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Robust H2/Hâ filtering for linear systems with error variance constraints
Copyright [2000] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this correspondence, we consider the robust H2/Hâ filtering problem for linear perturbed systems with steady-state error variance constraints. The purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied. (1) The filtering process is asymptotically stable. (2) The steady-state variance of the estimation error of each state is not more than the individual prespecified value. (3) The transfer function from exogenous noise inputs to error state outputs meets the prespecified Hâ norm upper bound constraint. We show that in both continuous and discrete-time cases, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like equations/inequalities. We present both the existence conditions and the explicit expression of desired robust filters. An illustrative numerical example is provided to demonstrate the flexibility of the proposed design approac
Pre-multisymplectic constraint algorithm for field theories
We present a geometric algorithm for obtaining consistent solutions to
systems of partial differential equations, mainly arising from singular
covariant first-order classical field theories. This algorithm gives an
intrinsic description of all the constraint submanifolds.
The field equations are stated geometrically, either representing their
solutions by integrable connections or, what is equivalent, by certain kinds of
integrable m-vector fields. First, we consider the problem of finding
connections or multivector fields solutions to the field equations in a general
framework: a pre-multisymplectic fibre bundle (which will be identified with
the first-order jet bundle and the multimomentum bundle when Lagrangian and
Hamiltonian field theories are considered). Then, the problem is stated and
solved in a linear context, and a pointwise application of the results leads to
the algorithm for the general case. In a second step, the integrability of the
solutions is also studied.
Finally, the method is applied to Lagrangian and Hamiltonian field theories
and, for the former, the problem of finding holonomic solutions is also
analized.Comment: 30 pp. Presented in the International Workshop on Geometric Methods
in Modern Physics (Firenze, April 2005
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
Consistency of a system of equations: What does that mean?
The concept of (structural) consistency also called structural solvability is an important basic tool for analyzing the structure of systems of equations. Our aim is to provide a sound and practically relevant meaning to this concept. The implications of consistency are expressed in terms of explicit density and stability results. We also illustrate, by typical examples, the limitations of the concept
Gauge Transformations, Twisted Poisson Brackets and Hamiltonization of Nonholonomic Systems
In this paper we study the problem of Hamiltonization of nonholonomic systems
from a geometric point of view. We use gauge transformations by 2-forms (in the
sense of Severa and Weinstein [29]) to construct different almost Poisson
structures describing the same nonholonomic system. In the presence of
symmetries, we observe that these almost Poisson structures, although gauge
related, may have fundamentally different properties after reduction, and that
brackets that Hamiltonize the problem may be found within this family. We
illustrate this framework with the example of rigid bodies with generalized
rolling constraints, including the Chaplygin sphere rolling problem. We also
see how twisted Poisson brackets appear naturally in nonholonomic mechanics
through these examples
Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization
Distributed network optimization has been studied for well over a decade.
However, we still do not have a good idea of how to design schemes that can
simultaneously provide good performance across the dimensions of utility
optimality, convergence speed, and delay. To address these challenges, in this
paper, we propose a new algorithmic framework with all these metrics
approaching optimality. The salient features of our new algorithm are
three-fold: (i) fast convergence: it converges with only
iterations that is the fastest speed among all the existing algorithms; (ii)
low delay: it guarantees optimal utility with finite queue length; (iii) simple
implementation: the control variables of this algorithm are based on virtual
queues that do not require maintaining per-flow information. The new technique
builds on a kind of inexact Uzawa method in the Alternating Directional Method
of Multiplier, and provides a new theoretical path to prove global and linear
convergence rate of such a method without requiring the full rank assumption of
the constraint matrix
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