Decentralised static output feedback stabilisation and synchronisation of networks

Dynamic multi-agent networks are important in a wide range of areas in science and engineering, including mobile sensor networks, distributed robotics such as underwater vehicles and cooperative unmanned air vehicles, biological synchronisation, networked economics and social networks. The paper makes a fundamental theoretical contribution to the field by blending methods from graph theory and control theory. [Impact Factor: 2.631, second highest of all Control Engineering journals]This is the author's pre-print. The definitive published version is available via doi:10.1016/j.automatica.2009.09.029In this paper global stabilisation of a complex network is attained by applying local decentralised output feedback control to a minimum number of nodes of the network. The stabilisation of the network is treated as a rank constrained problem. Strict positive realness conditions on the node level dynamics allow nonlinearities/uncertainties which satisfy the sector conditions to be considered. A network of Chua oscillators with 75 nodes is considered to demonstrate the efficacy of the approach

Stabilisation of Time Delay Systems with Nonlinear Disturbances Using Sliding Mode Control

This paper focuses on a class of control systems with delayed states and nonlinear disturbances using sliding mode techniques. Both matched and mismatched uncertainties are considered which are assumed to be bounded by known nonlinear functions. The bounds are used in the control design and analysis to reduce conservatism. A sliding function is designed and a set of sufficient conditions is derived to guarantee the asymptotic stability of the corresponding sliding motion by using the Lyapunov-Razumikhin approach which allows large time varying delay with fast changing rate. A delay dependent sliding mode control is synthesised to drive the system to the sliding surface in finite time and maintain a sliding motion thereafter. Effectiveness of the proposed method is demonstrated via a case study on a continuous stirred tank reactor system

Decentralised State Feedback Tracking Control for Large-Scale Interconnected Systems Using Sliding Mode Techniques

A class of large-scale interconnected systems with matched and unmatched uncertainties is studied in this thesis, with the objective of proposing a controller based on diffeomorphisms and some techniques to deal with the tracking problem of the system. The main research developed in this thesis includes: 1. Large-scale interconnected system is a complex system consisting of several semi-independent subsystems, which are typically located in distinct geographic or logical locations. In this situation, decentralised control which only collects the local information is the practical method to deal with large-scale interconnected systems. The decentralised methodology is utilised throughout this thesis, guaranteeing that systems exhibit essential robustness against uncertainty. 2. Sliding mode technique is involved in the process of controller design. By introducing a nonsingular local diffeomorphism, the large-scale system can be transformed into a system with a specific regular form, where the matched uncertainty is completely absent from the subspace spanned by the sliding mode dynamics. The sliding mode based controller is proposed in this thesis to successfully achieve high robustness of the closed-loop interconnected systems with some particular uncertainties. 3. The considered large-scale interconnected systems can always track the smooth desired signals in a finite time. Each subsystem can track its own ideal signal or all subsystems can track the same ideal signal. Both situations are discussed in this thesis and the results are mathematically proven by introducing the Lyapunov theory, even when operating under the presence of disturbances. At the end of each chapter, some simulation examples, like a coupled inverted pendulums system, a river pollution system and a high-speed train system, are presented to verify the correctness of the proposed theory. At the conclusion of this thesis, a brief summary of the research findings has been provided, along with a mention of potential future research directions in tracking control of large-scale systems, like more general boundedness of interconnections, possibilities of distributed control, collaboration with intelligent control and so on. Some mathematical theories involved and simulation code are included in the appendix section

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

Robust variable structure observer design for non-linear large-scale systems with non-linear interconnections

In this paper, a variable structure observer is designed for a class of non-linear large-scale interconnected systems in the presence of uncertainties and non-linear interconnections. The modern geometric approach is used to explore system structure and a transformation is employed to facilitate the observer design. Based on the Lyapunov direct method, a set of conditions are developed such that the proposed variable structure systems can be used to estimate the states of the original interconnected systems asymptotically. The internal dynamical structure of the isolated nominal subsystems as well as the structure of the uncertainties are employed to reduce the conservatism. The bounds on the uncertainties are non-linear and are employed in the observer design to reject the effect of the uncertainties. A numerical example is presented to illustrate the approach and the simulation results showthat the proposed approach is effective

Design of robust decentralised controllers for MIMO plants with delays through network structure exploitation

International audienceA methodology is proposed for the design of robust controllers for retarded and neutral-type time-delay systems, focusing on decentralised and overlapping fixed-order controllers for Multiple Input Multiple Output (MIMO) systems. The methodology is grounded in a direct optimisation approach and relies on the minimisation of spectral abscissa and H∞ cost functions, as a function of the controller or design parameters. First, an approach applicable to generic MIMO systems is presented, which imposes a suitable sparsity pattern with the possibility of fixing elements in the controller parameterisation. Second, if the system to be controlled has the structure of a network of coupled identical subsystems, then it is shown that this structure can be exploited by an improved algorithm for the design of decentralised controllers, thereby improving computational efficiency and scalability with the number of subsystems. Several numerical examples illustrate the effectiveness of the methodology, and its extension towards consensus type problems

Stabilisation operations as complex systems - order and chaos in the interoperability continuum

There is little knowledge in regards to the influence of complex systems thinking on the strategic modelling of stabilization operations. To better control the impact of information asymmetry in such context, this study focuses on gaining an understanding on how concepts and principles operate in theory and practice. Particularly, this study explores how the complexity of the environmental conditions influences stabilization operations as complex systems. Second, it addresses subsequent influences on a system’s required self-organizing ability to differentiate and integrate its various sub-systems, their organizational resources and competencies. Third, this study regards the development and adjustment of condition-dependent capabilities as key to reaching a state of dynamic equilibrium while processing, distributing and exchanging information. The aim of this study is both theoretical and practical: offering complex systems thinking as an alternative for the strategic modelling of stabilization operations and supporting the debate over the extent to which integration is feasible and desirable