Generalized vector control for brushless doubly fed machines with nested-loop rotor

This paper presents a generalized vector control system for a generic brushless doubly fed (induction) machine (BDFM) with nested-loop type rotor. The generic BDFM consists of p1/p2 pole-pair stator windings and a nested-loop rotor with N number of loops per nest. The vector control system is derived based on the basic BDFM equation in the synchronous mode accompanied with an appropriate synchronization approach to the grid. An analysis is performed for the vector control system using the generic BDFM vector model. The analysis proves the efficacy of the proposed approach in BDFM electromagnetic torque and rotor flux control. In fact, in the proposed vector control system, the BDFM torque can be controlled very effectively promising a high-performance BDFM shaft speed control system. A closed-loop shaft speed control system is composed based on the presented vector control system whose performance is examined both in simulations and experiments. The results confirm the high performance of the proposed approach in BDFM shaft speed control as well as a very close agreement between the simulations and experiments. Tests are performed on a 180-frame prototype BDFM. © 2012 IEEE.

Elemental unbiased estimators for the Generalized Pareto tail

Unbiased location- and scale-invariant `elemental' estimators for the GPD tail parameter are constructed. Each involves three log-spacings. The estimators are unbiased for finite sample sizes, even as small as N=3. It is shown that the elementals form a complete basis for unbiased location- and scale-invariant estimators constructed from linear combinations of log-spacings. Preliminary numerical evidence is presented which suggests that elemental combinations can be constructed which are consistent estimators of the tail parameter for samples drawn from the pure GPD family.

Elemental estimators for the Generalized Extreme Value tail

In a companion paper (McRobie(2013) arxiv:1304.3918), a simple set of `elemental' estimators was presented for the Generalized Pareto tail parameter. Each elemental estimator: involves only three log-spacings; is absolutely unbiased for all values of the tail parameter; is location- and scale-invariant; and is valid for all sample sizes $N$, even as small as $N= 3$. It was suggested that linear combinations of such elementals could then be used to construct efficient unbiased estimators. In this paper, the analogous mathematical approach is taken to the Generalised Extreme Value (GEV) distribution. The resulting elemental estimators, although not absolutely unbiased, are found to have very small bias, and may thus provide a useful basis for the construction of efficient estimators.

On the relation of slow feature analysis and Laplacian eigenmaps

The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow feature analysis (SFA), a biologically inspired, unsupervised learning algorithm originally designed for learning invariant visual representations. We show that SFA can be interpreted as a function approximation of LEMs, where the topological neighborhoods required for LEMs are implicitly defined by the temporal structure of the data. Based on this relation, we propose a generalization of SFA to arbitrary neighborhood relations and demonstrate its applicability for spectral clustering. Finally, we review previous work with the goal of providing a unifying view on SFA and LEMs. © 2011 Massachusetts Institute of Technology.

Generalized power method for sparse principal component analysis

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, and are therefore computationally intractable, we rewrite them into the form of an optimization program involving maximization of a convex function on a compact set. The dimension of the search space is decreased enormously if the data matrix has many more columns (variables) than rows. We then propose and analyze a simple gradient method suited for the task. It appears that our algorithm has best convergence properties in the case when either the objective function or the feasible set are strongly convex, which is the case with our single-unit formulations and can be enforced in the block case. Finally, we demonstrate numerically on a set of random and gene expression test problems that our approach outperforms existing algorithms both in quality of the obtained solution and in computational speed. © 2010 Michel Journée, Yurii Nesterov, Peter Richtárik and Rodolphe Sepulchre.

Synchronization with partial state feedback on SO(n)

In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in ℝn. We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames. ©2009 IEEE.