Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators

In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence a part of the system might repeat itself, and properties of this subsystem are representative of the dynamics on the whole phase space. In this paper an analysis of the second order N-node time-delay fully connected network is presented which is based on previous work by Correa and Piqueira \cite{Correa2013} for a 2-node network. This study is carried out using symmetry groups. We show the existence of multiple eigenvalues forced by symmetry, as well as the existence of Hopf bifurcations. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. We determine a finite set of frequencies $\omega$, that might correspond to Hopf bifurcations in each case for critical values of the delay. The $S_n$ map is used to actually find Hopf bifurcations along with numerical calculations using the Lambert W function. Numerical simulations are used in order to confirm the analytical results. Although we restrict attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal.Comment: 41 pages, 18 figure

A comparison of A-C and D-C lead compensation from D-C prototype networks

The object of this thesis is to study the difference in transient and frequency response characteristics between a prototype d-c phase lead compensating network and an equivalent a-c phase lead compensating network. A second order servo is selected to be compensated and five d-c prototype and equivalent a-c phase lead compensating networks are designed. The frequency characteristics of the a-c networks are obtained experimentally and these of the d-c networks are obtained analytically. The characteristics of both networks are compared and their differences are studied. The transient characteristics of the d-c and a-c compensated closed-loop systems to a step input are also investigated. Finally, conclusions are made from the experimental results. An attempt is also made to generalize the conclusions so as to apply to higher order systems --Abstract, page 2

Optimal Training Design for Channel Estimation in Decode-and-Forward Relay Networks With Individual and Total Power Constraints

In this paper, we study the channel estimation and the optimal training design for relay networks that operate under the decode-and-forward (DF) strategy with the knowledge of the interference covariance. In addition to the total power constraint on all the relays, we introduce individual power constraint for each relay, which reflects the practical scenario where all relays are separated from one another. Considering the individual power constraint for the relay networks is the major difference from that in the traditional point-to-point communication systems where only a total power constraint exists for all colocated antennas. Two types of channel estimation are involved: maximum likelihood (ML) and minimum mean square error (MMSE). For ML channel estimation, the channels are assumed as deterministic and the optimal training results from an efficient multilevel waterfilling type solution that is derived from the majorization theory. For MMSE channel estimation, however, the second-order statistics of the channels are assumed known and the general optimization problem turns out to be nonconvex. We instead consider three special yet reasonable scenarios. The problem in the first scenario is convex and could be efficiently solved by state-of-the-art optimization tools. Closed-form waterfilling type solutions are found in the remaining two scenarios, of which the first one has an interesting physical interpretation as pouring water into caves

Adaptive dynamic programming with eligibility traces and complexity reduction of high-dimensional systems

This dissertation investigates the application of a variety of computational intelligence techniques, particularly clustering and adaptive dynamic programming (ADP) designs especially heuristic dynamic programming (HDP) and dual heuristic programming (DHP). Moreover, a one-step temporal-difference (TD(0)) and n-step TD (TD(λ)) with their gradients are utilized as learning algorithms to train and online-adapt the families of ADP. The dissertation is organized into seven papers. The first paper demonstrates the robustness of model order reduction (MOR) for simulating complex dynamical systems. Agglomerative hierarchical clustering based on performance evaluation is introduced for MOR. This method computes the reduced order denominator of the transfer function by clustering system poles in a hierarchical dendrogram. Several numerical examples of reducing techniques are taken from the literature to compare with our work. In the second paper, a HDP is combined with the Dyna algorithm for path planning. The third paper uses DHP with an eligibility trace parameter (λ) to track a reference trajectory under uncertainties for a nonholonomic mobile robot by using a first-order Sugeno fuzzy neural network structure for the critic and actor networks. In the fourth and fifth papers, a stability analysis for a model-free action-dependent HDP(λ) is demonstrated with batch- and online-implementation learning, respectively. The sixth work combines two different gradient prediction levels of critic networks. In this work, we provide a convergence proofs. The seventh paper develops a two-hybrid recurrent fuzzy neural network structures for both critic and actor networks. They use a novel n-step gradient temporal-difference (gradient of TD(λ)) of an advanced ADP algorithm called value-gradient learning (VGL(λ)), and convergence proofs are given. Furthermore, the seventh paper is the first to combine the single network adaptive critic with VGL(λ). --Abstract, page iv

Institutional change in the natural sciences : a thesis presented in partial fulfilment of the requirements for the degree of Masters in Business Studies in Management at Massey University, Palmerston North, New Zealand /

This thesis investigates the Allan Wilson Centre for Molecular Ecology and Evolution, a Centre of Research Excellence financed by the New Zealand Government's CoRE fund, which was established in 2001. The CoRE fund represented a change from traditional science funding in New Zealand. Its aim was to make use of existing networks of scientists, from several institutions and disciplines, to form new 'Centres of Research Excellence', independent from any existing institution, but made up of members who remained in their existing positions. The aim of this thesis is to investigate whether the formation of the Allan Wilson Centre has made a difference to the way its members carry out their science and, if so, how. To do this, an actor-network approach is used to analyse the various 'modes of ordering' the Centre, to make sense of the networks represented by it. The results show an interesting shift in the way that science is carried out in the Allan Wilson Centre in contrast to the pre-Centre form. Although the focus of the Centre remains firmly on the science they do, they now also interact regularly with the discourse of management in order to better 'do' and 'encourage' their science, creating new successes but also new tensions. The importance of this thesis is two-fold. First, it provides a mechanism through which to 'hear' the voice of the Allan Wilson Centre and its members; and second, it provides a means through which science policy makers can see how this particular policy mechanism may have changed the process of science