Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor

We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the blood alcohol concentration and the output being the transdermal alcohol concentration. Our approach is based on the idea of reformulating the underlying dynamical system in such a way that the random parameters are now treated as additional space variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating the diffusivity in a multi-dimensional diffusion equation and thus well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods may all be employed. We use our technique to estimate a bivariate normal distribution based on data for multiple drinking episodes from a single subject.Comment: 10 page

Coverage and Field Estimation on Bounded Domains by Diffusive Swarms

In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as independent control inputs. We analyze the diffusion-based control strategy using standard operator semigroup-theoretic arguments. We show that the diffusion coefficient can be chosen to be dependent only on the robots' local measurements to ensure that the swarm density converges to a function proportional to the scalar field. The boundedness of the domain precludes the need to impose assumptions on decaying properties of the scalar field at infinity. Moreover, exponential convergence of the swarm density to the equilibrium follows from properties of the spectrum of the semigroup generator. In addition, we use the proposed coverage method to construct a time-inhomogenous diffusion process and apply the observability of the heat equation to reconstruct the scalar field over the entire domain from observations of the robots' random motion over a small subset of the domain. We verify our results through simulations of the coverage scenario on a 2D domain and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016

Precision pointing compensation for DSN antennas with optical distance measuring sensors

The pointing control loops of Deep Space Network (DSN) antennas do not account for unmodeled deflections of the primary and secondary reflectors. As a result, structural distortions due to unpredictable environmental loads can result in uncompensated boresight shifts which degrade pointing accuracy. The design proposed here can provide real-time bias commands to the pointing control system to compensate for environmental effects on pointing performance. The bias commands can be computed in real time from optically measured deflections at a number of points on the primary and secondary reflectors. Computer simulations with a reduced-order finite-element model of a DSN antenna validate the concept and lead to a proposed design by which a ten-to-one reduction in pointing uncertainty can be achieved under nominal uncertainty conditions

Dynamic simulation and exergetic optimization of a Concentrating Photovoltaic/ Thermal (CPVT) system

The development of a dynamic, theoretical model suitable for the prediction of the long-term performance of a parabolic-trough Concentrating Photovoltaic/Thermal CPVT system is discussed in the present study. The formulation of the mathematical model and the considered geometrical and operational parameters of the system, such as the characteristics of the employed PV modules and active cooling system are described in detail. The effect of heat capacity is taken into consideration in the thermal balances and thus the model is able to capture the transient behavior of the system. Besides, the model is validated using available experimental data of a manufactured prototype CPVT system. The daily performance of system is predicted for different values of the cooling fluid flow rate and temperature under various environmental conditions. At a second stage, an exergy analysis is conducted in order to point out the effect of the characteristics of the main system sub-components on the exergetic efficiency and exergy output of the CPVT system. It was established that the system exergetic performance is primarily influenced by the optical quality of the parabolic trough and the electrical efficiency of the PV module. Increasing these two factors to achievable values, e.g. ηopt = 0.75 and ηel = 0.25, can yield an increase of the system exergetic efficiency from 12% to 24%

Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed