Average Consensus and Stability Analysis in Networked Dynamic Systems

2022 ◽  
Vol 21 ◽  
pp. 31-43
Author(s):  
Rhouma Mlayeh
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Systems ◽  
Autonomous Systems ◽  
Sufficient Conditions ◽  
Average Value ◽  
Lyapunov Techniques ◽  
Average Consensus ◽  
Highly Nonlinear ◽  
Networked Dynamic Systems ◽  
Fixed Topology

This paper provides protocols for finitetime average consensus and finitetime stability of systems with controlled nonlinear dynamics innetwork under undirected fixed topology. Each node’s state is a high dimensional vector as a solution of the highly nonlinear first order dynamics with and without drift terms. This paper provides protocols for finitetime average consensus and finitetime stability of systems with controlled nonlinear dynamics innetwork under undirected fixed topology. Each node’s state is high Under the proposed interaction rules, agreements as a common average value or an average trajectory are reached, solving finitetime average consensus and the multisystem equilibrium is controlled leading to the finitetime stability of each system origin. Sufficient conditions are achieved using the Lyapunov techniques and the graph theory. In networked dynamic systems, the theoretical results of the paper cover a large class of underactuated autonomous systems as formation flight, multivehicle coordination, and heterogeneous multisystem behaviors. Some examples are introduced in simulation which approves the proposed protocols.

scholarly journals Average Consensus in Networks of Neutral Dynamical Agents with Fixed and Switching Topologies

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yingying Wu ◽  
Yuangong Sun
Keyword(s):  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Switching Topology ◽  
Linear Matrix ◽  
Switching Topologies ◽  
Average Consensus ◽  
Eigenvalues Of The Laplacian ◽  
Fixed Topology ◽  
Necessary And Sufficient ◽  
Theoretical Results

This paper addresses the average consensus problem of neutral multiagent systems in undirected networks with fixed and switching topologies. For the case of fixed topology, necessary and sufficient conditions to average consensus are established by decoupling the neutral multiagent system in terms of the eigenvalues of the Laplacian matrix. For the case of switching topology, sufficient conditions to average consensus are given in terms of linear matrix inequalities to determine the allowable upper bound of the time-varying communication delay. Finally, two examples are worked out to explain the effectiveness of the theoretical results.

scholarly journals Further results on robust fuzzy dynamic systems with LMI D-stability constraints

2014 ◽  
Vol 24 (4) ◽  
pp. 785-794 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Local System ◽  
Linear Matrix ◽  
Fuzzy Modelling ◽  
Ts Fuzzy Model ◽  
Input Noise ◽  
Takagi Sugeno

Abstract This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

scholarly journals Nonlinear analysis of fluctuations of microcirculation parameters in symmetrical organs of humans by laser doppler flowmetry

2019 ◽  
Vol 17 (4) ◽  
pp. 33-38 ◽  
Author(s):  
L. V. Mezentseva
Keyword(s):  
Nonlinear Dynamics ◽  
Blood Flow ◽  
Laser Doppler Flowmetry ◽  
Coefficient Of Variation ◽  
Correlation Dimension ◽  
The Body ◽  
Doppler Flowmetry ◽  
Average Value ◽  
Flow Fluctuations ◽  
The Right

Purpose– the study the nonlinear dynamics of microcirculation parameters in human symmetrical organs.Material and Methods. Parameters of microcirculation were measured in healthy volunteers (aged between 50 and 70 years) by means of laser Doppler flowmetry (LDF). LDF signal transducers were fixed symmetrically on the lower parts of the right and left shoulders (3 cm above the elbow bend). The degree of chaoticity of microcirculation parameters as a nonlinear dynamic process was estimated using Hausdorff’s index, relative entropy and characteristics of phase portraits. Along with components of the amplitude-and-frequency range for blood flow fluctuations (myogenic, neurogenic, respiratory, and cardiac) was estimated and correlations between all characteristics of microcirculation in both sides of the body were done.Results.Asymmetry of correlation relationships of nonlinear dynamics parameters and components of the amplitude-andfrequency range for blood flow fluctuations of right and left sides of the body was revealed. Hausdorff index in the left side correlated not only with the average value of perfusion and with the coefficient of variation in the same side (r1 = –0,68; r2 =–0,51), but also with correlation dimension of chaos in the opposite side (r=0,49). Similarly, entropy in the left side correlated not only with the average value of perfusion and coefficient of variation in the left (r1 =0,43; r2 =0,60), but also with the entropy and correlation dimension of chaos in the right side (r1 =0,48; r2 =–0,41). The neurogenic component in the left side positively correlated with the myogenic component in the same side (r=0,71). A positive correlation was observed between the neurogenic component in right side and myogenic component in the opposite side (r=0,57). Asymmetry of correlation relationships was also revealed for the respiratory and cardiac components.Conclusions. Our results illustrate the specific regulation of blood flow in micro vessels of paired organs, which is associated with functional asymmetry. The physiological mechanisms for this asymmetry require further experimental and clinical studies. 

Equivalence of Lp Stability and Exponential Stability of Nonlinear Lipschitzian Semigroups

2012 ◽  
Vol 55 (4) ◽  
pp. 882-889
Author(s):  
Song Xueli ◽  
Peng Jigen
Keyword(s):  
Exponential Stability ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Nonlinear Dynamic Systems ◽  
Nonlinear Semigroup ◽  
Exponentially Stable ◽  
Lipschitzian Semigroup

AbstractLp stability and exponential stability are two important concepts for nonlinear dynamic systems. In this paper, we prove that a nonlinear exponentially bounded Lipschitzian semigroup is exponentially stable if and only if the semigroup is Lp stable for some p > 0. Based on the equivalence, we derive two sufficient conditions for exponential stability of the nonlinear semigroup. The results obtained extend and improve some existing ones.

scholarly journals Multiconsensus of Nonlinear Multiagent Systems with Intermittent Communication

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jie Chen ◽  
Guang-Hui Xu ◽  
Liang Geng
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Function ◽  
Multiagent Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Control Parameters ◽  
Numerical Examples ◽  
Relative Information ◽  
Loop Dynamics ◽  
Intermittent Communication

Compared with single consensus, the multiconsensus of multiagent systems with nonlinear dynamics can reflect some real-world cases. This paper proposes a novel distributed law based only on intermittent relative information to achieve the multiconsensus. By constructing an appropriate Lyapunov function, sufficient conditions on control parameters are derived to undertake the reliability of closed-loop dynamics. Ultimately, the availability of results is completely validated by these numerical examples.

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