Robust Adaptive Synchronization of the Energy Resource System with Constraint

Abstract

Two different chaos synchronization methods are proposed for a class of energy resource demand supply-system with input constraint. Firstly, chaotic synchronization is achieved for a class of energy resource demand supply system with known system parameters based on the Lyapunov theory. Secondly, an adaptive control approach is investigated for a class of energy resource demand supply system with input constraint, and the parameters of the system are unknown based on the Lyapunov stability and robust adaptive theory. To address the input constraint, new auxiliary signals and design systems are employed. Numerical simulations are provided to illustrate the effectiveness of the proposed approach.

Adaptive Neural Networks Synchronization of a Four-Dimensional Energy Resource Stochastic System

“…In this section, external perturbations ( ) = ; uncertain nonlinear 1 ( 2 ) = 0.1 2 2 , 2 ( 2 ) = 0.1 It is worth pointing out that the method of [10] cannot be used to control the systems of this paper. There exist three reasons: (i) the system of this paper is four dimensional and the system in [10] is three dimensional; (ii) the system of this paper contains stochastic disturbances, and the system in [10] does not contain them; (iii) the controlled response system of this paper contains unknown nonlinearities, and [10] does not contain them.…”

“…where V is the actual controller to be designed and , then (3) becomes the chaotic systems studied widely, see [8,10], where (V ( )) can be described as…”

“…The proposed approaches in [1][2][3][4][5][6][7] assume that all the components of the considered energy resource demand-supply systems are in good operating conditions and do not consider the problem of saturation. Reference [10] proposed two different chaos synchronization methods for a class of energy resource demand-supply systems with input saturation, but the response system in [10] did not contain unknown uncertain nonlinearities and unknown stochastic disturbances. It is well known that stochastic disturbances also often exist in many practical systems.…”

“…Compared with the existing results, the main contributions of the proposed method are as follows: (i) the controlled response system of this paper contains unknown nonlinearities, and the proposed method can solve the unknown nonlinearity problem by neural networks, but the methods of [1][2][3][4][5][6][7][8]10] cannot solve this problem; (ii) the controlled response system of this paper contains stochastic disturbances, and the proposed method can solve the stochastic disturbances problem based on Itô's lemma and stochastic LaSalle's theorem, but the methods of [1][2][3][4][5][6][7][8]10] cannot solve this problem; (iii) an auxiliary design system is employed to address input constraints problem, and the methods of [1][2][3][4][5][6][7][8] can solve this problem.…”

Μελέτη Μεθόδων Χρήσης Χαοτικών Μη-Γραμμικών Συστημάτων Για Ασφαλή Τηλεπικοινωνιακά Συστήματα

“…Όπως έχει ήδη αναφερθεί, η δυνατότητα επίτευξης του συγχρονισμού μεταξύ δύο μη -γραμμικών συστημάτων είναι πρωταρχικής σημασίας, καθώς τα σύγχρονα αυτά συστήματα έχουν διάφορες εφαρμογές, π.χ. ως συστήματα διάχυσης φάσματος άμεσης ακολουθίας (direct sequence spread spectrum systems) [246], συστήματα ανανεώσιμων πηγών ενέργειας [247], [248], [249], συστήματα «multiagent» [250], [251], [252], ή ετερογενή δίκτυα με αβέβαιο οδηγό (heterogeneous network with an uncertain leader) [253]. Επιπροσθέτως, πρόσφατες εργασίες έχουν επικεντρωθεί σε μη -γραμμικά συστήματα, σε πολύπλοκα δίκτυα, καθώς και σε αποτελέσματα προερχόμενα από αναλύσεις βασισμένες στη θεωρία Lyapunov [254], [255], [256], [257].…”