Sampling and reconstruction of piecewise constant stochastic processes with Erlang stay time in states

A statistical sampling and reconstruction procedure is developed for the class of stochastic processes indicated in the title. The Erlang phase method and recurrent recalculation for conditional Markov processes are used. Formulas for the a posteriori distribution of the transition time are obtained for the respective first moments and sampling interval. The procedures are easy-to-implement computationally. The influence of process parameters on the procedure parameters is analyzed. An illustrative example is given.     

Optimal piecewise constant control of continuous time systems with time-varying delay

Necessary conditions are presented for the optimal piecewise constant control of continuous time systems with time-varying delay. The conventional Hamiltonian is used; the effect of the delay is included in the costate equation. A fixed endpoint problem is formulated for a scalar system. Restricting the control to be piecewise constant results in a condition on the Hamiltonian integrated between switching instants. The extension to more general terminal constraints for multivariable systems is straight-forward.     

Approximative piecewise constant bang-bang principle for differential repetitive processes

In the article, we consider a point controllability over all (infinite many) passes for linear differential repetitive processes. We prove the following approximative piecewise constant bang-bang principle: the set of points that can be reached with the aid of measurable controls on passes, taking the values in a convex compact set M ? ? ^r coincides with the closure of the set of points that can be reached with the aid of piecewise constant controls on passes, taking the values in the set of extreme points of M.     

Tracking of non-square nonlinear continuous time systems with piecewise constant model predictive control

The paper presents a model predictive control (MPC) algorithm for continuous-time, possibly non-square nonlinear systems. The algorithm guarantees the tracking of asymptotically constant reference signals by means of a control scheme were the integral action is directly imposed on the error variables rather than on the control moves. The plant under control, the state and control constraints and the performance index to be minimized are described in continuous time, while the manipulated variables are allowed to change at fixed and uniformly distributed sampling times. The algorithm is used to control a continuous fermenter where the manipulated variables are the dilution rate and the feed substrate concentration while the controlled variable is the biomass concentration.     

分片常值灰度图像的快速分割

PC模型是一个著名的基于区域的活动轮廓模型,它实际上是利用水平集方法解决分片常值灰度图像的分割问题。提出一个以偏微分方程形式表达的新模型,它可以看成是PC模型的一种改进。实验显示：新模型能够实现分片常值灰度图像的快速分割,同时迭代次数对初始轮廓的大小和位置不敏感。     

Evaluation of piecewise smooth subdivision surfaces

Published online: 23 July 2002     

Optimal design of rigid-plastic annular plates with piecewise constant thickness

Rigid-plastic stepped annular plates under uniform pressure load are considered. Both plate edges are supported. Four types of boundary conditions are studied. Tresca's yield condition is used. Such plate dimensions are sought for which the plate of constant volume has the maximal load carrying capacity.Notation a, d, R, h ₁, h₂ plate dimensions (Fig. 1) - Q ^* shear force - Q dimensionless shear force - M _r ^* radial bending moment - M ₁ dimensionless radial bending moment - M _t ^* circumferential bending moment - M ₂ dimensionless circumferential bending moment - M _k maximum value of bending moments in the rigid region - p ^* uniform pressure load - p dimensionless uniform pressure load - r radial coordinate - x dimensionless radial coordinate - , , dimensionless parameters for plate (5) - V plate volume - dimensionless plate volume - M ₀ ^* yield moment - ₀ yield stress - p ₀ load carrying capacity - p ₀ ^m maximum value of the load carrying capacity - p ₀ ^u load carrying capacity for uniform plate - ^m, ^m optimal parameters, which correspond to the maximum value ofp ₀ - s _i radius of circle between different plastic stages - () /x     

Simulating diffusions with piecewise constant coefficients using a kinetic approximation

Using a kinetic approximation of a linear diffusion operator, we propose an algorithm that allows one to deal with the simulation of a multi-dimensional stochastic process in a media which is locally isotropic except on some surface where the diffusion coefficient presents some discontinuities. Basic numerical examples are given in dimensions one to three on PDEs or stochastic PDEs with or without source terms. Finally, we compute the hydro-dynamic load in a porous media in the nuclear waste context.     

