توصيفگر ها :
ﮐﻨﺘﺮل ﺑﻬﯿﻨﻪ , ﺳﯿﺴﺘﻢ هايﺗﺄﺧﯿﺮي , ﺳﺮي ﻫﺎرﺗﻠﯽ , ﻣﺎﺗﺮﯾﺲ ﻋﻤﻠﯿﺎﺗﯽ اﻧﺘﮕﺮال , ﻣﺎﺗﺮﯾﺲ ﻋﻤﻠﯿﺎﺗﯽﺗﺄﺧﯿﺮ
چكيده فارسي :
در اين پايان‌نامه، يك روش عددي براي حل مسائل كنترل بهينه خطي تأخيري با تابعي معيار درجه دو ارائه شده است. روش پيشنهادي مبتني بر سري هارتلي است. ابتدا خواص و ويژگي‌هاي سري هارتلي بررسي شده است و سپس ماتريس‌هاي عملياتي انتگرال و تأخير متناظر با سري هارتلي محاسبه شده است. با استفاده از بسط متغيرهاي حالت و كنترل برحسب سري هارتلي و ماتريس‌هاي عملياتي انتگرال و تأخير ياد شده، مسأله كنترل بهينه تأخيري مورد مطالعه به يك مسأله بهينه‌سازي پارامتري تبديل شده است كه حل آن به مراتب ساده‌تر از حل مسأله اصلي است. به منظور ارزيابي دقت، كارآيي و قابليت كاربرد روش ارائه شده، مثال‌هاي متعددي بررسي و مطالعه شده است.
چكيده انگليسي :
The mathematical models associated to optimal control problems are formulated, for example, as systems of ordinary, partial, or stochastic differential equations or delayed dynamical systems, for both scalar and multi-criteria decision-making contexts. Time-delay equations are useful tools to express the dynamics of many control systems. Delays frequently occur in viscoelasticity, mechanics, incubation periods, population dynamics, physiology, information technologies, communication, and so on. The delay may appear in system state and (or) control vectors. Due to the undeniable presence of delay in most real-life phenomena, the control and especially TDOCPs have been of great importance to researchers. Although some delay systems have analytical methods to solve in general, analytical methods, especially in TDOCPs, have less implementation ability. On the contrary, the TDOCPs using the Pontryagin’s maximum principle result in a system of coupled two-point boundary value problems that involves both delays and advance terms. Finding the exact solution, except in exceptional cases, is very difficult. So different numerical approaches have been devised to overcome the problems arising from the applications of analytical methods The class of orthogonal functions and polynomial series have found wide applications such as in communication engineering, nuclear science, and engineering, digital protection of transmission lines, and digital signal processing Recently, considerable interest has been shown in applying these functions to a large number of diverse problems in the field of systems and control The approach for such kind of problem is that of converting the underlying differential equation governing the dynamical system to an algebraic form using an operational matrix of integration. The operational matrix based on the particular orthogonal functions can be determined uniquely. Worthwhile efforts have been paid to the applications of orthogonal functions for solving optimal control problems. In general, there are two methods for solving various types of optimal control problems which are known as indirect method and direct methods. The foundation of the indirect methods is based on the necessary conditions of optimality, the main idea of direct methods is to firstly discretize the optimal control problems under study and there solve the resulting parameter optimization problem. In this thesis, a direct method based on the Hartley series is presented for solving a class of time-delayed optimal control problems. The operational matrices of integration and delay corresponding to the Hartley series are used to convert the original optimal control problem to a parameter optimization problem. The main idea is converting such TDOCPs into a system of algebraic equations. Thus, we first expand the state and control variables in terms of the Hartley series with undetermined coefficients. The delay terms in the problem under consideration are expanded in terms of the Hartley series. Applying the operational matrices of the Hartley series including integration, differentiation, dual, product, delay, and substituting the estimated functions into the cost function, the given TDOCP is reduced to a system of algebraic equations to be solved. The convergence of the proposed method is extensively investigated. At last, the precision and applicability of the proposed method is studied through different types of numerical examples.
