3 research outputs found
ΠΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ΅ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ Π½Π΅ΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΡΠΌ ΡΠ΅ΠΆΠΈΠΌΠΎΠΌ ΠΊΠ°ΡΠΊΠ°Π΄Π½ΠΎΠ³ΠΎ ΡΠ΅ΡΠΌΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΎΡ Π»Π°Π΄ΠΈΡΠ΅Π»Ρ
ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ ΡΠΏΠΎΡΠΎΠ± ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΎΠ±ΡΠ΅ΠΊΡΠΎΠΌ Ρ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠΌΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°ΠΌΠΈ, ΠΊΠΎΡΠΎΡΡΠΉ ΠΎΠΏΠΈΡΡΠ²Π°Π΅ΡΡΡ ΡΠΈΡΡΠ΅ΠΌΠΎΠΉ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ
Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΏΠ°ΡΠ°Π±ΠΎΠ»ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΈΠΏΠ° Ρ Π½Π΅ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΡΠΌΠΈ Π³ΡΠ°Π½ΠΈΡΠ½ΡΠΌΠΈ ΡΡΠ»ΠΎΠ²ΠΈΡΠΌΠΈ. Π‘ΠΏΠΎΡΠΎΠ± Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π² Π΄ΠΈΡΠΊΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΠΈ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π΅ ΠΊ ΠΎΠ±ΡΠ΅ΠΊΡΡ Ρ ΡΠΎΡΡΠ΅Π΄ΠΎΡΠΎΡΠ΅Π½Π½ΡΠΌΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°ΠΌΠΈ, Π΄Π»Ρ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΊΠΎΡΠΎΡΠΎΠ³ΠΎ ΠΏΡΠΈΠΌΠ΅Π½ΡΠ΅ΡΡΡ ΠΏΡΠΈΠ½ΡΠΈΠΏ ΠΌΠ°ΠΊΡΠΈΠΌΡΠΌΠ° ΠΠΎΠ½ΡΡΡΠ³ΠΈΠ½Π°. Π’Π°ΠΊΠΎΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ Π΄Π»Ρ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ Π½Π΅ΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΠ΅ΡΠΌΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΎΡ
Π»Π°ΠΆΠ΄Π΅Π½ΠΈΡ. Π Π°ΡΡΡΠΈΡΠ°Π½Ρ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΡΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΡΠΎΠΊΠ° ΠΏΠΈΡΠ°Π½ΠΈΡ ΠΊΠ°ΡΠΊΠ°Π΄Π½ΠΎΠ³ΠΎ ΡΠ΅ΡΠΌΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠΎΠ΄ΡΠ»Ρ ΠΎΡ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ, ΠΊΠΎΡΠΎΡΡΠ΅ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ²Π°ΡΡ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡΠ½ΡΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ ΠΎΡ
Π»Π°ΠΆΠ΄Π΅Π½ΠΈΡ.ΠΠ°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΡΠΏΠΎΡΡΠ± ΡΠΎΠ·Π²βΡΠ·ΡΠ²Π°Π½Π½Ρ Π·Π°Π΄Π°ΡΡ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΊΠ΅ΡΡΠ²Π°Π½Π½Ρ ΠΎΠ±βΡΠΊΡΠΎΠΌ Π· ΡΠΎΠ·ΠΏΠΎΠ΄ΡΠ»Π΅Π½ΠΈΠΌΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°ΠΌΠΈ, ΡΠΎ ΠΎΠΏΠΈΡΡΡΡΡΡΡ ΡΠΈΡΡΠ΅ΠΌΠΎΡ Π½Π΅Π»iΠ½iΠΉΠ½ΠΈΡ
Π΄ΠΈΡΠ΅ΡΠ΅Π½ΡΡΠΉΠ½ΠΈΡ
ΡΡΠ²Π½ΡΠ½Ρ ΠΏΠ°ΡΠ°Π±ΠΎΠ»ΡΡΠ½ΠΎΠ³ΠΎ ΡΠΈΠΏΡ Π· Π½Π΅ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΠΈΠΌΠΈ ΠΊΡΠ°ΠΉΠΎΠ²ΠΈΠΌΠΈ ΡΠΌΠΎΠ²Π°ΠΌΠΈ. Π‘ΠΏΠΎΡΡΠ± ΠΏΠΎΠ»ΡΠ³Π°Ρ Ρ Π΄ΠΈΡΠΊΡΠ΅ΡΠΈΠ·Π°ΡΡΡ ΠΎΠ±βΡΠΊΡΡ Ρ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Ρ Π΄ΠΎ ΠΎΠ±βΡΠΊΡΠ° Π· Π·ΠΎΡΠ΅ΡΠ΅Π΄ΠΆΠ΅Π½ΠΈΠΌΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°ΠΌΠΈ, Π΄Π»Ρ ΠΎΠΏΡΠΈΠΌΡΠ·Π°ΡΡΡ ΡΠΊΠΎΠ³ΠΎ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΡΡΡΡΡ ΠΏΡΠΈΠ½ΡΠΈΠΏ ΠΌΠ°ΠΊΡΠΈΠΌΡΠΌΡ ΠΠΎΠ½ΡΡΡΠ³ΡΠ½Π° Π’Π°ΠΊΠΈΠΉ ΠΌΠ΅ΡΠΎΠ΄ Π·Π°ΡΡΠΎΡΠΎΠ²Π°Π½ΠΎ Π΄Π»Ρ ΠΎΠΏΡΠΈΠΌΡΠ·Π°ΡΡΡ Π½Π΅ΡΡΠ°ΡΡΠΎΠ½Π°ΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΡΠ΅ΡΡ ΡΠ΅ΡΠΌΠΎΠ΅Π»Π΅ΠΊΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΠΎΡ
