Topic
Piecewise
About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.
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TL;DR: This paper addresses the problem of delay-dependent robust and reliable static output feedback (SOF) control for uncertain discrete-time piecewise-affine (PWA) systems with time-delay and actuator failure in a singular system setup.
Abstract: This paper addresses the problem of delay-dependent robust and reliable $\mathscr {H}_{\infty }$ static output feedback (SOF) control for uncertain discrete-time piecewise-affine (PWA) systems with time-delay and actuator failure in a singular system setup. The Markov chain is applied to describe the actuator faults behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is converted into a singular PWA system. By constructing a mode-dependent piecewise Lyapunov–Krasovskii functional, a new $\mathscr {H}_{\infty }$ performance analysis criterion is then presented, where a novel summation inequality and S-procedure are succeedingly employed. Subsequently, thanks to the special structure of the singular system formulation, the PWA SOF controller design is proposed via a convex program. Illustrative examples are finally given to show the efficacy and less conservatism of the presented approach.
101 citations
TL;DR: An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved and the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost.
Abstract: This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomogeneous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each local region, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods.
101 citations
TL;DR: For describing the time-dependent mechanical property of rock during the creep, a new method of building creep model based on variable-order fractional derivatives is proposed in this article, where the order of the fractional derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order.
Abstract: For describing the time-dependent mechanical property of rock during the creep, a new method of building creep model based on variable-order fractional derivatives is proposed. The order of the fractional derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order. Through the segmentation treatment, according to different creep stages of the experimental results, it is found that the improved creep model based on variable-order fractional derivatives agrees well with the experimental data. In addition, the fact is verified that variable order of fractional derivatives can be regarded as a step function, which is reasonable and reliable. In addition, through further piecewise fitting, the parameters in the model are determined on the basis of existing experimental results. All estimated results show that the theoretical model proposed in the paper properly depicts the creep properties, providing an excellent agreement with the experimental data.
101 citations
TL;DR: In this paper, the application of the method of fundamental solutions to the Cauchy problem in two-dimensional isotropic linear elasticity is investigated, where the resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularised by employing the first-order Tikhonov functional, while the choice of the regularisation parameter is based on the L-curve method.
101 citations
TL;DR: In this article, boundary approximation techniques for homogeneous self-adjoint elliptic equations are described and convergence of such approximations is proved and error estimates are derived in a natural norm.
Abstract: Boundary approximation techniques are described for solving homogeneous self-adjoint elliptic equations. Piecewise expansions into particular solutions are used which approximate both the boundary and interface conditions in a least squares sense. Convergence of such approximations is proved and error estimates are derived in a natural norm. Numerical experiments are reported for the singular Motz problem which yield extremely accurate solutions with only a modest computational effort.
101 citations