Optimal control with stochastic PDE constraints and uncertain controls

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with the control function possibly decomposed into an unknown deterministic component and a known zero-mean stochastic component. The extra freedom provided by the stochastic dimension in defining cost functionals is explored, demonstrating the scope for controlling statistical aspects of the system response. One-shot stochastic finite element methods are used to find approximate solutions to control problems. It is shown that applying the stochastic collocation finite element method to the formulated problem leads to a coupling between stochastic collocation points when a deterministic optimal control is considered or when moments are included in the cost functional, thereby forgoing the primary advantage of the collocation method over the stochastic Galerkin method for the considered problem. The application of the presented methods is demonstrated through a number of numerical examples. The presented framework is sufficiently general to also consider a class of inverse problems, and numerical examples of this type are also presented. © 2011 Elsevier B.V.

Nanometer scale thermal drift of 4Gbit/s uncooled laser for tight-channel-spacing low-cost WDM

A 4Gbit/s directly modulated DBR laser is demonstrated with nanometre scale thermal tuning over an extended 20-70°C temperature range. >40dB side mode suppression over the entire temperature range is achieved. © 2005 Optical Society of America.

Uncooled DBR laser directly modulated at 3.125 Gb/s as athermal transmitter for low-cost WDM systems

An uncooled three-section tunable distributed Bragg reflector laser is demonstrated as an athermal transmitter for low-cost uncooled wavelength-division-multiplexing (WDM) systems with tight channel spacing. A ±0.02-nm thermal wavelength drift is achieved under continuous-wave operation up to 70 °C. Dynamic sidemode suppression ratio of greater than 35 dB is consistently obtained under 3.125-Gb/s direct modulation over a 20 °C-70 °C temperature range, with wavelength variation of as low as ±0.2 nm. This indicates that more than an order of magnitude reduction in coarse WDM channel spacing is possible using this source. © 2005 IEEE.