Optimālās vadības uzdevums sistēmām ar nobīdi
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Latvijas Universitāte
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Abstract
Darbā aplūkota parasto diferenciālvienādojumu sistēma ar nobīdi, kura ir atkarīga no vadības. Vienādojumu sistēmas ir specifiska ar to, ka sistēmas labā puse ir atkarīga no atrisinājuma uzvedības vesela laika segmentā [t-h; t].
Tiek sniegts atrisinājuma eksistences pierādījums, parādīts, ka vadības funkcijas izvēle, koncentrējot segmentu [t-h; t] dažādās daļās būtiski ietekmē sistēmas atrisinājumu.
Tiek sniegts attiecīgs ilustratīvais materiāls.
This work considers a system of ordinary differential equations with delay. The specific is that right hand side of the system depends on values of the state in a whole segment [t-h, t] and a control function , which represents, in some sense, the importance of different parts of the segment [t-h, t]. The theorem of the existence of a solution of such systems is obtained and there is shown that state continuously depends on the control . Illustration of such dependence is also given.
This work considers a system of ordinary differential equations with delay. The specific is that right hand side of the system depends on values of the state in a whole segment [t-h, t] and a control function , which represents, in some sense, the importance of different parts of the segment [t-h, t]. The theorem of the existence of a solution of such systems is obtained and there is shown that state continuously depends on the control . Illustration of such dependence is also given.