طراحی کنترل بهینه برای سیستم های منفرد خطی نامتغیر با زمان با استفاده از توابع متعامد

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه مهندسی کامپیوتر، دانشکده فنی و مهندسی، واحد قوچان، دانشگاه آزاد اسلامی، قوچان، ایران.

2 گروه مهندسی کامپیوتر، دانشکده فنی و مهندسی، واحد قوچان، دانشگاه آزاد اسلامی، قوچان، ایران.

چکیده

حل مسائل کنترل بهینه‌یسینگولار به‌روش کلاسیک دارای پیچیدگی­‌بهینه‌سازیی است که برای ساده‌تر‌شدن حل این گونه مسائل با  تقریب توابع موجود در مسئله با پایه‌ی ‌بهینه‌سازی متعامد به‌جای حل دستگاه معادله‌ی دینامیکی یک سری مسئله‌ی استاتیکی حل می‌شود. این مقاله با استفاده از خصوصیات عملگر‌بهینه‌سازی ماتریسیویولت لژاندر و سری فوریه الگوریتمی ارائه شده است. در‌این الگوریتم متغیر‌بهینه‌سازی حالت، متغیر‌بهینه‌سازی مشتق حالت و بردار کنترل توسط پایه‌ی ‌بهینه‌سازی متعامد یکه‌ی ویولت لژاندرو سری فوریه با ضرایب مجهول بسط داده شده است. برای محاسبه‌یبردار کنترل بهینه و مسیر بهینهی سیستم‌‌بهینه‌سازی سینگولارخطی با تابع هزینهی درجه دو معرفی شده است که با استفاده از خصوصیات توابع متعامد معرفی‌شده ارتباط بین ضرایب  و  پیدا می‌شود. با استفاده از روش پیشنهادی، دینامیک‌‌بهینه‌سازی سیستم به معادلات جبری تبدیل شده و مسئله‌ی بهینه‌سازیدینامیکی از فضای دینامیکی به فضای استاتیکی نگاشت داده شده است که باعث‌بهینه‌سازی مسئلهی استاتیکی با تابع هزینه‌یدرجه دوم و قید‌بهینه‌سازی خطی میشود. ابتدا برای حل مسئله با استفاده از این الگوریتم با پایه‌ی متعامد یکهی ویولت لژاندر استفاده شده است و سپس با پایهی متعامد سری فوریه، حل مسئله تکرار می شود.

کلیدواژه‌ها


عنوان مقاله [English]

Optimal control design for linear - invariant linear singular systems with time using orthogonal functions

نویسندگان [English]

  • Hamid Tabatabaee 1
  • Mahdi Memari 2
1 Department of Computer Engineering, Faculty of Engineering, Quchan branch, Islamic Azad University, Quchan, Iran.
2 Department of Computer Engineering, Faculty of Engineering, Quchan branch, Islamic Azad University, Quchan, Iran.
چکیده [English]

The problem of solving optimal control of Singular problems in the classic method has a complexity that is solved by approximation of the equations in the problem with orthogonal bases instead of solving the dynamic equation system of a set of static problems. In return for a more relaxed solution, it will face some errors in the computation .however, it has an appropriate precision. Legendre and Fourier series are presented using the specifications of the Fourier transform of Legendre and Fourier series . In this algorithm, the state variables, and the state - derivative variables and the control vector are extended by the orthogonal basis of Legendre and Fourier series with unknown coefficients. in order to compute optimal control vector and optimal path of linear Singular systems with quadratic cost function , we are introduced by using the properties of orthogonal functions introduced by the coefficients and .using the proposed method , the system dynamics are converted into algebraic equations and the problem of dynamic optimization of dynamic space has been mapped to static space optimization problem with quadratic cost function and linear constraints . First, it is used to solve the problem using an orthogonal basis of raw material and then the problem solving with orthogonal basis of Fourier series is repeated. Finally, the application and effectiveness of the proposed method are presented.

کلیدواژه‌ها [English]

  • Optimal control
  • Orthogonal Functions
  • Singular Matrix
  • Violet
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