Structural engineering of evolving complex dynamical networks

Networks are ubiquitous in nature and many natural and man-made systems can be modelled as networked systems. Complex networks, systems comprising a number of nodes that are connected through edges, have been frequently used to model large-scale systems from various disciplines such as biology, ecology, and engineering. Dynamical systems interacting through a network may exhibit collective behaviours such as synchronisation, consensus, opinion formation, flocking and unusual phase transitions. Evolution of such collective behaviours is highly dependent on the structure of the interaction network. Optimisation of network topology to improve collective behaviours and network robustness can be achieved by intelligently modifying the network structure. Here, it is referred to as "Engineering of the Network". Although coupled dynamical systems can develop spontaneous synchronous patterns if their coupling strength lies in an appropriate range, in some applications one needs to control a fraction of nodes, known as driver nodes, in order to facilitate the synchrony. This thesis addresses the problem of identifying the set of best drivers, leading to the best pinning control performance. The eigen-ratio of the augmented Laplacian matrix, that is the largest eigenvalue divided by the second smallest one, is chosen as the controllability metric. The approach introduced in this thesis is to obtain the set of optimal drivers based on sensitivity analysis of the eigen-ratio, which requires only a single computation of the eigenvector associated with the largest eigenvalue, and thus is applicable for large-scale networks. This leads to a new "controllability centrality" metric for each subset of nodes. Simulation results reveal the effectiveness of the proposed metric in predicting the most important driver(s) correctly.     Interactions in complex networks might also facilitate the propagation of undesired effects, such as node/edge failure, which may crucially affect the performance of collective behaviours. In order to study the effect of node failure on network synchronisation, an analytical metric is proposed that measures the effect of a node removal on any desired eigenvalue of the Laplacian matrix. Using this metric, which is based on the local multiplicity of each eigenvalue at each node, one can approximate the impact of any node removal on the spectrum of a graph. The metric is computationally efficient as it only needs a single eigen-decomposition of the Laplacian matrix. It also provides a reliable approximation for the "Laplacian energy" of a network. Simulation results verify the accuracy of this metric in networks with different topologies. This thesis also considers formation control as an application of network synchronisation and studies the "rigidity maintenance" problem, which is one of the major challenges in this field. This problem is to preserve the rigidity of the sensing graph in a formation during motion, taking into consideration constraints such as line-of-sight requirements, sensing ranges and power limitations. By introducing a "Lattice of Configurations" for each node, a distributed rigidity maintenance algorithm is proposed to preserve the rigidity of the sensing network when failure in a sensing link would result in loss of rigidity. The proposed algorithm recovers rigidity by activating, almost always, the minimum number of new sensing links and considers real-time constraints of practical formations. A sufficient condition for this problem is proved and tested via numerical simulations. Based on the above results, a number of other areas and applications of network dynamics are studied and expounded upon in this thesis

A stability-theory perspective to synchronisation of heterogeneous networks

Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau

Cooperative control of multi-uavs under communication constraints.

This research aims to develop an analysis and control methodology for the multiple un-manned aerial vehicles (UAVs), connected over a communication network. The wireless communication network between the UAVs is vulnerable to errors and time delays, which may lead to performance degradation or even instability. Analysis on the effects of the potential communication constraints in the multiple UAV control is a critical issue for successful operation of multiple UAVs. Therefore, this thesis proposes a systematic method by incorporating three steps: proposing the analysis method and metrics considering the wireless communication dynamics, designing the structure of the cooperative controller for UAVs, and applying the analysis method to the proposed control in representative applications. For simplicity and general insights on the effect of communication topology, a net-worked system is first analysed without considering the agent or communication dynamics. The network theory specifies important characteristics such as robustness, effectiveness, and synchronisability with respect to the network topology. This research not only reveals the trade-off relationship among the network properties, but also proposes a multi-objective optimisation (MOO) method to find the optimal network topology considering these trade-offs. Extending the analysis to the networked control system with agent and communication dynamics, the effect of the network topology with respect to system dynamics and time delays should be considered. To this end, the effect of communication dynamics is then analysed in the perspective of robustness and performance of the controller. The key philosophy behind this analysis is to approximate the networked control system as a transfer function, and to apply the concepts such as stability margin and sensitivity function in the control theory. Through the analysis, it is shown that the information sharing between the agents to determine their control input deteriorates the robustness of their stability against system uncertainties. In order to compensate the robustness and cancel out the effect of uncertainties, this thesis also develops two different adaptive control methods. The proposed adaptive control methods in this research aim to cope with unmatched uncertainty and time-varying parameter uncertainty, respectively. The effect of unmatched uncertainty is reduced on the nominal performance of the controller, using the parameter-robust linear quadratic Gaussian method and adaptive term. On the other hand, time-varying parameter uncertainty is estimated without requiring the persistent excitation using concurrent learning with the directional forgetting algorithm. The stability of the tracking and parameter estimation error is proved using Lyapunov analysis. The proposed analysis method and control design are demonstrated in two application examples of a formation control problem without any physical interconnection between the agents, and an interconnected slung-load transportation system. The performance of the proposed controllers and the effect of topology and delay on the system performance are evaluated either analytically or numerically.PhD in Aerospac

