Switching systems and entropy

Switching systems are non-autonomous dynamical systems obtained by switching between two or more autonomous dynamical systems as time goes on. They can be mainly found in control theory, physics, economy, biomathematics, chaotic cryptography and of course in the theory of dynamical systems, in both discrete and continuous time. Much of the recent interest in these systems is related to the emergence of new properties by the mechanism of switching, a phenomenon known in the literature as Parrondo's paradox. In this paper we consider a discrete-time switching system composed of two affine transformations and show that the switched dynamics has the same topological entropy as the switching sequence. The complexity of the switching sequence, as measured by the topological entropy, is fully transferred, for example, to the switched dynamics in this particular case.     

Introduction to the Special Issue on Discrete Event Models of Continuous Systems

Automatic control systems rely on models to predict the near future and identification algorithms to adapt the models to changing process behaviour. The traditionally highly complex models of the activated sludge process developed for scientific purposes cannot be identified from on-line measurements and are not suited for process control purposes in their present form. Model decoupling based on the different time scales of the dynamic processes is one possible way of attacking this problem. It allows the implementation of more simple and realistically applicable controllers in combination with predictions based on simplified models in hierarchical control structure. This paper discusses these concepts and presents a reduced order model describing carbonaceous removal, nitrification, and denitrification in a medium time scale (several hours/days). The model parameters are identifiable from available on-line measurements and the dynamic behaviour is verified against computer simulations of the IAWQ activated sludge model no. 1.     

Economic lot sizing: The capacity reservation model

Capacity reservation contracts allow a consumer to purchase up to a certain capacity at a unit price lower than that of the spot market, while the consumer’s excess orders are realized at the spot price. In this paper, we consider a lot sizing problem where the consumer places orders following a capacity reservation contract. In particular, we study the general problem and the polynomial time solvable special cases of the problem and propose corresponding algorithms for them.     

具有2n线性复杂度的2n周期二元序列的3错线性复杂度

线性复杂度和k错线性复杂度是度量密钥流序列的密码强度的重要指标.通过研究周期为2n的二元序列线性复杂度,提出将k错线性复杂度的计算转化为求Hamming重量最小的错误序列.基于Games-Chan算法,讨论了线性复杂度为2n的2n周期二元序列的3错线性复杂度分布情况;给出了对应k错线性复杂度序列的完整计数公式, k=3,4.对于一般的线性复杂度为2n-m的2n周期二元序列,也可以使用该方法给出对应k错线性复杂度序列的计数公式.     

New Interior-Point Algorithm for Symmetric Optimization Based on a Positive-Asymptotic Barrier Function

Abstract

We define a new interior-point method (IPM), which is suitable for solving symmetric optimization (SO) problems. The proposed algorithm is based on a new search direction. In order to obtain this direction, we apply the method of algebraically equivalent transformation on the centering equation of the central path. We prove that the associated barrier cannot be derived from a usual kernel function. Therefore, we introduce a new notion, namely the concept of the positive-asymptotic kernel function. We conclude that this algorithm solves the problem in polynomial time and has the same complexity as the best known IPMs for SO.