Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements

The official published version of the article can be found at the link below.This paper is concerned with the robust filtering problem for a class of nonlinear stochastic systems with missing measurements and parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution, and the nonlinearities are expressed by the statistical means. The purpose of the filtering problem is to design a filter such that, for all admissible uncertainties and possible measurements missing, the dynamics of the filtering error is exponentially mean-square stable, and the individual steady-state error variance is not more than prescribed upper bound. A sufficient condition for the exponential mean-square stability of the filtering error system is first derived and an upper bound of the state estimation error variance is then obtained. In terms of certain linear matrix inequalities (LMIs), the solvability of the addressed problem is discussed and the explicit expression of the desired filters is also parameterized. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany

A Body-Nonlinear Green's Function Method with Viscous Dissipation Effects for Large-Amplitude Roll of Floating Bodies

A novel time-domain body-nonlinear Green’s function method is developed for evaluating large-amplitude roll damping of two-dimensional floating bodies with consideration of viscous dissipation effects. In the method, the instantaneous wetted surface of floating bodies is accurately considered, and the viscous dissipation effects are taken into account based on the “fairly perfect fluid” model. As compared to the method based on the existing inviscid body-nonlinear Green’s function, the newly proposed method can give a more accurate damping coefficient of floating bodies rolling on the free surface with large amplitudes according to the numerical tests and comparison with experimental data for a few cases related to ship hull sections with bilge keels

A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

Brueckner-Hartree-Fock and its renormalized calculations for finite nuclei

We have performed self-consistent Brueckner-Hartree-Fock (BHF) and its renormalized theory to the structure calculations of finite nuclei. The $G$-matrix is calculated within the BHF basis, and the exact Pauli exclusion operator is determined by the BHF spectrum. Self-consistent occupation probabilities are included in the renormalized Brueckner-Hartree-Fock (RBHF). Various systematics and convergences are studies. Good results are obtained for the ground-state energy and radius. RBHF can give a more reasonable single-particle spectrum and radius. We present a first benchmark calculation with other {\it ab initio} methods using the same effective Hamiltonian. We find that the BHF and RBHF results are in good agreement with other $\it{ab}$ $\it{initio}$ methods

Finite difference approximations for a size-structured population model with distributed states in the recruitment

In this paper we consider a size-structured population model where individuals may be recruited into the population at different sizes. First and second order finite difference schemes are developed to approximate the solution of the mathematical model. The convergence of the approximations to a unique weak solution with bounded total variation is proved. We then show that as the distribution of the new recruits become concentrated at the smallest size, the weak solution of the distributed states-at-birth model converges to the weak solution of the classical Gurtin-McCamy-type size-structured model in the weak$^*$ topology. Numerical simulations are provided to demonstrate the achievement of the desired accuracy of the two methods for smooth solutions as well as the superior performance of the second-order method in resolving solution-discontinuities. Finally we provide an example where supercritical Hopf-bifurcation occurs in the limiting single state-at-birth model and we apply the second-order numerical scheme to show that such bifurcation occurs in the distributed model as well

Isovector Giant Dipole Resonance of Stable Nuclei in a Consistent Relativistic Random Phase Approximation

A fully consistent relativistic random phase approximation is applied to study the systematic behavior of the isovector giant dipole resonance of nuclei along the $\beta$-stability line in order to test the effective Lagrangians recently developed. The centroid energies of response functions of the isovector giant dipole resonance for stable nuclei are compared with the corresponding experimental data and the good agreement is obtained. It is found that the effective Lagrangian with an appropriate nuclear symmetry energy, which can well describe the ground state properties of nuclei, could also reproduce the isovector giant dipole resonance of nuclei along the $\beta$-stability line.Comment: 4 pages, 1 Postscript figure, to be submitted to Chin.Phys.Let