37,528 research outputs found
H∞ control of nonlinear systems: a convex characterization
The nonlinear H∞-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to H∞-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed
Memristor models for machine learning
In the quest for alternatives to traditional CMOS, it is being suggested that
digital computing efficiency and power can be improved by matching the
precision to the application. Many applications do not need the high precision
that is being used today. In particular, large gains in area- and power
efficiency could be achieved by dedicated analog realizations of approximate
computing engines. In this work, we explore the use of memristor networks for
analog approximate computation, based on a machine learning framework called
reservoir computing. Most experimental investigations on the dynamics of
memristors focus on their nonvolatile behavior. Hence, the volatility that is
present in the developed technologies is usually unwanted and it is not
included in simulation models. In contrast, in reservoir computing, volatility
is not only desirable but necessary. Therefore, in this work, we propose two
different ways to incorporate it into memristor simulation models. The first is
an extension of Strukov's model and the second is an equivalent Wiener model
approximation. We analyze and compare the dynamical properties of these models
and discuss their implications for the memory and the nonlinear processing
capacity of memristor networks. Our results indicate that device variability,
increasingly causing problems in traditional computer design, is an asset in
the context of reservoir computing. We conclude that, although both models
could lead to useful memristor based reservoir computing systems, their
computational performance will differ. Therefore, experimental modeling
research is required for the development of accurate volatile memristor models.Comment: 4 figures, no tables. Submitted to neural computatio
Tensor Computation: A New Framework for High-Dimensional Problems in EDA
Many critical EDA problems suffer from the curse of dimensionality, i.e. the
very fast-scaling computational burden produced by large number of parameters
and/or unknown variables. This phenomenon may be caused by multiple spatial or
temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit
simulation), nonlinearity of devices and circuits, large number of design or
optimization parameters (e.g. full-chip routing/placement and circuit sizing),
or extensive process variations (e.g. variability/reliability analysis and
design for manufacturability). The computational challenges generated by such
high dimensional problems are generally hard to handle efficiently with
traditional EDA core algorithms that are based on matrix and vector
computation. This paper presents "tensor computation" as an alternative general
framework for the development of efficient EDA algorithms and tools. A tensor
is a high-dimensional generalization of a matrix and a vector, and is a natural
choice for both storing and solving efficiently high-dimensional EDA problems.
This paper gives a basic tutorial on tensors, demonstrates some recent examples
of EDA applications (e.g., nonlinear circuit modeling and high-dimensional
uncertainty quantification), and suggests further open EDA problems where the
use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and
System
Modeling of strain-induced Pockels effect in Silicon
We propose a theoretical model to describe the strain-induced linear
electro-optic (Pockels) effect in centro-symmetric crystals. The general
formulation is presented and the specific case of the strained silicon is
investigated in detail because of its attractive properties for integrated
optics. The outcome of this analysis is a linear relation between the second
order susceptibility tensor and the strain gradient tensor, depending
generically on fifteen coefficients. The proposed model greatly simplifies the
description of the electro-optic effect in strained silicon waveguides,
providing a powerful and effective tool for design and optimization of optical
devices.Comment: typos corrected in eq. 29 with respect to the published versio
Decentralised delay-dependent static output feedback variable structure control
In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. Then, a decentralised delay-dependant static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using the Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach
Progressive construction of a parametric reduced-order model for PDE-constrained optimization
An adaptive approach to using reduced-order models as surrogates in
PDE-constrained optimization is introduced that breaks the traditional
offline-online framework of model order reduction. A sequence of optimization
problems constrained by a given Reduced-Order Model (ROM) is defined with the
goal of converging to the solution of a given PDE-constrained optimization
problem. For each reduced optimization problem, the constraining ROM is trained
from sampling the High-Dimensional Model (HDM) at the solution of some of the
previous problems in the sequence. The reduced optimization problems are
equipped with a nonlinear trust-region based on a residual error indicator to
keep the optimization trajectory in a region of the parameter space where the
ROM is accurate. A technique for incorporating sensitivities into a
Reduced-Order Basis (ROB) is also presented, along with a methodology for
computing sensitivities of the reduced-order model that minimizes the distance
to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced
optimization framework is applied to subsonic aerodynamic shape optimization
and shown to reduce the number of queries to the HDM by a factor of 4-5,
compared to the optimization problem solved using only the HDM, with errors in
the optimal solution far less than 0.1%
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