All Years Seminars
[INMA] 2012-10-16 (14.00) : Averaging on Riemannian Manifolds: The Curses of Curvature and Topology
At Euler building
Speaker :
Bijan AFSARI (Center for Imaging Science, Johns Hopkins University)
Abstract : A Riemannian manifold differs from a Euclidean space in its (non-trivial) curvature and topology. Current methods for defining notions of average for manifold-valued data extend
existing definitions from a Euclidean space to a Riemannian manifold. In this talk, we con-
sider some of these definitions and examine to what extent the curvature and topology of
the underlying manifold cause the corresponding averages to behave differently from their
Euclidean counterparts. We will start with very basic definitions and some historical re-
marks. The main theme of the talk is that the curses of curvature and topology, in one way
or another, haunt averaging on manifolds. In that regard, we consider both the inherent
properties (e.g., existence and uniqueness, noise sensitivity, continuity, etc) as well as algorithmic/computational properties associated with these averages. For example, we argue
that averaging on a Riemannian manifold can become increasingly difficult as the curvature
increases (in absolute value). As another example, we define a property called the averaging
property, which indicates how contaminating a set of data points with noise would change
their average; and we show that on a positively curved manifold, Riemannian averaging can
amplify the noise. We also study the adverse consequence of this fact on the smoothness
properties of recursive-iterative averages on such manifolds. Recursive-iterative averages
represent interesting examples of dynamical systems on manifolds and can be related to con-
sensus algorithms on manifolds. The global behavior of these systems is complicated since
both the curvature and topology of the manifold play roles. We study this global behavior
in the example of cyclic pursuit. Throughout the talk, we will consider numerous examples,
introduce the latest available results, and allude to open problems.
This talk is partly based on the speakers Ph.D. thesis under the supervision of P. S. Krishnaprasad and K. Grove at the University of Maryland. The rest of the talk is based on the joint work with R. Tron and R. Vidal at JHU. The presented research has been supported, in part, by grants from NSF, NIH, and ARL.
[INMA] 2012-10-02 (14.00) : Potential realization of nonlinear systems
At Euler building
Speaker :
Martin GUAY
( Queen's University, Canada)
Abstract : This presentation considers the problem of representing a sufficiently smooth nonlinear dynamical as a structured potential-driven system. The problem is related to recent nonlinear control contributions where feedback controllers are designed for systems modeled as structured potential-driven systems, for example gradient systems, generalized Hamiltonian systems and systems given in Brayton--Moser form. In recent years, matching conditions, expressed as partial differential equations, were developed to transform general nonlinear system in potential-driven forms. Departing from this approach, the present work proposes a geometric decomposition technique to re-express a given vector field into a desired potential-driven form. The proposed method is based on a decomposition of a differential one-form associated that encodes the divergence of the given vector fields into its exact and anti-exact components, and into its co-exact and anti-coexact components. The decomposition method, based on the Hodge decomposition theorem, is rendered constructive by introducing a dual operator to the standard homotopy operator. The dual operator inverts locally the co-differential operator, and is used in the present paper to identify the structure of the dynamics. Applications of the proposed approach to gradient systems, Hamiltonian systems, and generalized Hamiltonian systems are given to illustrate the proposed approach, as well as the three-dimensional rigid body problem.
[INMA] 2012-09-25 (14.00) : Randomly sampling rows from orthonormal matrices, with application to least squares problems
At Euler building
Speaker :
Ilse IPSEN (North Carolina State University )
Abstract : The Blendenpik algorithm is a fast method for solving least squares
problems for matrices A of full column rank. Blendenpik consists of the preconditioned iterative solver LSQR, where the preconditioner is obtained by randomly sampling rows of A.
We show that the condition number of the preconditioned matrix can be determined by randomly sampling rows from a specific matrix Q with orthonormal columns. We consider two sampling strategies, and present different probabilistic bounds for the condition numbers of the sampled matrices. Our bounds depend on the coherence of Q, or on its leverage scores. Numerical experiments confirm the accuracy of the bounds, even for small matrix dimensions.
[INMA] 2012-09-18 (14.00) : Adaptive oscillators: tools to provide entrainment in upper- and lower-limb periodic movement assistance
At Euler building
Speaker :
Ronsse, Renaud
Abstract : In this talk, we will overview recent experiments that were conducted to develop a new approach for rhythmic/periodic movement assistance. This new approach builds upon attractive properties of adaptive oscillators, i.e. dynamic systems having the capacity to achieve input-output synchronization while learning the input features (frequency, amplitude, etc.) in dedicated state variables. The talk will both present some theoretical results to do the synthesis of a simple adaptive oscillator (i.e. to tune its dynamic behavior), and the experiments that we performed over the last 3 years. These experiments investigated the assistance of both the upper- and the lower-limb, with dedicated robotic devices.
[INMA] 2012-08-28 (14.00) : On the Value of Model Information in Decentralized Control Design
At Euler building
Speaker :
Fahrad FAROKHI (KTH (Stockholm))
Abstract :
Large-scale control systems are often composed of several smaller interconnected units. For these systems, it is common to employ local controllers, which observe and act locally. At the heart of common control design procedures for distributed systems lies the often implicit assumption that the designer has access to the global plant model information when designing a local controller. However, there are several reasons why such plant model information would not be globally known. One reason could be that the designer wants the parameters of each local controller to only depend on local model information, so that the controllers are not modified if the model parameters of a particular subsystem change. It might also be the case that the design of each local controller is done by individual designers with no access to the global plant model, for instance, due to the fact that the designers refuse to share their model information since they consider it private. This class of problems, which we refer to as limited model information control design, is the topic of the presentation. In this presentation, first, we investigate the achievable closed-loop performance of discrete-time linear time-invariant plants under a separable quadratic cost performance with structured static state-feedback controllers. To do so, we introduce control design strategies as mappings, which construct controllers by accessing the plant model information in a constrained way according to a given design graph. We compare control design strategies using the competitive ratio as a performance metric, that is, we compare the worst case control performance for a given design strategy normalized with the optimal control performance based on full model information. We study the trade-off between the amount of model information exploited by a control design strategy and the best possible closed-loop performance. We generalize this setup to structured dynamic state-feedback controllers for H_2 performance. Finally, we discuss a very recent extension in which we generalize the set of applicable controllers to nonlinear and adaptive discrete-time systems to achieve a competitive ratio equal to one.
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