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eBook details

• Title: Existence and Uniqueness of the Optimal Control in Hilbert Spaces for a Class of Linear Systems (Report)
• Author : Mihai Popescu
• Release Date : January 01, 2010
• Genre: Computers,Books,Computers & Internet,
• Pages : * pages
• Size : 90 KB

Description

1. Introduction A particular importance should be assigned to the analysis of the control of linear systems, since they represent the mathematical model for various dynamic phenomena. One of the fundamental problems is the functional optimization that defines the performance index of the dynamic product. Thus, under differential and algebraic restrictions, one determines the control corresponding to functional extremisation under consideration [1,2]. Variational calculation offers methods that are difficult to use in order to investigate the existence and uniqueness of optimal control. The method of determining the field of extremals (sweep method), that analyzes the existence of conjugated points across the optimal transfer trajectory (a sufficient optimum condition), proves to be a very efficient one in this context [3-5]. Through their resulting applications, time and energy minimization problems represent an important goal in system dynamics [6-11]. Recent results for controllable systems express the minimal energy through the controllability operator [11-13]. Also, stability conditions for systems whose energy tends to zero in infinite time are obtained in the literature [13,14]. By using linear operators in Hilbert spaces, in this study we shall analyze the existence and uniqueness of optimal control in transfer problems. The goal of this paper is to propose new methods for studying the optimal control for exactly controllable linear system. The minimization of time and energy in transfer problem is considered. The minimization of the energy can be seen as being a particular case of the linear regulator problem in automatics. Using the adjoint system, a necessary and sufficient condition for exact controllability is established, with application to the optimization of a broad class of Mayer-type functionals.

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