The paper deals with a filter design for nonlinear continuous stochastic systems with discrete-time measurements. The general recursive solution is given by the Fokker-Planck equation (FPE) and by the Bayesian rule. The stress is laid on the computation of the predictive conditional probability density function from the FPE. The solution of the FPE and its integration into the estimation algorithm is the cornerstone for the whole recursive computation. A new usable numerical scheme for the FPE is designed. In the scheme, the separation technique based on the upwind volume method and the finite difference method for hyperbolic and parabolic part of the FPE is used. It is supposed that separation of the FPE and choice of a suitable numerical method for each part can achieve better estimation quality comparing to application of a single numerical method to the unseparated FPE. The approach is illustrated in some numerical examples.
In this paper, the problem of nonlinear viscoelastic rectangular thin plate subjected to tangential follower force is examined. The nonlinear strain-displacement relation is used to express non-linearity. After obtaining the equilibrium equation of the system in Laplace domain and performing the Laplace inverse transformation, the nonlinear differential equation of plate constituted by Kelvin-Voigt model and subjected to tangential follower force in time domain is obtained. Multi-scales method is firstly used to solve the governing equation, and the influence of the initial amplitude on the nonlinear frequency ratio is studied. Secondly, the differential quadrature method (DQM) is employed to confirm the obtained results. and Obsahuje seznam literatury
An analytical solution for nonlinear vibration of an initially stressed beam with elastic end restraints resting on two-parameter foundation is obtained. The mode functions for linear vibration of a beam with elastic end restraints resting on a linear elastic foundation are obtained first and used to solve the nonlinear vibration equation recalling elliptic integrals. The results obtained from the present solution are compared against those obtained from finite element method and found in close agreement. The effects of elastic support stiffnesses at the beam ends, foundation stiffness, initial axial load and vibration amplitude on the natural frequency are studied. and Obsahuje seznam literatury
In this paper we prove the existence of mild solutions and the controllability for semilinear differential inclusions with nonlocal conditions. Our results extend some recent theorems.
In this paper we consider the equation \[y^{\prime \prime \prime} + q(t){y^{\prime }}^{\alpha} + p(t) h(y) =0,\] where $p,q$ are real valued continuous functions on $[0,\infty)$ such that $q(t) \ge 0$, $p(t) \ge 0$ and $h(y)$ is continuous in $(-\infty ,\infty)$ such that $h(y)y>0$ for $y \ne 0$. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.
This paper presents a relaxed scheme for controller synthesis of continuous-time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions' derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller synthesis is attainable via linear matrix inequalities, which are efficiently solved by commercially available software.
It is shown that gigantic nonresonance pararnetric arnplification of weak external signals is possible in neural networks. The mechanisrn of amplificatiori is determined by periodic rnodulation of neuron threshold or otlier parameters. Brain rhythms can play the role of periodic rnodulation. The paper develops Hopfield hypothesis abont the connection of some brain rhythms and signál amplification. In artificial networks a special centra! generátor for pararnetric rnodulation is necessary.
We study the existence and multiplicity of positive nonsymmetric and sign-changing nonantisymmetric solutions of a nonlinear second order ordinary differential equation with symmetric nonlinear boundary conditions, where both of the nonlinearities are of power type. The given problem has already been studied by other authors, but the number of its positive nonsymmetric and sign-changing nonantisymmetric solutions has been determined only under some technical conditions. It was a long-standing open question whether or not these conditions can be omitted. In this article we provide the answer. Our main tool is the shooting method.
In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.