scholarly journals An analytical characterization for an optimal change of Gaussian measures

2006 ◽  
Vol 2006 ◽  
pp. 1-9
Author(s):  
Henry Schellhorn
Keyword(s):  
Mean Reversion ◽  
The State ◽  
Time Varying ◽  
Gaussian Measures ◽  
State Variable ◽  
Time Integral ◽  
Free Set ◽  
Initial Measure ◽  
Nikodym Derivative ◽  
Optimal Change

We consider two Gaussian measures. In the “initial” measure the state variable is Gaussian, with zero drift and time-varying volatility. In the “target measure” the state variable follows an Ornstein-Uhlenbeck process, with a free set of parameters, namely, the time-varying speed of mean reversion. We look for the speed of mean reversion that minimizes the variance of the Radon-Nikodym derivative of the target measure with respect to the initial measure under a constraint on the time integral of the variance of the state variable in the target measure. We show that the optimal speed of mean reversion follows a Riccati equation. This equation can be solved analytically when the volatility curve takes specific shapes. We discuss an application of this result to simulation, which we presented in an earlier article.

DC Circuit Model of TiO2-based Memristors

2015 ◽  
Vol 24 (03n04) ◽  
pp. 1550004
Author(s):  
Anas Mazady ◽  
Mehdi Anwar
Keyword(s):  
Circuit Model ◽  
The State ◽  
Device Physics ◽  
Time Varying ◽  
State Equations ◽  
Material Combination ◽  
Switching Mechanism ◽  
State Variable ◽  
Varying Length

DC circuit model of TiO2 memristors is developed based on the reported I-V data. The method described can easily be implemented to realize memristor based circuitries that serve different application platforms fabricated using any material combination. The time varying length of conductive filaments inside memristor, responsible for the observed switching mechanism, is implemented as the state variable and the state equations are modified accordingly. Once the device physics is taken into account the circuit model can be further adapted to predict the behavior of memristor with altered dimensions.

scholarly journals Exploring the Limits of Floating-Point Resolution for Hardware-In-the-Loop Implemented with FPGAs

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 219 ◽  
Author(s):  
Alberto Sanchez ◽  
Elías Todorovich ◽  
Angel de Castro
Keyword(s):  
The State ◽  
Floating Point ◽  
Hardware In The Loop ◽  
State Variables ◽  
Numerical Resolution ◽  
Digital Devices ◽  
State Variable ◽  
Simulation Step ◽  
Field Programmable ◽  
The Difference

As the performance of digital devices is improving, Hardware-In-the-Loop (HIL) techniques are being increasingly used. HIL systems are frequently implemented using FPGAs (Field Programmable Gate Array) as they allow faster calculations and therefore smaller simulation steps. As the simulation step is reduced, the incremental values for the state variables are reduced proportionally, increasing the difference between the current value of the state variable and its increments. This difference can lead to numerical resolution issues when both magnitudes cannot be stored simultaneously in the state variable. FPGA-based HIL systems generally use 32-bit floating-point due to hardware and timing restrictions but they may suffer from these resolution problems. This paper explores the limits of 32-bit floating-point arithmetics in the context of hardware-in-the-loop systems, and how a larger format can be used to avoid resolution problems. The consequences in terms of hardware resources and running frequency are also explored. Although the conclusions reached in this work can be applied to any digital device, they can be directly used in the field of FPGAs, where the designer can easily use custom floating-point arithmetics.

scholarly journals On the existence of a solution for some distributed optimal control hyperbolic system

2000 ◽  
Vol 23 (5) ◽  
pp. 297-311 ◽  
Author(s):  
Dariusz Idczak ◽  
Stanislaw Walczak
Keyword(s):  
Optimal Control ◽  
Hyperbolic System ◽  
Convex Set ◽  
Linear Time ◽  
Time Varying ◽  
Optimal Process ◽  
Existence Of A Solution ◽  
Distributed Optimal Control ◽  
Absolutely Continuous ◽  
State Variable

We consider a Bolza problem governed by a linear time-varying Darboux-Goursat system and a nonlinear cost functional, without the assumption of the convexity of an integrand with respect to the state variable. We prove a theorem on the existence of an optimal process in the classes of absolutely continuous trajectories of two variables and measurable controls with values in a fixed compact and convex set.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

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