یک الگوریتم برای کنترل بهينه يك كلاس از سيستمهاي خطي متغير با زمان تأخیری با رویکرد کاهش زمان محاسبات و افزایش سرعت در مسائل مهندسی
محورهای موضوعی : مهندسی برق و کامپیوترمهدی یوسفی طبری 1 , زهرا رحمانی 2 * , علی وحیدیان کامیاد 3 , سیدجلیل ساداتی 4
1 - دانشکده مهندسی برق، دانشگاه صنعتی نوشیروانی بابل
2 - دانشکده مهندسی برق، دانشگاه صنعتی نوشیروانی بابل
3 - دانشکده علوم ریاضی، دانشگاه فردوسی مشهد
4 - دانشکده مهندسی برق، دانشگاه صنعتی نوشیروانی بابل
کلید واژه: کنترل بهینه, سیستم‌های تأخیری, اصل حداکثر پونتریاگین,
چکیده مقاله :
سیستم‌های تأخیر زمانی در چند دهه اخیر بسیار مورد توجه قرار گرفته‌اند و بسیاری از آنها در سیستم‌ها و شاخه‌های مختلف علوم مانند مهندسی، شیمی، فیزیک و مدل‌های بیماری ظاهر می‌شوند. وجود تأخیر، تحلیل و کنترل چنین سیستم‌هایی را بسیار پیچیده‌تر می‌کند. استفاده از اصل حداکثر پونتریاگین برای مسائل کنترل بهینه با تأخیر زمانی منجر به یک مسأله مقدار مرزی می‌شود که شامل هر دو شرایط تأخیر و تقدم است. در این مقاله، یک مسأله کنترل بهینه با تأخیر زمانی را در نظر می‌گیریم. در بخش اول ابتدا با استفاده از اصل حداکثر پونتریاگین برای مسائل کنترل بهینه با تأخیر زمانی، شرایط بهینه لازم را برای این مسأله به‌دست می‌آوریم و سپس الگوریتمی جدید برای حل عددی این مسأله ارائه می‌گردد که بر پایه یک تقریب برای مشتقات و درون‌یابی خطی برای جملات تأخیر است. نهایتاً معادلات حاصل به یک مسأله برنامه‌ریزی خطی تبدیل می‌شوند که می‌توان آنها را به‌صورت عددی حل نمود. کارايي روش پيشنهادی با شبیه‌سازی عددی مورد ارزیابی قرار می‌گیرد.
Time-delay systems have been very much considered in the last few decades. Many of these time-delay systems appear in different systems and branches of science such as engineering, chemistry, physics, disease models. The presence of delay makes the analysis and control of such systems much more complicated. In fact, the application of Pontryagin’s maximum principle to the optimal control problems with time-delay results in boundary value problem involving both delay and advance terms. In this paper, we consider a time-delay optimal control problems. The first section, using the Pontryagin's maximum principle for optimal control problems with time delay, the necessary optimality conditions for this problem, are obtained. Then a new algorithm is proposed to solve this problem numerically. This algorithm is based on an approximation for derivatives and linear interpolation for delayed arguments. Finally, the resulting equations becomes a linear programming problem that can be solved numerically. The efficiency of the proposed method is evaluated by solving several numerical examples.
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