ΠΎΠ»ΠΎΠ΄ΠΆΠ΅Π½Π½Ρ. Π ΠΎΠ·ΡΠ°Ρ
ΠΎΠ²Π°Π½ΠΎ ΠΎΠΏΡΠΈΠΌΠ°Π»ΡΠ½Ρ Π·Π°Π»Π΅ΠΆΠ½ΠΎΡΡΡ ΡΡΡΡΠΌΡ ΠΆΠΈΠ²Π»Π΅Π½Π½Ρ ΠΊΠ°ΡΠΊΠ°Π΄Π½ΠΎΠ³ΠΎ ΡΠ΅ΡΠΌΠΎΠ΅Π»Π΅ΠΊΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄ΡΠ»Ρ Π²ΡΠ΄ ΡΠ°ΡΡ, ΡΠΊΡ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΡΡΡΡ ΠΌΡΠ½ΡΠΌΠ°Π»ΡΠ½Ρ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ ΠΎΡ
ΠΎΠ»ΠΎΠ΄ΠΆΠ΅Π½Π½Ρ.The purpose of the present paper is to obtain optimality conditions and to develop numerical methods for solving the optimization problem of an unsteady one-dimensional process with distributed parameters, as well as their application to optimization of transient thermoelectric cooling. This method is applied for optimization of transient thermoelectric cooling process. Optimal dependences of current on time have been calculated for stage thermoelectric cooler power supply with the purpose of minimizing the cooling temperature within a preset time interval. Results of computer experiment for one- and two-stage coolers are presented
Optimal boundary control for hyperdiffusion equation
summary:In this paper, we consider the solution of optimal control problem for hyperdiffusion equation involving boundary function of continuous time variable in its cost function. A specific direct approach based on infinite series of Fourier expansion in space and temporal integration by parts for analytical solution is proposed to solve optimal boundary control for hyperdiffusion equation. The time domain is divided into number of finite subdomains and optimal function is estimated at each subdomain to obtain desired state with minimum energy. Proposed method has high flexibility so that decision makers are able to trace optimal control in a prescribed subinterval. The implementation of the theory is presented and the effectiveness of the boundary control is investigated by some numerical examples
ON THE CHERNOUS'KO TIME-OPTIMAL PROBLEM FOR THE EQUATION OF HEAT CONDUCTIVITY IN A ROD
The time-optimal problem for the controllable equation of heat conductivity in a rod is considered. By means of the Fourier expansion, the problem reduced to a countable system of one-dimensional control systems with a combined constraint joining control parameters in one relation. In order to improve the time of a suboptimal control constructed by F.L. Chernous'ko, a method ofΒ grouping coupled terms of the Fourier expansion of a control function is applied, and a synthesis of the improved suboptimal control is obtained in an explicit form