25,520 research outputs found
Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems
We present a method for approximating the solution of a parameterized,
nonlinear dynamical system using an affine combination of solutions computed at
other points in the input parameter space. The coefficients of the affine
combination are computed with a nonlinear least squares procedure that
minimizes the residual of the governing equations. The approximation properties
of this residual minimizing scheme are comparable to existing reduced basis and
POD-Galerkin model reduction methods, but its implementation requires only
independent evaluations of the nonlinear forcing function. It is particularly
appropriate when one wishes to approximate the states at a few points in time
without time marching from the initial conditions. We prove some interesting
characteristics of the scheme including an interpolatory property, and we
present heuristics for mitigating the effects of the ill-conditioning and
reducing the overall cost of the method. We apply the method to representative
numerical examples from kinetics - a three state system with one parameter
controlling the stiffness - and conductive heat transfer - a nonlinear
parabolic PDE with a random field model for the thermal conductivity.Comment: 28 pages, 8 figures, 2 table
Adaptive multichannel control of time-varying broadband noise and vibrations
This paper presents results obtained from a number of applications in which a recent adaptive algorithm for broadband multichannel active noise control is used. The core of the algorithm uses the inverse of the minimum-phase part of the secondary path for improvement of the speed of convergence. A further improvement of the speed of convergence is obtained by using double control filters for elimination of adaptation loop delay. Regularization was found to be necessary for robust operation. The regularization technique which is used preserves the structure to eliminate the adaptation loop delay. Depending on the application at hand, a number of extensions are used for this algorithm. For an application with rapidly changing disturbance spectra, the core algorithm was extended with an iterative affine projection scheme, leading to improved convergence rates as compared to the standard nomalized lms update rules. In another application, in which the influence of the parametric uncertainties was critical, the core algorithm was extended with low authority control loops operating at high sample rates. In addition, results of other applications are given, such as control of acoustic energy density and control of time-varying periodic and non-periodic vibrations
Stochastic analysis of an error power ratio scheme applied to the affine combination of two LMS adaptive filters
The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions
Defect loops in gauged Wess-Zumino-Witten models
We consider loop observables in gauged Wess-Zumino-Witten models, and study
the action of renormalization group flows on them. In the WZW model based on a
compact Lie group G, we analyze at the classical level how the space of
renormalizable defects is reduced upon the imposition of global and affine
symmetries. We identify families of loop observables which are invariant with
respect to an affine symmetry corresponding to a subgroup H of G, and show that
they descend to gauge-invariant defects in the gauged model based on G/H. We
study the flows acting on these families perturbatively, and quantize the fixed
points of the flows exactly. From their action on boundary states, we present a
derivation of the "generalized Affleck-Ludwig rule, which describes a large
class of boundary renormalization group flows in rational conformal field
theories.Comment: 43 pages, 2 figures. v2: a few typos corrected, version to be
published in JHE
Integrable lattices and their sublattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices
An integrable self-adjoint 7-point scheme on the triangular lattice and an
integrable self-adjoint scheme on the honeycomb lattice are studied using the
sublattice approach. The star-triangle relation between these systems is
introduced, and the Darboux transformations for both linear problems from the
Moutard transformation of the B-(Moutard) quadrilateral lattice are obtained. A
geometric interpretation of the Laplace transformations of the self-adjoint
7-point scheme is given and the corresponding novel integrable discrete 3D
system is constructed.Comment: 15 pages, 6 figures; references added, some typos correcte
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Iterative procedures for identification of nonlinear interconnected systems
This work addresses the identification problem of a discrete-time nonlinear system composed by linear and nonlinear subsystems. Systems in this class will be represented by Linear Fractional
Transformations. Iterative identification procedures are examined, that alternate between the estimation of the linear and the nonlinear components. The burden of identification falls naturally on the nonlinear subsystem, as techniques for identification of linear systems have long been established. Two approaches are
examined. A point-wise identification of the nonlinearity, recently proposed in the literature, is applied and its advantages and
drawbacks are outlined. An alternative procedure that employs piecewise affine approximation techniques is proposed. Numerical examples demonstrate the efficiency of the proposed algorithm
Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control
Today's fast linear algebra and numerical optimization tools have pushed the
frontier of model predictive control (MPC) forward, to the efficient control of
highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated
that exact optimal control law can be computed, e.g., by mixed-integer
programming (MIP) under piecewise-affine (PWA) system models. Despite the
elegant theory, online solving hybrid MPC is still out of reach for many
applications. We aim to speed up MIP by combining geometric insights from
hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start
techniques. Following a line of work in approximate explicit MPC, the proposed
learning-control algorithm, LNMS, gains computational advantage over MIP at
little cost and is straightforward for practitioners to implement
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