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Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances
Copyright [2004] 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 paper, we study the robust exponential filter design problem for a class of uncertain time-delay systems with both Markovian jumping parameters and nonlinear disturbances. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainties appearing in the state and output equations are real, time dependent, and norm bounded. The time-delay and the nonlinear disturbances are assumed to be unknown. The purpose of the problem under investigation is to design a linear, delay-free, uncertainty-independent state estimator such that, for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. We address both the filtering analysis and synthesis issues, and show that the problem of exponential filtering for the class of uncertain time-delay jump systems with nonlinear disturbances can be solved in terms of the solutions to a set of linear (quadratic) matrix inequalities. A numerical example is exploited to demonstrate the usefulness of the developed theory
Mean field games based on the stable-like processes
In this paper, we investigate the mean field games with K classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process associated with rather general integro-differential generators of LĀ“evy-Khintchine type (with variable coefficients), with the major stress on applications to stable and stable- like processes, as well as their various modifications like tempered stable-like processes or their mixtures with diffusions. We show that nonlinear measure-valued kinetic equations describing the dynamic law of large numbers limit for system with large number N of agents are solvable and that their solutions represent 1/N-Nash equilibria for approximating systems of N agents
Positive Definite Solutions of the Nonlinear Matrix Equation
This paper is concerned with the positive definite solutions to the matrix
equation where is the unknown and is
a given complex matrix. By introducing and studying a matrix operator on
complex matrices, it is shown that the existence of positive definite solutions
of this class of nonlinear matrix equations is equivalent to the existence of
positive definite solutions of the nonlinear matrix equation
which has been extensively studied in the
literature, where is a real matrix and is uniquely determined by It is
also shown that if the considered nonlinear matrix equation has a positive
definite solution, then it has the maximal and minimal solutions. Bounds of the
positive definite solutions are also established in terms of matrix .
Finally some sufficient conditions and necessary conditions for the existence
of positive definite solutions of the equations are also proposed
A distributed primal-dual interior-point method for loosely coupled problems using ADMM
In this paper we propose an efficient distributed algorithm for solving
loosely coupled convex optimization problems. The algorithm is based on a
primal-dual interior-point method in which we use the alternating direction
method of multipliers (ADMM) to compute the primal-dual directions at each
iteration of the method. This enables us to join the exceptional convergence
properties of primal-dual interior-point methods with the remarkable
parallelizability of ADMM. The resulting algorithm has superior computational
properties with respect to ADMM directly applied to our problem. The amount of
computations that needs to be conducted by each computing agent is far less. In
particular, the updates for all variables can be expressed in closed form,
irrespective of the type of optimization problem. The most expensive
computational burden of the algorithm occur in the updates of the primal
variables and can be precomputed in each iteration of the interior-point
method. We verify and compare our method to ADMM in numerical experiments.Comment: extended version, 50 pages, 9 figure
Some symmetry classifications of hyperbolic vector evolution equations
Motivated by recent work on integrable flows of curves and 1+1 dimensional
sigma models, several O(N)-invariant classes of hyperbolic equations for an -component vector are considered. In each
class we find all scaling-homogeneous equations admitting a higher symmetry of
least possible scaling weight. Sigma model interpretations of these equations
are presented.Comment: Revision of published version, incorporating errata on geometric
aspects of the sigma model interpretations in the case of homogeneous space
Unique Determination of Sound Speeds for Coupled Systems of Semi-linear Wave Equations
We consider coupled systems of semi-linear wave equations with different
sound speeds on a finite time interval and a bounded Lipschitz domain
in , with boundary . We show the coupled
systems are well posed for variable coefficient sounds speeds and short times.
Under the assumption of small initial data, we prove the source to solutions
map on associated with the nonlinear problem is
sufficient to determine the source-to-solution map for the linear problem. We
can then reconstruct the sound speeds in for the coupled nonlinear
wave equations under certain geometric assumptions. In the case of the full
source to solution map in this reconstruction could also be
accomplished under fewer geometric assumptions.Comment: minor update
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