Growth rates for persistently excited linear systems

We consider a family of linear control systems $\dot{x}=Ax+\alpha Bu$ where $\alpha$ belongs to a given class of persistently exciting signals. We seek maximal $\alpha$-uniform stabilisation and destabilisation by means of linear feedbacks $u=Kx$. We extend previous results obtained for bidimensional single-input linear control systems to the general case as follows: if the pair $(A,B)$ verifies a certain Lie bracket generating condition, then the maximal rate of convergence of $(A,B)$ is equal to the maximal rate of divergence of $(-A,-B)$. We also provide more precise results in the general single-input case, where the above result is obtained under the sole assumption of controllability of the pair $(A,B)$

Decohering localized waves

In the absence of confinement localization of waves takes place due to randomness or nonlinearity and relies on their phase coherence. We quantitatively probe the sensitivity of localized wave packets to random phase fluctuations and confirm the necessity of phase coherence for localization. Decoherence resulting from a dynamical random environment leads to diffusive spreading and destroys linear and nonlinear localization. We find that maximal spreading is achieved for optimal phase fluctuation characteristics which is a consequence of the competition between diffusion due to decoherence and ballistic transport within the mean free path distance.Comment: Updated affiliatio

Realities of long-term post investment performance for venture-backed enterprises

This paper constructs a model of long-run performance for SMEs that have received venture capital backing. The model explains performance by financial structure. FAME data are used for estimating performance equations over the period 1989 to 2004 for UK businesses in their post-investment period. The econometrics uses robust techniques, including least absolute error (LAE) and Tukey trimean estimation. It is shown that the key determinants of performance (measured by ROSF) are profit margins and risk, with lesser, but significant, roles played by liquidity and gearing. The sample is used to identify consistently high performers, and chronic low performers. From the latter group, two detailed case studies illustrate how chronic low performance can emerge, in each case caused by failure to achieve technological milestones, and thereby failing, ultimately, to convince investors of potential company worth

Consensus and Flocking Under Communication Failures for a Class of Cucker-Smale Systems

We study sufficient conditions for the emergence of consensus and flocking in a class of strongly cooperative non-linear multi-agent systems subject to arbitrary communication failures. Our approach is based on a combination of Lyapunov analysis along with the formulation of a novel persistence of excitation condition for cooperative systems. This assumption can be interpreted in terms of average connectedness of the interaction graph of the system, and provides quantitative convergence rates towards consensus and flocking

Design and Implementation of a Real-time Adaptive Oxygen Transfer Rate Estimator

Oxygen transfer rate (OTR) is the most signicant signal for aerobic bioprocess control, since most microbic metabolic activity relies on oxygen consumption. However, accurate estimation of OTR is challenging due to the difficulty of determining uncertain oxygen transfer parameters and system dynamics. This paper presents an adaptive estimator, which incorporates exhaust gas, stir speed and dissolved oxygen measurements, to predict the real-time OTR. The design of this estimator takes into account the headspace dilution effect, off-gas sensor dynamics and uncertain oxygen transfer parameters. Accurate and real-time OTR signal is derived by combining the low latency property of stir speed and dissolved oxygen signals with the high accuracy property of off-gas measurements. Proof of convergence of this adaptive estimator is provided under persistently exciting input constraint. Matlab simulation and E. coli fermentation experiment are provided to demonstrate the validity of the adaptive estimator. Through simulation and fermentation experiment, the estimated real-time OTR is shown to accurately track quick changes of oxygen demand in the culture. Thus, it can be applied to a variety of controls and estimation purposes, such as determining when the culture is in oxidative or overflow metabolism. Other related works on bioreactor fermentation control is also provided. A Kalman filter is developed and implemented for real-time feed rate signal estimation. Problems with OUR calculation is discussed when increased oxygen concentrations in the inlet gas and mass flow control are introduced. Two bioreactor related Matlab GUIs, i.e. fermentation GUI and display graph software, are also introduced in the appendices

Instabilities of Hexagonal Patterns with Broken Chiral Symmetry

Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are investigated. They are relevant for the dynamics close to onset of rotating non-Boussinesq or surface-tension-driven convection. Steady and oscillatory, long- and short-wave instabilities of the hexagons are found. For the long-wave behavior coupled phase equations are derived. Numerical simulations of the Ginzburg-Landau equations indicate bistability between spatio-temporally chaotic patterns and stable steady hexagons. The chaotic state can, however, not be described properly with the Ginzburg-Landau equations.Comment: 11 pages, 7 figures, submitted to Physica

Model-free Continuation of Periodic Orbits in Certain Nonlinear Systems Using Continuous-Time Adaptive Control

This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger class of periodically excited nonlinear systems with matched uncertainties and known structure. A candidate adaptive feedback design is also proposed in the case of scalar problems with unmodeled nonlinearities. In the former case, rigorous analysis shows guaranteed performance bounds for the associated prediction and estimation errors. Together with an assumption of persistent excitation, there follows asymptotic convergence to periodic responses determined uniquely by an a priori unknown periodic reference input and independent of initial conditions, as required by the control-based continuation paradigm. In particular, when the reference input equals the sought periodic response, the steady-state control input vanishes. Identical conclusions follow for the case of scalar dynamics with unmodeled nonlinearities, albeit with slow rates of convergence. Numerical simulations validate the theoretical predictions for individual parameter values. Integration with the software package COCO demonstrate successful continuation along families of stable and unstable periodic orbits with a minimum of parameter tuning. The results expand the envelope of known noninvasive feedback strategies for use in experimental model validation and engineering design