基于观测器的一类时滞不确定非线性离散系统的鲁棒模糊控制

讨论一类基于Takagi-Sugeno(T-S)模糊模型的具有时滞的不确定非线性离散系统的模糊鲁棒控制问题。在系统状态不可测的情况下。设计模糊观测器。利用LMI方法，得到模糊控制系统鲁棒稳定的充分条件。     

Differentiability of Consistency Functions for DAE Systems

In the present paper, parametric initial-value problems for differential-algebraic (DAE) systems are investigated. It is known that the initial values of DAE systems must satisfy not only the original equations in the system but also the derivatives of these equations with respect to time. Whether or not this actually imposes additional constraints on the initial values depends on the particular problem.Often the initial values are not determined uniquely, so that the resulting degrees of freedom can be used to optimize a given performance index. For this purpose, the class of so-called consistency functions is defined. These functions map a set of parameters, which include also those undetermined initial values, to consistent initial values for the DAE system. Because of frequent gradient evaluations of the performance index and the constraints with respect to these system parameters needed by many optimization procedures, we state conditions such that the consistency functions represent differentiable functions with respect to these parameters. Several examples are provided to illustrate the verification of the theoretical assumptions and their differentiability properties.The authors would like to thank the referees for helpful suggestions and comments     

Performance analysis of single stage kanban controlled production systems using parametric decomposition

We present a new approach that permits efficient performance analysis of kanban systems with general demand processes, material arrival processes, and service times. The approach is based on parametric characterization of the traffic processes (arrival and departure) in the network and uses two-moment approximations to estimate performance measures at individual stations. We derive traffic flow constraints that are particular to closed queuing networks with synchronization stations and use these to establish relationships between the parameters characterizing arrival and departure processes at the stations in the network. The resultant set of non-linear equations is solved to estimate network performance measures. Numerical studies show that the approach is not only fast but also reasonably accurate when compared to simulation. These studies also provide insights with respect to the impact of different types of variability on the performance of a kanban system. This work also provides a fundamental building block that can be used in the analysis of multi-stage kanban systems. AMS Subject Classifications 68M20, 60K20, 90B05, 90B30     

Noncollinear optical parametric amplification in lithium triborate seeded by a cw Ti:sapphire laser

Experimental investigations of a type-I noncollinear phase-matched optical parametric amplification based on lithium triborate, which was pumped by a 5-ns second-harmonic pulses from a Q-switched Nd:YAG, seeded by a cw Ti:sapphire laser at 800 nm, was presented. The experiments generated 2-ns signal output pulses at 800 nm, the maximum signal output pulse energy reached 19 μJ, the corresponding parametric gain was 44 dB. Furthermore, the experiments demonstrate that the 65 nm-FWHM parametric fluorescence gain spectrum could also be observed. A quantitative account of the ultrabroadband parametric fluorescence gain spectrum was given with our theory. The experimental measurements are in agreement with theoretical calculations.     

A closed-form representation of mixed-integer program value functions

We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients.     

Strongly polynomial-time approximation for a class of bicriteria problems

Consider the following problem: given a ground set and two minimization objectives of the same type find a subset from a given subset-class that minimizes the first objective subject to a budget constraint on the second objective. Using Megiddo's parametric method we improve an earlier weakly polynomial time algorithm.     

Parameterized approximations for the two-sided assortment optimization

We consider the problem faced by an online service platform that matches suppliers with consumers. Unlike traditional matching models, which treat them as passive participants, we allow both sides of the market to exercise their choices. To model this setting, we introduce a two-sided assortment optimization model wherein each participant's choice is modeled using a multinomial logit choice function, and the platform's objective is to maximize its expected revenue. We first show that the problem is NP-hard even when the number of suppliers is limited to two and provide a mixed-integer linear programming formulation. Next, we discuss two simple greedy heuristics and argue that these can lead to arbitrarily bad solutions. We then develop relaxations that provide upper and lower bounds and investigate the tightness of these relaxations by obtaining parametric approximation guarantees. Finally, we present numerical results on synthetic data demonstrating the practical utility of these relaxations.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.