Model predictive control of continuous-time nonlinear systems with piecewise constant control

A new model predictive control (MPC) algorithm for nonlinear systems is presented. The plant under control, the state and control constraints, and the performance index to be minimized are described in continuous time, while the manipulated variables are allowed to change at fixed and uniformly distributed sampling times. In so doing, the optimization is performed with respect to sequences, as in discrete-time nonlinear MPC, but the continuous-time evolution of the system is considered as in continuous-time nonlinear MPC.     

Computing stable poses of piecewise smooth objects

When a three dimensional object is known to be lying on a planar surface, its pose is restricted from six to three degrees of freedom. Computer vision algorithms can exploit the few stable poses of modeled objects to simplify scene interpretation and more accurately determine object location. This paper presents necessary and sufficient conditions for the pose of a piecewise smooth curved three-dimensional object to be stable. For objects whose surfaces are represented by implicit algebraic equations, these conditions can be expressed as systems of polynomial equations that are readily solved by homotopy continuation. Examples from the implemented algorithm are presented.     

Analysis and recognition of piecewise constant texture images

New methods of recognition of texture-valued images have been proposed and analyzed. These methods derive from the well-known morphological approach to analysis and recognition [1, 2] of intensity-valued images. In order to convert texture characteristics into numeric intensity values, texture detectors have been developed. The proposed algorithms are tested in application to the problem of digit recognition. Sergey O. Evsegneev. Born 1979. Graduated from the Faculty of Physics, Moscow State University, in 2003. Postgraduate student at the same faculty. Scientific interests: image analysis and recognition.     

Robust Morse decompositions of piecewise constant vector fields

In this paper, we introduce a new approach to computing a Morse decomposition of a vector field on a triangulated manifold surface. The basic idea is to convert the input vector field to a piecewise constant (PC) vector field, whose trajectories can be computed using simple geometric rules. To overcome the intrinsic difficulty in PC vector fields (in particular, discontinuity along mesh edges), we borrow results from the theory of differential inclusions. The input vector field and its PC variant have similar Morse decompositions. We introduce a robust and efficient algorithm to compute Morse decompositions of a PC vector field. Our approach provides subtriangle precision for Morse sets. In addition, we describe a Morse set classification framework which we use to color code the Morse sets in order to enhance the visualization. We demonstrate the benefits of our approach with three well-known simulation data sets, for which our method has produced Morse decompositions that are similar to or finer than those obtained using existing techniques, and is over an order of magnitude faster.     

Estimation in bivariate nonnormal distributions with stochastic variance functions

Data sets in numerous areas of application can be modelled by symmetric bivariate nonnormal distributions. Estimation of parameters in such situations is considered when the mean and variance of one variable is a linear and a positive function of the other variable. This is typically true of bivariate t distribution. The resulting estimators are found to be remarkably efficient. Hypothesis testing procedures are developed and shown to be robust and powerful. Real life examples are given.     

Note on the design of linear systems with piecewise constant feedback gains

The purpose of this correspondence is to report some relations that can be used to extend the scope of a computational algorithm for the suboptimal design of linear regulator systems. This algorithm was presented in [1], and can be used to determine suboptimal piecewise constant feedback gains to be used instead of the optimal continuously time-varying ones [3]. This correspondence deals with the extension to the case where, in addition to the piecewise constant gains, the switching times are also optimized.     

Steady Navier–Stokes equations in a domain with piecewise smooth boundary

We are concerned with the boundary value problem for the steady Navier–Stokes equations in a 2D bounded domain with piecewise smooth boundary. Existence and uniqueness of the solution to the above problem is proved in weighted Sobolev spaces by means of the Mellin transform and the regularizer method.     

Analysis of piecewise constant delay systems via block-pulse functions

The solution of linear piecewise constant delay systems has been derived by using the block pulse series expansion method. A matrix called the delay operational matrix is introduced first to manipulate the time delay. Then the solution is obtained through using the matrix and the properties of block pulse functions.