Browsing by Subject "Piece-wise"
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Item Open Access A comprehensive approach to universal piecewise nonlinear regression based on trees(IEEE, 2014) Vanli, N. D.; Kozat, S. S.In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We use a tree notion in order to partition the space of regressors in a nested structure. The introduced algorithms adapt not only their regression functions but also the complete tree structure while achieving the performance of the 'best' linear mixture of a doubly exponential number of partitions, with a computational complexity only polynomial in the number of nodes of the tree. While constructing these algorithms, we also avoid using any artificial 'weighting' of models (with highly data dependent parameters) and, instead, directly minimize the final regression error, which is the ultimate performance goal. The introduced methods are generic such that they can readily incorporate different tree construction methods such as random trees in their framework and can use different regressor or partitioning functions as demonstrated in the paper.Item Open Access Dwell-time computation for stability of switched systems with time delays(IET, 2013) Caliskan, S. Y.; Özbay, Hitay; Niculescu, S. I.The aim of this study is to find an improved dwell time that guarantees the stability of switched systems with heterogeneous constant time-delays. Piecewise Lyapunov-Krasovkii functionals are used for each candidate system to investigate the stability of the switched time-delayed system. Under the assumption that each candidate system is stable for small delay values, a sufficient condition for dwell-time that guarantees the asymptotic stability is derived. Numerical examples are given to compare the results with the previously obtained dwell-time bounds.Item Open Access Lot sizing with piecewise concave production costs(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014) Koca, E.; Yaman, H.; Aktürk, M. S.We study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming algorithm to solve this problem and answer an open question in the literature: we show that the problem is polynomially solvable when the breakpoints of the production cost function are time invariant and the number of breakpoints is fixed. For the special cases with capacities and subcontracting, the time complexity of our algorithm is as good as the complexity of algorithms available in the literature. We report the results of a computational experiment where the dynamic programming is able to solve instances that are hard for a mixed-integer programming solver. We enhance the mixed-integer programming formulation with valid inequalities based on mixing sets and use a cut-and-branch algorithm to compute better bounds. We propose a state space reduction-based heuristic algorithm for large instances and show that the solutions are of good quality by comparing them with the bounds obtained from the cut-and-branch.Item Open Access Stability analysis of switched systems using Lyapunov-Krasovskii functionals(Elsevier, 2011) Çalişkan, S.Y.; Özbay, Hitay; Niculescu, S.-I.Piecewise Lyapunov-Razumikhin functions are previously used for obtaining a lower bound for the dwell time of the switched time delay systems under the assumption that each candidate system is delay dependently stable. In this work, using Lyapunov-Krasovskii functionals, a less conservative lower bound for the dwell time is obtained. Improvement in the dwell time is illustrated with an example. © 2011 IFAC.