Group Regional Consensus of Networked Lagrangian Systems With Input Disturbances

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Jun Liu ◽  
Zhonghua Miao ◽  
Jinchen Ji ◽  
Jin Zhou
Keyword(s):  
Control Algorithm ◽  
Sufficient Conditions ◽  
Coordinated Control ◽  
Multirobot Systems ◽  
Lagrangian Systems ◽  
Parametric Uncertainties ◽  
Lagrangian Dynamics ◽  
Numerical Examples ◽  
The Stability ◽  
Networked Lagrangian Systems

Networked multirobot systems under the coordinated control can perform tasks more effectively than a group of individually operating robots. This paper studies the group regional consensus of networked multirobot systems (formulated by second-order Lagrangian dynamics) having input disturbances under directed acyclic topology. An adaptive control protocol is designed to achieve group regional consensus of the networked Lagrangian systems with parametric uncertainties for both leader and leaderless cases. Sufficient conditions are established to guarantee group regional consensus for any prior given desired consensus errors. Compared with the existing work, a distinctive feature of the proposed control algorithm is that the stability analysis indicates the global validity of the obtained consensus results. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.

scholarly journals Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model

2016 ◽  
Vol 26 (4) ◽  
pp. 441-452 ◽  
Author(s):  
Andrzej Ruszewski
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
New Model ◽  
The Stability ◽  
Partition Method ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Linear Scalar

Abstract The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.

scholarly journals Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yuangong Sun ◽  
Zhaorong Wu ◽  
Fanwei Meng
Keyword(s):  
Stability Analysis ◽  
Complex Systems ◽  
Linear Systems ◽  
Algebraic Structure ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov functions play a key role in the stability analysis of complex systems. In this paper, we study the existence of a class of common weak linear copositive Lyapunov functions (CWCLFs) for positive switched linear systems (PSLSs) which generalize the conventional common linear copositive Lyapunov functions (CLCLFs) and can be used as handy tool to deal with the stability of PSLSs not covered by CLCLFs. We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained results.

scholarly journals Formation Control of Robotic Swarm Using Bounded Artificial Forces

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Long Qin ◽  
Yabing Zha ◽  
Quanjun Yin ◽  
Yong Peng
Keyword(s):  
Formation Control ◽  
Control Algorithm ◽  
Stability And Convergence ◽  
Multirobot Systems ◽  
Convergence Properties ◽  
Swarm Behavior ◽  
Detailed Simulation ◽  
Robotic Swarm ◽  
The Stability ◽  
Significant Attention

Formation control of multirobot systems has drawn significant attention in the recent years. This paper presents a potential field control algorithm, navigating a swarm of robots into a predefined 2D shape while avoiding intermember collisions. The algorithm applies in both stationary and moving targets formation. We define the bounded artificial forces in the form of exponential functions, so that the behavior of the swarm drove by the forces can be adjusted via selecting proper control parameters. The theoretical analysis of the swarm behavior proves the stability and convergence properties of the algorithm. We further make certain modifications upon the forces to improve the robustness of the swarm behavior in the presence of realistic implementation considerations. The considerations include obstacle avoidance, local minima, and deformation of the shape. Finally, detailed simulation results validate the efficiency of the proposed algorithm, and the direction of possible futrue work is discussed in the conclusions.

scholarly journals Leader-Following Regional Multiple-Bipartite Consensus for Networked Lagrangian Systems with Coopetition Interactions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 920
Author(s):  
Tiehui Zhang ◽  
Hengyu Li ◽  
Zhaoyan Wang ◽  
Shaorong Xie
Keyword(s):  
Auxiliary Variable ◽  
Cooperative Networks ◽  
Lagrangian Systems ◽  
Final States ◽  
Analysis Theory ◽  
Nonlinear Control Theory ◽  
Leader Following ◽  
Bipartite Consensus ◽  
The Stability ◽  
Networked Lagrangian Systems

This paper investigates the leader-following regional multiple-bipartite consensus problems of networked Lagrangian systems (NLSs) in coopetition networks. Our framework expands the application scopes of traditional regional consensus in cooperative networks. With the aid of a novel auxiliary variable embedded in the control protocols, the final states of NLSs are guaranteed to realise multi-regional symmetry in the constructed multiple symmetric regions. By utilising the characteristic of acyclic topology in the structurally balanced graph, the stability of the closed system is performed by perturbation analysis theory, nonlinear control theory, functional analysis theory, and so on. Finally, the effectiveness of our approach is verified by numerical simulations.

