Showing 1-25 of 864 resultsfor "Index Terms":Nonnegative Solution
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Stability analysis of a new kind series system
An n-unit series repairable system with a repairman doing other work is discussed in this paper. We are devoted to studying the unique existence of the solution and the exponential stability of the system. C0-semigroup theory is used to prove the existence of a unique non-negative solution of the system. Then by analysing the spectra distribution of the system operator and the quasi-compactness of...Show More
On an attraction–repulsion chemotaxis system with a logistic source
This paper is devoted to the attraction–repulsion chemotaxis system with a logistic source: \begin{cases} u_t=\Delta u-\chi\nabla\cdot(u\nabla v)+\mu\nabla\cdot(u\nabla w)+\mathcal{R}(u),\quad x\in\Omega,\ t>0,\\ \varrho v_t=\Delta v-\alpha_1 v+\beta_1 u,\quad x\in\Omega,\ t>0,\\ \varrho w_t=\Delta w-\alpha_2 w+\beta_2 u,\quad x\in\Omega,\ t>0, \end{cases}where $\Omega \subset \mathbb {R}^N(N\...Show More
Long-time behaviour of solutions of a non-linear diffusion problem with non-local source term
This paper is devoted to the long-time behaviour of solutions for the Dirichlet problem of the non-local porous medium equation ${u_t = \Delta(u^m) + \lambda f(u)/(\int_{\Omega } f(u)dx)^q}$ for the case f(u) = a + up with m > p ≥ 1, λ, q > 0 and a > 0. We first prove the existence and uniqueness of the solution of the associated steady-state problem. Then, for the non-negative initial data u0(x) ...Show More
We study the quadratic matrix equation X2 − EX − F = 0, where E is diagonal and F is an M‐matrix. Quadratic matrix equations of this type arise in noisy Wiener–Hopf problems for Markov chains. The solution of practical interest is a particular M‐matrix solution. The existence and uniqueness of M‐matrix solutions and numerical methods for finding the desired M‐matrix solution are discussed by trans...Show More
Existence of a second island of stability of predictor-corrector schemes for calculating synthetic seismograms
As the first step towards a general analysis of the stability of optimally accurate predictor-corrector (P-C) time domain discretized schemes for solving the elastic equation of motion, we analyze the stability of two P-C schemes for a 1-D homogeneous case. Letting Δt be the time step, h be the spatial grid interval, β be the velocity of seismic wave propagation and be the dimensionless Courant pa...Show More
Existence of positive stationary solutions for a diffusive variable-territory predator–prey model
We consider the steady-state diffusive variable-territory predator–prey system \begin{equation} {cases} { {- \Delta u = \lambda u - \alpha (x)u^2 -\beta u\upsilon \quad in \, \Omega,}}\\ {- \Delta \upsilon = \upsilon \left (u - 1- \frac{\upsilon }{u} \right ) \quad in \, \Omega,}\\ {\partial _v u =\partial _v\upsilon = 0 \qquad on \, \partial \Omega,} \end{equation} where α(x) is a non-negative c...Show More
On the continuous-time algebraic Riccati equation and its closed-form solution
49th IEEE Conference on Decision and Control (CDC)
Year: 2010 | Conference Paper |
Cited by: Papers (2)
In the present paper we obtain a closed-form solution for the class of continuous-time algebraic Riccati equations (CTARE), whenever the eigenvalues of the A matrix are distinct. The obtained closed-form solution gives insight on issues such as loss of controllability and it might also prove comparable in terms of numerical precision over current solving algorithms. We also consider further extens...Show More
Ghostbusters: A parts-based NMF algorithm
24th IET Irish Signals and Systems Conference (ISSC 2013)
Year: 2013 | Conference Paper |
Cited by: Papers (7)
An exact nonnegative matrix decomposition algorithm is proposed. This is achieved by 1) Taking a nonlinear approximation of a sparse real-valued dataset at a given tolerance-to-error constraint, c; Choosing an arbitrary lectic ordering on the rows or column entries; And, then systematically applying a closure operator, so that all closures are selected. Assuming a nonnegative hierarchical closure ...Show More
Blow-up and Global Solutions for a Porous Medium Equation Under Robin Boundary Conditions
2020 Chinese Control And Decision Conference (CCDC)
Year: 2020 | Conference Paper |
This paper deals with blow-up and global solutions for a porous medium equation under Robin boundary conditions. By constructing auxiliary functions and using modified differential inequality techniques, we establish conditions to ensure that the solution blows up in some finite time or remains global. Moreover, an upper and a lower bound for blow-up time are derived. Finally, an example is given ...Show More
Closed-form solution for the Kalman filter gains of time-varying systems
A method for derivation of closed-form solutions for the differential Riccati matrix equation for specific time-varying systems is presented. It allows more insight into the nature of the solution. It reduces the on-line computation requirements, since it does not require on-line solution of a differential equation. Sufficient conditions for the existence of the closed-form solution are given. The...Show More
A New DOA Estimation Algorithm Based on PSO-Gauss-Newton
Xuerong Cui;Rongrong Zhou;Haihua Chen;Yucheng Zhang;Shibao Li;Jingyao Zhang
2021 IEEE 9th International Conference on Information, Communication and Networks (ICICN)
Year: 2021 | Conference Paper |
Cited by: Papers (4)
Direction-of-Arrival (DOA) estimation is a basic and important problem in sensor array signal processing. In order to solve this problem, many algorithms have been proposed. Among them, the Stochastic Maximum Likelihood (SML) algorithm has become one of the most concerned algorithms because of its high DOA accuracy. However, the computational complexity of SML algorithm is very high, so Gauss-Newt...Show More
Solution of high order matrix Riccati equations with condition and accuracy estimates
Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design
Year: 1996 | Conference Paper |
The numerical solution of matrix algebraic Riccati equations with condition and forward error estimates is considered. Programs implementing the Schur and the matrix sign function methods with scaling enhancing the numerical stability are developed, based on LA-PACK package. A comparison of the accuracy of the two methods in the solution of well conditioned and ill conditioned Riccati equations of...
