Connectability-Based Controllability of Large Scale Nonlinear Dynamic Thermal Systems

2009 ◽  
Author(s):  
Rahmat Shoureshi ◽  
Virdi Permana
Keyword(s):  
Graph Theory ◽  
Nonlinear Systems ◽  
Lie Algebra ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Rank Condition ◽  
Thermal Systems ◽  
Necessary And Sufficient ◽  
Controllability And Observability

A new approach using graph-theory to determine the controllability and observability of large scale nonlinear dynamic thermal systems is presented. The novelty of this method is in adapting graph theory for a nonlinear class and establishing graphic conditions that describe the necessary and sufficient conditions for a class of nonlinear systems to be controllable and observable which is equivalent to the analytical method of Lie algebra rank condition. Graph theory of directed graph (digraph) is utilized to model the system and its adaptation to nonlinear problems is defined. The necessary and sufficient conditions for controllability are investigated through the structural property of a digraph called connectability. In comparison to the Lie Algebra, this approach has proven to be easier, from a computational point of view, thus it is found to be useful when dealing with large scale systems. This paper presents the problem statement, properties of structured system, and analytical method of Lie algebra rank condition for controllability and observability of bilinear systems. The main results of graphical approach which describe the necessary and sufficient conditions for controllability of nonlinear systems are presented and applied to the problem of a coupled two heat exchangers, connected in an arbitrary fashion.

scholarly journals Controllability and Observability of a Large Scale Thermodynamical System via Connectability Approach

2010 ◽  
Author(s):  
Virdiansyah Permana ◽  
Rahmat Shoureshi
Keyword(s):  
Graph Theory ◽  
Lie Algebra ◽  
Large Scale ◽  
Point Of View ◽  
Rank Condition ◽  
Computational Point ◽  
New Approach ◽  
Class System ◽  
Necessary And Sufficient ◽  
Controllability And Observability

This study presents a new approach to determine the controllability and observability of a large scale nonlinear dynamic thermal system using graph-theory. The novelty of this method is in adapting graph theory for nonlinear class and establishing a graphic condition that describes the necessary and sufficient terms for a nonlinear class system to be controllable and observable, which equivalents to the analytical method of Lie algebra rank condition. The directed graph (digraph) is utilized to model the system, and the rule of its adaptation in nonlinear class is defined. Subsequently, necessary and sufficient terms to achieve controllability and observability condition are investigated through the structural property of a digraph called connectability. It will be shown that the connectability condition between input and states, as well as output and states of a nonlinear system are equivalent to Lie-algebra rank condition (LARC). This approach has been proven to be easier from a computational point of view and is thus found to be useful when dealing with a large system.

PBW deformations of quantum symmetric algebras and their group extensions

2016 ◽  
Vol 15 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Piyush Shroff ◽  
Sarah Witherspoon
Keyword(s):  
Finite Group ◽  
Lie Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group Extensions ◽  
Enveloping Algebra ◽  
Symmetric Algebras ◽  
Necessary And Sufficient ◽  
Special Case

We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of the necessary and sufficient conditions on parameter functions to define a quantum Drinfeld orbifold algebra, thus clarifying the conditions. In case the acting group is trivial, we determine conditions under which such a PBW deformation is a generalized enveloping algebra of a color Lie algebra; our PBW deformations include these algebras as a special case.

AN W ALGEBRAS AND CLASSIFICATION

1992 ◽  
Vol 07 (36) ◽  
pp. 3419-3423
Author(s):  
LIU CHAO ◽  
BOYU HOU
Keyword(s):  
Lie Algebra ◽  
Regular Element ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Arbitrary Degree ◽  
Wznw Model ◽  
Necessary And Sufficient

The necessary and sufficient conditions for the existence of a regular element of arbitrary degree under arbitrary integral gradation of the Lie algebra g is presented. Such elements, while chosen as constraints in WZNW model, give rise to a W-algebra. It is then found that there might be some isomorphic relations between different W-algebras. The necessary conditions for such isomorphisms to appear are also given. Up to the A4 cases these conditions are checked to be sufficient.

scholarly journals Graded modules over simple Lie algebras

2019 ◽  
Vol 53 (supl) ◽  
pp. 45-86
Author(s):  
Yuri Bahturin ◽  
Mikhail Kochetov ◽  
Abdallah Shihadeh
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Simple Lie Algebras ◽  
Simple Modules ◽  
Graded Modules ◽  
Finite Dimensional ◽  
Necessary And Sufficient

The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra sl2(C), we consider specific gradings on simple modules of arbitrary dimension.

scholarly journals Absolute stability of a class of fractional positive nonlinear systems

2019 ◽  
Vol 29 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Time Systems ◽  
The Absolute ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

scholarly journals A remark on irreducible representations of Lie algebras

1979 ◽  
Vol 27 (3) ◽  
pp. 332-336 ◽  
Author(s):  
JU. A. Bahturin
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Irreducible Representations ◽  
Bounded Degree ◽  
Precise Form ◽  
Representations Of Lie Algebras ◽  
Necessary And Sufficient

AbstractIn addition to the results of the paper (Bachturin (1974)) we give the precise form of the necessary and sufficient conditions ensuring that all irreducible representations of a Lie algebra were of finite bounded degree.

scholarly journals Post-Lie algebra structures for nilpotent Lie algebras

2018 ◽  
Vol 28 (05) ◽  
pp. 915-933
Author(s):  
Dietrich Burde ◽  
Christof Ender ◽  
Wolfgang Alexander Moens
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Nilpotent Lie Algebras ◽  
Dimension Formula ◽  
Necessary And Sufficient

We study post-Lie algebra structures on [Formula: see text] for nilpotent Lie algebras. First, we show that if [Formula: see text] is nilpotent such that [Formula: see text], then also [Formula: see text] must be nilpotent, of bounded class. For post-Lie algebra structures [Formula: see text] on pairs of [Formula: see text]-step nilpotent Lie algebras [Formula: see text] we give necessary and sufficient conditions such that [Formula: see text] defines a CPA-structure on [Formula: see text], or on [Formula: see text]. As a corollary, we obtain that every LR-structure on a Heisenberg Lie algebra of dimension [Formula: see text] is complete. Finally, we classify all post-Lie algebra structures on [Formula: see text] for [Formula: see text], where [Formula: see text] is the three-dimensional Heisenberg Lie algebra.

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