scholarly journals Some Numerical Examples on the Stability of Fractional Linear Dynamical Systems

2018 ◽  
Vol 17 (3) ◽  
pp. 51-66
Author(s):  
S Priyadharsini
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Linear Models ◽  
Sufficient Conditions ◽  
Characteristic Polynomials ◽  
Caputo Fractional Derivatives ◽  
Linear Dynamical Systems ◽  
Numerical Examples ◽  
Eigen Values ◽  
The Stability

The concept of stability of a class of fractional-order linear system is considered in this paper. Existing sufficient conditions are assumed to guarantee the stability of linear models with the Caputo fractional derivatives. The results have been developed by using the concept of Laplace transform, and approximations of Mittag-Leffler.  Furthermore, results concerning asymptotical stability of linear fractional-order models are also achieved. The proposed method is based upon Eigen values and the characteristic polynomials. Numerical illustrations are specified to exhibit effectiveness of the proposed method.

scholarly journals Dynamics in a Delayed Competition System on a Weighted Network

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yaohua Tong ◽  
Xiaoling Wang
Keyword(s):  
Steady State ◽  
Time Delays ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Weighted Network ◽  
Competition System ◽  
Numerical Examples ◽  
Competitive Systems ◽  
Positive Steady States ◽  
The Stability

In this paper, we study the stability of positive steady states in a delayed competition system on a weighted network, which does not satisfy the comparison principle appealing to classical competitive systems. By introducing some auxiliary equations and constructing proper contracting rectangles, we present some sufficient conditions on the stability of the unique positive steady state. Moreover, some numerical examples are given to explore the complex dynamics of this nonmonotone model, which implies the nontrivial roles of weights and time delays.

scholarly journals New stability conditions for positive continuous-discrete 2D linear systems

2011 ◽  
Vol 21 (3) ◽  
pp. 521-524 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stability Conditions ◽  
Stability Tests ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

New stability conditions for positive continuous-discrete 2D linear systemsNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

scholarly journals Robust Nonfragile Controllers Design for Fractional Order Large-Scale Uncertain Systems with a Commensurate Order1<α<2

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianyu Lin
Keyword(s):  
Fractional Order ◽  
Uncertain Systems ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Order System ◽  
Lyapunov Inequality ◽  
Numerical Examples ◽  
Decentralized Stabilization ◽  
Controller Gain ◽  
The Stability

The paper concerns the problem of stabilization of large-scale fractional order uncertain systems with a commensurate order1<α<2under controller gain uncertainties. The uncertainties are of norm-bounded type. Based on the stability criterion of fractional order system, sufficient conditions on the decentralized stabilization of fractional order large-scale uncertain systems in both cases of additive and multiplicative gain perturbations are established by using the complex Lyapunov inequality. Moreover, the decentralized nonfragile controllers are designed. Finally, some numerical examples are given to validate the proposed method.

Robust stability and stabilization of uncertain fractional order systems subject to input saturation

2017 ◽  
Vol 24 (16) ◽  
pp. 3676-3683 ◽  
Author(s):  
Esmat Sadat Alaviyan Shahri ◽  
Alireza Alfi ◽  
JA Tenreiro Machado
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
State Feedback ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
Stability And Stabilization ◽  
The Stability ◽  
Robust Stability And Stabilization

This paper studies the stability and the stabilization for a class of uncertain fractional order (FO) systems subject to input saturation. The Lipschitz condition and the Gronwall–Bellman lemma are adopted and sufficient conditions are derived to stabilize systems by designing a state feedback controller. Numerical examples demonstrate the effectiveness of the proposed method.

scholarly journals Second-Order Containment Control of Multiagent Systems in the Presence of Uncertain Topologies with Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Fuyong Wang ◽  
Hongyong Yang ◽  
Zhongxin Liu ◽  
Zengqiang Chen
Keyword(s):  
Multiagent Systems ◽  
Control Algorithm ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Matrix ◽  
Time Varying ◽  
Containment Control ◽  
Communication Topology ◽  
The Stability ◽  
Switching Communication Topologies

This paper considers the containment control problem of second-order multiagent systems in the presence of time-varying delays and uncertainties with dynamically switching communication topologies. Moreover, the control algorithm is proposed for containment control, and the stability of the proposed containment control algorithm is studied with the aid of Lyapunov-Krasovskii function when the communication topology is jointly connected. Some sufficient conditions in terms of linear matrix inequalities (LMIs) are provided for second-order containment control with multiple stationary leaders. Finally, simulations are given to verify the effectiveness of the obtained theoretical results.

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