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Show MoreGlobal existence and blow-up solutions for a class of nonlinear reaction diffusion equations under nonlinear boundary flux
2019 Chinese Control And Decision Conference (CCDC)
Year: 2019 | Conference Paper |
The positive classical solutions of nonlinear reaction diffusion equations is given under nonlinear boundary flux in bounded domain. By constructing auxiliary functions and applying the maximum principle, the sufficient conditions for the existence of global and blow-up solutions are guaranteed. Meanwhile, the estimate of the global solution, the upper bound for "blow-up time", and the upper estim...Show More
Fast Spatio-Temporal Signal Recovery Based on Differential Smoothness Regularization
2024 IEEE International Conference on Signal, Information and Data Processing (ICSIDP)
Year: 2024 | Conference Paper |
Spatio-temporal signal recovery has been extensively studied, focusing on leveraging signal structures, such as low-rankness and high spatio-temporal smoothness, to recover complete signals. This paper introduces a fast algorithm for spatial-temporal signal recovery based on the differential smoothness regularization, utilizing the alternating direction method of multipliers (ADMM). Our proposed a...Show More
Periodic strong solution for the optimal filtering problem of linear discrete-time periodic systems
The periodic Riccati difference equation (PRDE) for the optimal filtering problem of linear periodic discrete-time systems is addressed. Specifically, the author provides a number of results on the existence, uniqueness, and stability properties of symmetric periodic nonnegative-definite solutions of the periodic Riccati difference equation in the case of nonreversible and nonstabilizable periodic...Show More
The H/sub infinity / state estimation problem for linear periodic systems is considered. Special emphasis is given to the infinite-time horizon case and the existence of an unbiased periodic asymptotically stable observer that achieves a prescribed H/sub infinity / performance criterion is discussed. Asymptotic properties of the finite horizon estimation problem are investigated, and it is shown t...Show More
Stability analysis of general linear methods for the nonautonomous pantograph equation
This paper is concerned with the study of the stability of general linear methods for the nonautonomous pantograph equation. Linear and nonlinear problems are considered separately. We derive the asymptotic stability of numerical methods with strict stability at infinity for neutral equations. Also, we obtain some bounds for the error growth for algebraically stable methods applied to non-neutral ...Show More
We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply connected. We characterize the way in which the curvature of the free boundary can tend to infinity. Indeed, if curvature tends to infinity, then two components of the free boundary are close, and the solution locally resembles...Show More
Robust control problems associated with time‐varying delay nonlinear parabolic equations
In this paper, we study a robust control problem for a class of systems gouverned by nonlinear parabolic equations with multiple time‐varying delays, in order to take account the influence of noise in data. Firstly, the control is the forcing. We formulate the robust control problem, we prove the existence and the uniqueness of the solution and we give necessary conditions of optimality. Secondly,...Show More
Convergence properties of the Riccati difference equation in optimal filtering of nonstabilizable systems
This paper studies the convergence and properties of the solutions of the Riccati difference equation. Special emphasis is given to systems which are not necessarily stabilizable (in the filtering sense), particularly those having uncontrollable roots on the unit circle. Besides generalizing and unifying previous work, the results have application to a number of important problems including filter...Show More
Values and strategies for infinite time linear quadratic games
For a class of infinite time linear quadratic games it is shown that an appropriate solution of an algebraic Riccati type equation determines the value of the game but not necessarily any equilibrium strategies. In the case of nonexistence of equilibrium strategies, ε-optimal strategies are constructed through the solutions of a differential Riccati equation.Show More
Cyclomonotonicity and stabilizability properties of solutions of the difference periodic Riccati equation
The Kalman filter associated with a discrete-time linear T-periodic system is tested. The problem considered is that of selecting an initial covariance matrix such that the periodic filter based on the first T values of the Kalman filter gain is stabilizing. Sufficient conditions are given that hinge on the cyclomonotonicity of the solution of the periodic Riccati equation. Potential applications ...Show More
Periodic oscillations of matrix Riccatti equations in time-invariant systems
Periodic oscillations arising in matrix Riccati equntions having constant coefficient matrices are investigated in this paper. The algorithm deriving such periodic solutions and the condition for their existence are obtained. Since matrix Riccati equations play a crucial role in optimal estimation and control theories, tn scattering theory, and in other important applications, the stability of sol...Show More
Numerical improvements for solving Riccati equations
In this paper, we discuss some ideas for improving the efficiency and accuracy of numerical methods for solving algebraic Riccati equations (AREs) based on invariant or deflating subspace methods. The focus is on AREs for which symmetric solutions exist, and our methods apply to both standard linear-quadratic-Gaussian (or H/sub 2/) AREs and to so-called H/sub /spl infin//-type AREs arising from ei...Show More
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