Supplementing Frequency Domain Interpolation Methods for Character Animation

The animation of human characters entails difficulties exceeding those met simulating objects, machines or plants. A person's gait is a product of nature affected by mood and physical condition. Small deviations from natural movement are perceived with ease by an unforgiving audience. Motion capture technology is frequently employed to record human movement. Subsequent playback on a skeleton underlying the character being animated conveys many of the subtleties of the original motion. Played-back recordings are of limited value, however, when integration in a virtual environment requires movements beyond those in the motion library, creating a need for the synthesis of new motion from pre-recorded sequences. An existing approach involves interpolation between motions in the frequency domain, with a blending space defined by a triangle network whose vertices represent input motions. It is this branch of character animation which is supplemented by the methods presented in this thesis, with work undertaken in three distinct areas. The first is a streamlined approach to previous work. It provides benefits including an efficiency gain in certain contexts, and a very different perspective on triangle network construction in which they become adjustable and intuitive user-interface devices with an increased flexibility allowing a greater range of motions to be blended than was possible with previous networks. Interpolation-based synthesis can never exhibit the same motion variety as can animation methods based on the playback of rearranged frame sequences. Limitations such as this were addressed by the second phase of work, with the creation of hybrid networks. These novel structures use properties of frequency domain triangle blending networks to seamlessly integrate playback-based animation within them. The third area focussed on was distortion found in both frequency- and time-domain blending. A new technique, single-source harmonic switching, was devised which greatly reduces it, and adds to the benefits of blending in the frequency domain

Autonomy in the real real-world: A behaviour based view of autonomous systems control in an industrial product inspection system

The thesis presented in this dissertation appears in two sequential parts that arose from an exploration of the use of Behaviour Based Artificial Intelligence (BBAI) techniques in a domain outside that of robotics, where BBAI is most frequently used. The work details a real-world physical implementation of the control and interactions of an industrial product inspection system from a BBAI perspective. It concentrates particularly on the control of a number of active laser scanning sensor systems (each a subsystem of a larger main inspection system), using a subsumption architecture. This industrial implementation is in itself a new direction for BBAI control and an important aspect of this thesis. However, the work has also led on to the development of a number of key ideas which contribute to the field of BBAI in general. The second part of the thesis concerns the nature of physical and temporal constraints on a distributed control system and the desirability of utilising mechanisms to provide continuous, low-level learning and adaptation of domain knowledge on a sub-behavioural basis. Techniques used include artificial neural networks and hill-climbing state-space search algorithms. Discussion is supported with examples from experiments with the laser scanning inspection system. Encouraging results suggest that concerted design effort at this low level of activity will benefit the whole system in terms of behavioural robustness and reliability. Relevant aspects of the design process that should be of value in similar real-world projects are identified and emphasised. These issues are particularly important in providing a firm foundation for artificial intelligence based control systems

Uniqueness theorem for a coupled system of wave equations with incomplete internal observation and application to approximate controllability

We show that a Kalman rank condition is necessary and sufficient for the uniqueness of solution to a system of wave equations associated with incomplete internal observation without any restriction neither on the controlled subregion nor on the coupling matrices. The obtained result can be applied to the approximate internal controllability of the corresponding system

Uniqueness theorem for a coupled system of wave equations with incomplete internal observation and application to approximate controllability

We show that a Kalman rank condition is necessary and sufficient for the uniqueness of solution to a system of wave equations associated with incomplete internal observation without any restriction neither on the controlled subregion nor on the coupling matrices. The obtained result can be applied to the approximate internal controllability of the corresponding system

Co-conception contrôle / communication pour économiser l'énergie dans les systèmes commandés en réseau sans fil

Energy is a key resource in Networked Control Systems, in particular in applications concerning wireless networks. This thesis investigates how to save energy in wireless sensor nodes with control and communication co-Design. This thesis reviews existing techniques and approaches that are used to save energy from a communication and a control point of view. This review is organized according to the layered communication architecture covering from bottom to top the Physical, Data Link, Network, and Application layers. Then, from the conclusion that the radio chip is an important energy consumer, a joint radio-Mode management and feedback law policy is derived. The radio-Mode management exploits the capabilities of the radio chip to switch to low consuming radio-Modes to save energy, and to adapt the transmission power to the channel conditions. This results in an event-Based control scheme where the system runs open loop at certain time. A natural trade-Off appears between energy savings and control performance. The joint policy is derived in the framework of Optimal Control with the use of Dynamic Programming. This thesis solves the optimal problem in both infinite and finite horizon cases. Stability of the closed loop system is investigated with Input-To-State Stability framework. The main conclusion of this thesis, also shown in simulation, is that cross-Layer design in Networked Control System is essential to save energy in the wireless nodes.L'énergie est une ressource clé dans les systèmes commandés en réseau, en particulier dans les applications concernant les réseaux sans fil. Cette thèse étudie comment économiser l'énergie dans les capteurs sans fil avec une co-Conception contrôle et communication. Cette thèse examine les techniques et les approches existantes qui sont utilisées pour économiser l'énergie d'un point de vue de la communication et du contrôle. Cet étude est organisée selon une architecture de communication par couches couvrant de bas en haut les couches Physique, Liaison, Réseau, et Application. Puis, à partir de la conclusion que la puce radio est un important consommateur d'énergie, une loi conjointe de gestion des modes radio et de contrôle en boucle fermée est établie. La gestion des modes radio exploite les capacités de la puce radio à communter dans des modes de basses consommation pour économiser l'énergie, et d'adapter la puissance de transmission aux conditions du canal. Il en résulte un système de contrôle basé sur des événements où le système fonctionne en boucle ouverte à certains moments. Un compromis naturel apparaît entre l'économie d'énergie et les performances de contrôle. La loi conjointe est établie avec une formulation de contrôle optimal utilisant la Programmation Dynamique. Cette thèse résout le problème optimal dans les deux cas d'horizon infini et fini. La stabilité du système en boucle fermée est étudiée avec la formulation Input-To-State Stability (ISS). La principale conclusion de cette thèse, également illustrée dans la simulation, est que la conception à travers différentes couches dans les systèmes commandés en réseau est essentielle pour économiser l'énergie dans les noeuds sans fil