Nonlinear analysis of dynamical complex networks

Copyright © 2013 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences

Realization of reactive control for multi purpose mobile agents

Mobile robots are built for different purposes, have different physical size, shape, mechanics and electronics. They are required to work in real-time, realize more than one goal simultaneously, hence to communicate and cooperate with other agents. The approach proposed in this paper for mobile robot control is reactive and has layered structure that supports multi sensor perception. Potential field method is implemented for both obstacle avoidance and goal tracking. However imaginary forces of the obstacles and of the goal point are separately treated, and then resulting behaviors are fused with the help of the geometry. Proposed control is tested on simulations where different scenarios are studied. Results have confirmed the high performance of the method

Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics

Similarity Decomposition Approach to Oscillatory Synchronization for Multiple Mechanical Systems With a Virtual Leader

This paper addresses the oscillatory synchronization problem for multiple uncertain mechanical systems with a virtual leader, and the interaction topology among them is assumed to contain a directed spanning tree. We propose an adaptive control scheme to achieve the goal of oscillatory synchronization. Using the similarity decomposition approach, we show that the position and velocity synchronization errors between each mechanical system (or follower) and the virtual leader converge to zero. The performance of the proposed adaptive scheme is shown by numerical simulation results.Comment: 15 pages, 3 figures, published in 2014 Chinese Control Conferenc

Decentralized Multi-Agent Formation Control with Pole-Region Placement via Cone-Complementarity Linearization

[EN] An output-feedback decentralised formation control strategy is pursued under pole-region constraints, assuming that the agents have access to relative position measurements with respect to a set of neighbors in a graph describing the sensing topology. No communication between the agents is assumed; however, a shared one-way communication channel with a pilot is needed for steering tasks. Each agent has a separate copy of the same controller. A virtual structure approach is presented for the formation steering as a whole; actual formation control is established via cone-complementarity linearization algorithms for the appropriate matrix inequalities. In contrast to other research where only stable consensus is pursued, the proposed method allows us to specify settling-time, damping and bandwidth limitations via pole regions. In addition, a full methodology for the decoupled handling of steering and formation control is provided. Simulation results in the example section illustrate the approachThe first author is grateful for the financial support via the grant GVA/2021/082 from Generalitat Valenciana. Part of the authors' research activity in related topics is funded via the grant PID2020-116585GB-I00 through MCIN/AEI/10.13039/501100011033 and by the European Union.González Sorribes, A.; Sala, A.; Armesto, L. (2022). Decentralized Multi-Agent Formation Control with Pole-Region Placement via Cone-Complementarity Linearization. International Journal of Applied Mathematics and Computer Science. 32(3):415-428. https://doi.org/10.34768/amcs-2022-003041542832

Distributed Adaptive Control for Nonlinear Heterogeneous Multi-agent Systems with Different Dimensions and Time Delay

A distributed neural network adaptive feedback control system is designed for a class of nonlinear multi-agent systems with time delay and nonidentical dimensions. In contrast to previous works on nonlinear heterogeneous multi-agent with the same dimension, particular features are proposed for each agent with different dimensions, and similar parameters are defined, which will be combined parameters of the controller. Second, a novel distributed control based on similarity parameters is proposed using linear matrix inequality (LMI) and Lyapunov stability theory, establishing that all signals in a closed loop system are eventually ultimately bounded. The consistency tracking error steadily decreases to a field with a small number of zeros. Finally, simulated examples with different time delays are utilized to test the effectiveness of the proposed control technique

Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators

This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents' poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result when compared to the literature on formation control. In order to illustrate the proposed pose consensus protocol and its extension to the problem of formation control, we present a numerical simulation with a large number of free-flying agents and also an application of cooperative manipulation by using real mobile manipulators

Synchronous MDADT-Based Fuzzy Adaptive Tracking Control for Switched Multiagent Systems via Modified Self-Triggered Mechanism

In this paper, a self-triggered fuzzy adaptive switched control strategy is proposed to address the synchronous tracking issue in switched stochastic multiagent systems (MASs) based on mode-dependent average dwell-time (MDADT) method. Firstly, a synchronous slow switching mechanism is considered in switched stochastic MASs and realized through a class of designed switching signals under MDADT property. By utilizing the information of both specific agents under switching dynamics and observers with switching features, the synchronous switching signals are designed, which reduces the design complexity. Then, a switched state observer via a switching-related output mask is proposed. The information of agents and their preserved neighbors is utilized to construct the observer and the observation performance of states is improved. Moreover, a modified self- triggered mechanism is designed to improve control performance via proposing auxiliary function. Finally, by analysing the re- lationship between the synchronous switching problem and the different switching features of the followers, the synchronous slow switching mechanism based on MDADT is obtained. Meanwhile, the designed self-triggered controller can guarantee that all signals of the closed-loop system are ultimately bounded under the switching signals. The effectiveness of the designed control method can be verified by some simulation results