Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems

It is shown that, if a parametrized fämily of extremals F can be stratified in a way compatible with the flow map generated by F, then those trajectories of the family which realize the minimal values of the cost in F are indeed optimal in comparison with all trajectories which lie in the region R covered by the trajectories of F. It is not assumed that F is a field covering the state space injectively. As illustration, an optimal synthesis is constructed for a system where the flow of extremals exhibits a simple cusp singularity.     

Combining Swaps and Node Weights in an Adaptive Greedy Approach for the Maximum Clique Problem

In this work, the NP-hard maximum clique problem on graphs is considered. Starting from basic greedy heuristics, modifications and improvements are proposed and combined in a two-phase heuristic procedure. In the first phase an improved greedy procedure is applied starting from each node of the graph; on the basis of the results of this phase a reduced subset of nodes is selected and an adaptive greedy algorithm is repeatedly started to build cliques around such nodes. In each restart the selection of nodes is biased by the maximal clique generated in the previous execution. Computational results are reported on the DIMACS benchmarks suite. Remarkably, the two-phase procedure successfully solves the difficult Brockington-Culberson instances, and is generally competitive with state-of-the-art much more complex heuristics.     

Capture of an Ensemble of Microparticles in the Field of Laser Multibeam Interference

Capture of an ensemble of polymeric microspheres in a water suspension under the action of optical gradient forces in the field of interfering laser beams has been investigated for the case of two-, three-, and four-beam interference. The self-diffraction and diffraction of radiation on induced ordered spatial distribution of particles have been obtained.     

Three methods for analyzing forced vibration of a fluid-filled cylindrical shell

The forced vibration of an infinite elastic circular cylindrical shell filled with fluid is studied. Three methods are employed to analyze the forced vibration problem of this shell-fluid coupled system, that is, wave propagation approach (wave mode superposition), theorem of residues and a numerical integral method. In order to explain these methods more explicitly, before being used to investigate the vibration of an infinite fluid-filled elastic circular cylindrical shell, all these three methods are employed firstly to analyze the forced vibration problem of an infinite beam and an infinite elastic circular cylindrical shell in vacuo. Advantage and disadvantage of these three methods are discussed and their interesting relationship is revealed. That is, to any circumferential wavenumber and frequency of the external force, there is an unchangeable relationship between the general coordinates of various waves in the wave propagation approach and the residuals in the theorem of residues.     

Randomization helps to perform independent tasks reliably

This paper is about algorithms that schedule tasks to be performed in a distributed failure‐prone environment, when processors communicate by message‐passing, and when tasks are independent and of unit length. The processors work under synchrony and may fail by crashing. Failure patterns are imposed by adversaries. Linearly‐bounded adversaries may fail up to a constant fraction of the processors. Weakly‐adaptive adversaries have to select, prior to the start of an execution, a subset of processors to be failure‐prone, and then may fail only the selected processors, at arbitrary steps, in the course of the execution. Strongly adaptive adversaries have a total number of failures as the only restriction on failure patterns. The measures of complexity are work, measured as the available processor steps, and communication, measured as the number of point‐to‐point messages. A randomized algorithm is developed, that attains both ??(n log*n) expected work and ??(n log*n) expected communication, against weakly‐adaptive linearly‐bounded adversaries, in the case when the numbers of tasks and processors are both equal to n. This is in contrast with performance of algorithms against strongly‐adaptive linearly‐bounded adversaries, which has to be Ω(n log n/log log n) in terms of work. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

On the departure process of a leaky bucket system with long-range dependent input traffic

Due to the strong experimental evidence that the traffic to be offered to future broadband networks will display long-range dependence, it is important to study the possible implications that such traffic may have for the design and performance of these networks. In particular, an important question is whether the offered traffic preserves its long-range dependent nature after passing through a policing mechanism at the interface of the network. One of the proposed solutions for flow control in the context of the emerging ATM standard is the so-called leaky bucket scheme. In this paper we consider a leaky bucket system with long-range dependent input traffic. We adopt the following popular model for long-range dependent traffic: Time is discrete. At each unit time a random number of sessions is initiated, having the distribution of a Poisson random variable with mean λ. Each of these sessions has a random duration τ, where the integer random variable τ has finite mean, infinite variance, and a regularly varying tail, i.e., P(τ >К) ~ К^-Lα L(К), where 1 < α < 2 L(·) is a slowly varying function. Once a session is initiated, it generates one cell at each unit of time until its termination. We examine the departure process of the leaky bucket policing mechanism driven by such an arrival process, and show that it too is long-range dependent for any token buffer size and any - finite or infinite - cell buffer size. Moreover, upper and lower bounds for the covariance sequence of the output process are established. The above results demonstrate that long-range dependence cannot be removed by the kinds of flow control schemes that are currently being envisioned for broadband networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

GDDP: Generalized Dual Dynamic Programming Theory

This document presents theoretical considerations about the solution of dynamic optimization problems integrating the Benders Theory, the Dynamic Programming approach and the concepts of Control Theory. The so called Generalized Dual Dynamic Programming Theory (GDDP) can be considered as an extension of two previous approaches known as Dual Dynamic Programming (DDP): The first is the work developed by Pereira and Pinto [3–5], which was revised by Velásquez and others [8,9]. The second is the work developed by Read and others [2,6,7].