Decentralized control and synchronization of time-varying complex dynamical network

summary:A new class of controlled time-varying complex dynamical networks with similarity is investigated and a decentralized holographic-structure controller is designed to stabilize the network asymptotically at its equilibrium states. The control design is based on the similarity assumption for isolated node dynamics and the topological structure of the overall network. Network synchronization problems, both locally and globally, are considered on the ground of decentralized control approach. Each sub-controller makes use of the information on the corresponding node's dynamics and the resulting overall controller is composed of those sub-controllers. The overall controller can be obtained by means of a combination of typical control designs and appropriate parametric tuning for each isolated node. Several numerical simulation examples are given to illustrate the feasibility and the efficiency of the proposed control design

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

This article presents an adaptive integral sliding mode control (SMC) design method for parameter identification and hybrid synchronization of chaotic systems connected in ring topology. To employ the adaptive integral sliding mode control, the error system is transformed into a special structure containing nominal part and some unknown terms. The unknown terms are computed adaptively. Then the error system is stabilized using integral sliding mode control. The controller of the error system is created that contains both the nominal control and the compensator control. The adapted laws and compensator controller are derived using Lyapunov stability theory. The effectiveness of the proposed technique is validated through numerical examples

Control of Networked Robotic Systems

With the infrastructure of ubiquitous networks around the world, the study of robotic systems over communication networks has attracted widespread attention. This area is denominated as networked robotic systems. By exploiting the fruitful technological developments in networking and computing, networked robotic systems are endowed with potential and capabilities for several applications. Robots within a network are capable of connecting with control stations, human operators, sensors, and other robots via digital communication over possibly noisy channels/media. The issues of time delays in communication and data losses have emerged as a pivotal issue that have stymied practical deployment. The aim of this dissertation is to develop control algorithms and architectures for networked robotic systems that guarantee stability with improved overall performance in the presence of time delays in communication. The first topic addressed in this dissertation is controlled synchronization that is utilized for networked robotic systems to achieve collective behaviors. Exploiting passivity property of individual robotic systems, the proposed control schemes and interconnections are shown to ensure stability and convergence of synchronizing errors. The robustness of the control algorithms to constant and time-varying communication delays is also studied. In addition to time delays, the number of communication links, which prevents scalability of networked robotic systems, is another challenging issue. Thus, a synchronizing control with practically feasible constraints of network topology is developed. The problem of networked robotic systems interacting with human operators is then studied subsequently. This research investigates a teleoperation system with heterogeneous robots under asymmetric and unknown communication delays. Sub-task controllers are proposed for redundant slave robot to autonomously achieve additional tasks, such as singularity avoidance, joint angle limits, and collision avoidance. The developed control algorithms can enhance the efficiency of teleoperation systems, thereby ameliorating the performance degradation due to cognitive limitations of human operator and incomplete information about the environment. Compared to traditional robotic systems, control of robotic manipulators over networks has significant advantages; for example, increased flexibility and ease of maintenance. With the utilization of scattering variables, this research demonstrates that transmitting scattering variables over delayed communications can stabilize an otherwise unstable system. An architecture utilizing delayed position feedback in conjunction with scattering variables is developed for the case of time-varying communication delays. The proposed control architecture improves tracking performance and stabilizes robotic manipulators with input-output communication delays. The aforementioned control algorithms and architectures for networked robotic systems are validated via numerical examples and experiments

Adaptive sliding mode observation in a network of dynamical systems

This paper considers the problem of reconstructing state information in all the nodes of a complex network of dynamical systems. The individual nodes comprise a known linear part and unknown but bounded uncertainties in certain channels of the system. A supervisory adaptive sliding mode observer configuration is proposed for estimating the states. A linear matrix inequality (LMI) approach is suggested to synthesise the gains of the sliding mode observer. Although deployed centrally to estimate all the states of the complex network, the design process depends only on the dynamics of an individual node of the network. The methodology is demonstrated by considering a network of Chua oscillators

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples

Impulsive Synchronization of Multilinks Delayed Coupled Complex Networks with Perturb Effects

This paper investigates impulsive synchronization of multilinks delayed coupled complex networks with perturb effects. Based on the comparison theory of impulsive differential system, a novel synchronization criterion is derived and an impulsive controller is designed simultaneously. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria

An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable