Nonlinear adaptive control using non-parametric Gaussian Process prior models

Nonparametric Gaussian Process prior models, taken from Bayesian statistics methodology are used to implement a nonlinear adaptive control law. The expected value of a quadratic cost function is minimised, without ignoring the variance of the model predictions. This leads to implicit regularisation of the control signal (caution), and excitation of the system. The controller has dual features, since it is both tracking a reference signal and learning a model of the system from observed responses. The general method and its main features are illustrated on a simulation example

Neural networks for modelling and control of a non-linear dynamic system

The authors describe the use of neural nets to model and control a nonlinear second-order electromechanical model of a drive system with varying time constants and saturation effects. A model predictive control structure is used. This is compared with a proportional-integral (PI) controller with regard to performance and robustness against disturbances. Two feedforward network types, the multilayer perceptron and radial-basis-function nets, are used to model the system. The problems involved in the transfer of connectionist theory to practice are discussed

Eccentric discs in binaries with intermediate mass ratios: Superhumps in the VY Sculptoris stars

We investigate the role of the eccentric disc resonance in systems with mass ratios q greater than 1/4, and demonstrate the effects that changes in the mass flux from the secondary star have upon the disc radius and structure. The addition of material with low specific angular momentum to its outer edge restricts a disc radially. Should the mass flux from the secondary be reduced, it is possible for the disc in a system with mass ratio as large as 1/3 to expand to the 3:1 eccentric inner Lindblad resonance and for superhumps to be excited.Comment: 6 pages with 7 figures, accepted by MNRA

Thermal and structural modeling of superinsulation

Model permits direct physical measurement of the thermal response of critical components of space telescopes, thus providing flexibility for systems studies and design changes

Mechanochemical models for generating biological pattern and form in development

The central issue in development is the formation of spatial patterns of cells in the early embryo. The mechanisms which generate these patterns are unknown. Here we describe the new Oster-Murray mechanochemical approach to the problem, the elements of which are experimentally well documented. By way of illustration we derive one of the basic models from first principles and apply it to a variety of problems of current interest and research. We specifically discuss the formation of skin organ patterns, such as feather and scale germs, cartilage condensations in the developing vertebrate limb and finally wound healing

Adaptive, cautious, predictive control with Gaussian process priors

Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law. Predictions, including propagation of the state uncertainty are made over a k-step horizon. The expected value of a quadratic cost function is minimised, over this prediction horizon, without ignoring the variance of the model predictions. The general method and its main features are illustrated on a simulation example

Localized shear generates three-dimensional transport

Understanding the mechanisms that control three-dimensional (3D) fluid transport is central to many processes including mixing, chemical reaction and biological activity. Here a novel mechanism for 3D transport is uncovered where fluid particles are kicked between streamlines near a localized shear, which occurs in many flows and materials. This results in 3D transport similar to Resonance Induced Dispersion (RID); however, this new mechanism is more rapid and mutually incompatible with RID. We explore its governing impact with both an abstract 2-action flow and a model fluid flow. We show that transitions from one-dimensional (1D) to two-dimensional (2D) and 2D to 3D transport occur based on the relative magnitudes of streamline jumps in two transverse directions.Comment: Copyright 2017 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishin

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular revealing for the Swift-Hohenberg equations a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of an weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.Comment: 9 pages, 10 figures, submitted to Chao