A novel method of topology identification for general complex dynamical networks with incomplete measurements

2018 ◽  
Vol 29 (05) ◽  
pp. 1840001
Author(s):  
Xinwei Wang ◽  
Guo-Ping Jiang ◽  
Xu Wu
Keyword(s):  
Linear Matrix Inequalities ◽  
Topological Structure ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Complex Dynamical Network ◽  
Topology Identification ◽  
Dynamical Network ◽  
General Complex ◽  
Novel Method ◽  
Mathematical Derivation

Recovering the topological structure of a general complex dynamical network with the incomplete measurements of transmitted drive states is investigated in this paper. The incomplete measurements, which cannot be ignored, have not been well considered in topology identification issue. Different from previous studies, we propose a novel method which can handle the situation of incomplete measurements well. The proposed method can fix the excessive deviation of the controller caused by the incomplete measurements, and overcome the special restrictions on the node dynamics raised by the previous methods. By means of LaSalle’s invariance principle, mathematical derivation of the mechanism is deduced rigorously to obtain the sufficient criteria in the form of linear matrix inequalities. Numerical simulations with the complex dynamical network composed of chaotic dynamical nodes are given to illustrate the effectiveness of our proposed method.

scholarly journals Input and Output Passivity of Complex Dynamical Networks with General Topology

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Jinliang Wang
Keyword(s):  
Linear Matrix Inequalities ◽  
General Topology ◽  
Linear Matrix ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Dynamical Network ◽  
Dynamical Network ◽  
Input And Output ◽  
Generalized Complex

The input passivity and output passivity are investigated for a generalized complex dynamical network, in which the coupling may be nonlinear, time-varying, and nonsymmetric. By constructing some suitable Lyapunov functionals, some input and output passivity criteria are derived in form of linear matrix inequalities (LMIs) for complex dynamical network. Finally, a numerical example and its simulation are given to illustrate the efficiency of the derived results.

Topological Identification of Complex Dynamical Network with Communities and Node Delay

2013 ◽  
Vol 411-414 ◽  
pp. 2093-2097
Author(s):  
Jiang Ang Zhang ◽  
Yan Dong Chu ◽  
Wen Ju Du
Keyword(s):  
Parameter Identification ◽  
Hierarchical Structure ◽  
Invariance Principle ◽  
Topological Structure ◽  
Complex Dynamical Networks ◽  
Complex Dynamical Network ◽  
Network Systems ◽  
Dynamical Network ◽  
General Complex ◽  
Real Complex

Recently, various papers investigated the topology identification and parameter identification of uncertain general complex dynamical networks. However, in many real complex dynamical network systems, there exists community or hierarchical structure and node delay. Based on LaSalle’s invariance principle, in this letter, an adaptive controlling method is proposed to identify unknown topological structure for general weighted complex dynamical network with community and node delay. Illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme.

Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

2018 ◽  
Vol 10 (10) ◽  
pp. 4-19
Author(s):  
Magomed G. GADZHIYEV ◽  
◽  
Misrikhan Sh. MISRIKHANOV ◽  
Vladimir N. RYABCHENKO ◽  
◽  
...  
Keyword(s):  
Power System ◽  
Electric Power ◽  
Linear Matrix Inequalities ◽  
Electric Power System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Power System Controllers

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Contractors and Linear Matrix Inequalities

2015 ◽  
Vol 1 (3) ◽  
Author(s):  
Jeremy Nicola ◽  
Luc Jaulin
Keyword(s):  
Fixed Point ◽  
Large Class ◽  
Linear Matrix Inequalities ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Constraints ◽  
Linear Matrix ◽  
Nonlinear Constraints ◽  
Matrix Inequalities ◽  
Convex Constraints

Linear matrix inequalities (LMIs) comprise a large class of convex constraints. Boxes, ellipsoids, and linear constraints can be represented by LMIs. The intersection of LMIs are also classified as LMIs. Interior-point methods are able to minimize or maximize any linear criterion of LMIs with complexity, which is polynomial regarding to the number of variables. As a consequence, as shown in this paper, it is possible to build optimal contractors for sets represented by LMIs. When solving a set of nonlinear constraints, one may extract from all constraints that are LMIs in order to build a single optimal LMI contractor. A combination of all contractors obtained for other non-LMI constraints can thus be performed up to the fixed point. The resulting propogation is shown to be more efficient than other conventional contractor-based approaches.

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