Delayed decision-making in bistable models

Switching between two modes of operation is a common property of biological systems. In continuous-time differential equation models, this is often realised by bistability, i.e. the existence of two asymptotically stable steadystates. Several biological models are shown to exhibit delayed switching, with a pronounced transient phase, in particular for near-threshold perturbations. This study shows that this delay in switching from one mode to the other in response to a transient input is reflected in local properties of an unstable saddle point, which has a one dimensional unstable manifold with a significantly slower eigenvalue than the stable ones. Thus, the trajectories first approximatively converge to the saddle point, then linger along the saddle's unstable manifold before quickly approaching one of the stable equilibria. ©2010 IEEE.

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.

Rhythmic feedback control of a blind planar juggler

The paper considers the feedback stabilization of periodic orbits in a planar juggler. The juggler is "blind," i.e, he has no other sensing capabilities than the detection of impact times. The robustness analysis of the proposed control suggests that the arms acceleration at impact is a crucial design parameter even though it plays no role in the stability analysis. Analytical results and convergence proofs are provided for a simplified model of the juggler. The control law is then adapted to a more accurate model and validated in an experimental setup. © 2007 IEEE.

Feedback control of impact dynamics: The bouncing ball revisited

We study the the design of a tracking controller for the popular bouncing ball model: the continuous-time actuation of a table is used to control the impacts of the table with a bouncing ball. The proposed control law uses the impact times as the sole feedback information. We show that the acceleration of the table at impact plays no role in the stability analysis but is an important parameter for the robustness of the feedback system to model uncertainty, in particular to the uncertainty on the coefficient of restitution. © 2006 IEEE.

Timing feedback control of a rhythmic system

This paper addresses the question relative to the role of sensory feedback in rhythmic tasks. We study the properties of a sinusoidally vibrating wedge-billiard as a model for 2-D bounce juggling. If this wedge is actuated with an harmonic sinusoidal input, it has been shown that some periodic orbits are exponentially stable. This paper explores an intuitive method to enlarge the parametric stability region of the simplest of these orbits. Accurate processing of timing is proven to be an important key to achieve frequency-locking in rhythmic tasks. © 2005 IEEE.

Feedback mechanisms for global oscillations in Lure systems

The paper presents two mechanisms for global oscillations in feedback systems, based on bifurcations in absolutely stable systems. The external characterization of the oscillators provides the basis for a (energy-based) dissipativity theory for oscillators, thereby opening new possibilities for rigorous stability analysis of high-dimensional systems and interconnected oscillators. © 2004 Elsevier B.V. All rights reserved.

Flexible conversion ratio fast reactors: Overview

Conceptual designs of lead-cooled and liquid salt-cooled fast flexible conversion ratio reactors were developed. The performance achievable by the unity conversion ratio cores of these reactors was compared to an existing supercritical carbon dioxide-cooled (S-CO2) fast reactor design and an uprated version of an existing sodium-cooled fast reactor. All concepts have cores rated at 2400 MWt. The cores of the liquid-cooled reactors are placed in a large-pool-type vessel with dual-free level, which also contains four intermediate heat exchangers (IHXs) coupling a primary coolant to a compact and efficient supercritical CO2 Brayton cycle power conversion system. The S-CO2 reactor is directly coupled to the S-CO2 Brayton cycle power conversion system. Decay heat is removed passively using an enhanced reactor vessel auxiliary cooling system (RVACS) and a passive secondary auxiliary cooling system (PSACS). The selection of the water-cooled versus air-cooled heat sink for the PSACS as well as the analysis of the probability that the PSACS may fail to complete its mission was performed using risk-informed methodology. In addition to these features, all reactors were designed to be self-controllable. Further, the liquid-cooled reactors utilized common passive decay heat removal systems whereas the S-CO2 uses reliable battery powered blowers for post-LOCA decay heat removal to provide flow in well defined regimes and to accommodate inadvertent bypass flows. The multiple design limits and challenges which constrained the execution of the four fast reactor concepts are elaborated. These include principally neutronics and materials challenges. The neutronic challenges are the large positive coolant reactivity feedback, small fuel temperature coefficient, small effective delayed neutron fraction, large reactivity swing and the transition between different conversion ratio cores. The burnup, temperature and fluence constraints on fuels, cladding and vessel materials are elaborated for three categories of material - materials currently available, available on a relatively short time scale and available only with significant development effort. The selected fuels are the metallic U-TRU-Zr (10% Zr) for unity conversion ratio and TRU-Zr (75% Zr) for zero conversion ratio. The principal selected cladding and vessel materials are HT-9 and A533 or A508, respectively, for current availability, T-91 and 9Cr-1Mo steel for relatively short-term availability and oxide dispersion strengthened ferritic steel (ODS) available only with significant development. © 2009 Elsevier B.V. All rights reserved.

Some remarks about periodic feedback stabilization

Periodic feedback stabilization is a very natural solution to overcome the topological obstructions which may occur when one tries to asymptotically (locally) stabilize a (locally) controllable nonlinear system around an equilibrium point. The object of this paper is to give a simple geometric interpretation of this fact, to show that one obtains a weakened form of those obstructions when periodic feedback is used, and to illustrate the success of periodic feedback stabilization on a representative system which contains a drift.

A sustainable PWR fuel cycle with complete TRU recycling using fertile-free fuel

The feasibility of a conventional PWR fuel cycle with complete recycling of TRU elements in the same reactor is investigated. A new Combined Non-fertile and Uranium (CONFU) fuel assembly where about 20% of the uranium fuel pins are replaced with fertile free fuel (FFF) hosting TRU generated in the previous cycle is proposed. In this sustainable fuel cycle based on the CONFU fuel assembly concept, the amount and radiotoxicity of the nuclear waste can be significantly reduced in comparison with the conventional once-through UO 2 fuel cycle. It is shown that under the constraints of acceptable power peaking limits, the CONFU assembly exhibits negative reactivity feedback coefficients comparable in values to those of the reference UO2 fuel. Moreover, the effective delayed neutron fraction is about the same as for UO2-fueled cores. Therefore, feasibility of the PWR core operation and control with complete TRU recycle has been shown in principle. However, gradual build up of small amounts of Cm and Cf challenges fuel reprocessing and fabrication due to the high spontaneous fissions rates of these nuclides and heat generation by some Pu, Am, and Cm isotopes. Feasibility of the processing steps becomes more attainable if the time between discharge and reprocessing is 20 years or longer. The implications for the entire fuel cycle will have to be addressed in future studies.