Browsing by Subject "Piecewise-continuous"
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Item Open Access Conditions of well-posedness for planar conewise linear systems(Sage Publications, 2023-04-24) Namdar, Daniyal; Özgüler, Arif BülentA planar (2D) conewise linear system (CLS) is considered. This is a piecewise linear system of two states and multiple modes, where each mode is linear with its state-space constrained into a polyhedral, finitely generated, convex cone. It is allowed to have a discontinuous vector field and sliding modes. Alternative conditions for well-posedness of Caratheodory solutions of this system that have intuitive interpretations with respect to eigenvectors and cone-boundary vectors are derived. It is also shown that a well-known condition for well-posedness of bimodal systems also applies to two adjacent modes of this system without any change.Item Open Access Signal denoising by piecewise continuous polynomial fitting(IEEE, 2010) Yıldız, Aykut; Arıkan, OrhanPiecewise smooth signal denoising is cast as a non-linear optimization problem in terms of transition boundaries and a parametric smooth signal family. Optimal transition boundaries for a given number of transitions are obtained by using particle swarm optimization. The piecewise smooth section parameters are obtained as the maximum likelihood estimates conditioned on the optimal transition boundaries. The proposed algorithm is extended to the case where the number of transition boundaries are unknown by sequentially increasing number of sections until the residual error is at the level of noise standard deviation. Performance comparison with the state of the art techniques reveals the important advantages of the proposed technique. ©2010 IEEE.Item Open Access Wiener disorder problem with observations at fixed discrete time epochs(Institute for Operations Research and the Management Sciences (I N F O R M S), 2010) Dayanik, S.Suppose that a Wiener process gains a known drift rate at some unobservable disorder time with some zero-modified exponential distribution. The process is observed only at known fixed discrete time epochs, which may not always be spaced in equal distances. The problem is to detect the disorder time as quickly as possible by means of an alarm that depends only on the observations of Wiener process at those discrete time epochs. We show that Bayes optimal alarm times, which minimize expected total cost of frequent false alarms and detection delay time, always exist. Optimal alarms may in general sound between observation times and when the space-time process of the odds that disorder happened in the past hits a set with a nontrivial boundary. The optimal stopping boundary is piecewise-continuous and explodes as time approaches from left to each observation time. On each observation interval, if the boundary is not strictly increasing everywhere, then it irst decreases and then increases. It is strictly monotone wherever it does not vanish. Its decreasing portion always coincides with some explicit function. We develop numerical algorithms to calculate nearly optimal detection algorithms and their Bayes risks, and we illustrate their use on numerical examples. The solution of Wiener disorder problem with discretely spaced observation times will help reduce risks and costs associated with disease outbreak and production quality control, where the observations are often collected and/or inspected periodically.