ارائه‌ی یک روش تکراری برای حل مسائل کنترل بهینه‌ی گسسته شامل سیستم‌های به ‌هم متصل غیرخطی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه آموزشی ریاضیات کاربردی، دانشکده علوم ریاضی و آمار، دانشگاه بیرجند، بیرجند، ایران

2 گروه آموزشی مهندسی برق، دانشکده فنی و مهندسی، دانشگاه بجنورد، بجنورد، ایران

چکیده

این مقاله ارائه دهنده‌ی یک روش تکراری برای حل مسائل کنترل بهینه‌ی‌ گسسته شامل سیستم‌های به ‌هم متصل غیرخطی می‌باشد. با این روش، مسأله‌ی مقدار مرزی گسسته و به ‌هم متصل غیرخطی، بدست آمده از شرایط لازم بهینگی، به دنباله‌ای از مسائل مقدار مرزی گسسته‌ی خطی نامتغیر با زمان تبدیل می‌شود. همچنین، مسأله‌ی مقدار مرزی خطی در هر تکرار از روش پیشنهادی شامل چندین زیرمسئله‌ی خطی جدا از هم بوده که بصورت موازی و مستقل از هم قابل حل می‌باشند. حل مسائل مذکور با استفاده از تکنیک‌های متداول یافتن پاسخ معادلات تفاضلی خطی منجر به قانون کنترل بهینه به‌ فرم سری‌ با همگرایی یکنواخت می‌گردد. بعلاوه، یک رویکرد کاربردی برای تعمیم کنترل بهینه‌ی طراحی شده به فرم فیدبک حالت ارائه می‌شود. در ادامه، پیاده سازی روش پیشنهادی با طراحی یک الگوریتم تکراری با دقت بالا و پیچیدگی محاسباتی کم انجام می‌شود بطوری که قانون کنترل زیر بهینه تنها با تعداد کمی ‌تکرار از این الگوریتم حاصل می‌شود. در نهایت، کارایی این روش با شبیه ‌سازی و حل چند مثال‌ عددی نشان داده می‌شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

An efficient iterative method for the optimal control of discrete nonlinear interconnected dynamical systems

نویسندگان [English]

  • Manijeh Hasanabadi 1
  • Asadollah Mahmoudzadeh Vaziri 1
  • Amin Jajarmi 2
1 Department of Mathematics, Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran
2 Department of Electrical Engineering, University of Bojnord, Bojnord, Iran
چکیده [English]

This article introduces an iterative method for solving discrete optimal control problems involving interconnected nonlinear systems. Using this approach, the discrete and coupled nonlinear boundary value problem (BVP) obtained from the necessary optimality conditions transforms into a sequence of linear time invariant BVPs. Furthermore, the linear BVP at each iteration of the proposed method consists of several decoupled sub-problems, which can be solved in parallel and are unrelated to each other. The solution of these problems, employing common techniques for solving linear difference equations, leads to an optimal control law in a converging series form with uniform convergence. Moreover, a practical approach is presented to extend the designed optimal control to a feedback form. Subsequently, the implementation of the proposed method involves the design of a highly accurate iterative algorithm with low computational complexity, ensuring that the suboptimal control law is obtained with a minimal number of iterations. Finally, the efficacy of this technique is demonstrated through simulation and the solution of various numerical examples.

کلیدواژه‌ها [English]

  • Nonlinear interconnected systems
  • optimal control
  • discrete equations
  • iterative method
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