITH MINIMUM ENERGY BY THE PROCESS OF HEAT CONDUCTIVITY WITH PULSE IMPACT
Abstract
The paper considers an approximate solution of the control problem with the minimum energy for an object described by the heat conduction equation. In this case, the process is described by a linear parabolic equation and the system is controlled by impulse external influences.
The optimal control problem consists in determining a control parameter from the class of admissible controls such that the desired temperature distribution is achieved at the final time instant. In this case, the expenditure of energy, which is expressed by the quadratic functional, should be minimal.
References
2. DyhtaV.A., Samsonyuk O.N. Optimalnoe impulsnoe upravlenie s prilozheniyami. –M.: FIZMATLIT, 2003.-256 s.
3. Dyhta V.A. Princip maksimuma dlya optimalnyh impulsnyh processov pri ogranicheniyah na obraz upravlyayushej mery //Optimizaciya, upravlenie, intellekt. – Zhurn. Vseros. Assoc. Matem.programmirovaniyav ANN. – 1995, - №1. – S. 100-109.
4. Bressan A., Rampazzo F. Impulsive control system with commutative vector fields // J.Optim. Theory and Appl. – 1991. – V.71, №1. –P.67-83.
5. Bressan A., Rampazzo F. Impulsive control systems without commutativity assumptions // J.Optim. Theory and Appl. – 1994. – V.81, №3. –P.435-457.
6. Egorov A.I. Osnovy teorii upravleniya. M.: FIZMATLIT, 2004. – 504 s.
7. Egorov A.I. Optimalnoe upravlenie teplovymi i diffuzionnymi processami. M.: Nauka, 1978. -460 c.
8. Mamedov R.S. Pulse control of process of heat conductivity with minimal energy. The international Conference “Problems of cybernetics and informatics” Vol. II ,Baku 2006.
9. Mamedov R.S., Qasimov S.Y. Solution of the synthesis problem of boundary optimal rod cooling process with a heat conductive viscosity//“EUREKA” physics Enginering,24(2017), 42-49.
10. Abdullayev V.M. Identification of the function of response to loading for stationary systems // Cybern. Syst. Anal. 2017. Vol.53., No. 2, p. 417-425.
11. Aida-zade K.R., Abdullayev V.M.Control Synthesis for Temperature Maintaining Process in a Heat Supply Problem. // Cybern. Syst. Anal. 2020. Vol. 56, No.3, P.380-391.
12. Aida-zade K.R., Abdullayev V.M. Optimizing placement of the control points at synthesis of the heating process control // Autom. Remote Control, 2017. Vol. 78. No.9. P. 1585–1599.
CC BY-ND
A work licensed in this way allows the following:
1. The freedom to use and perform the work: The licensee must be allowed to make any use, private or public, of the work.
2. The freedom to study the work and apply the information: The licensee must be allowed to examine the work and to use the knowledge gained from the work in any way. The license may not, for example, restrict "reverse engineering."
2. The freedom to redistribute copies: Copies may be sold, swapped or given away for free, in the same form as the original.
