作者：
Wu, CWIBM Corp
Div Res Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA
There are, in general, two classes of results regarding the synchronization of chaos in an array of coupled identical chaotic systems. The first class of results relies on Lyapunov's direct method and gives analyt...
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There are, in general, two classes of results regarding the synchronization of chaos in an array of coupled identical chaotic systems. The first class of results relies on Lyapunov's direct method and gives analytical criteria for global or local synchronization. The second class of results relies on linearization around the synchronization manifold and the computation of Lyapunov exponents. The computation of Lyapunov exponents is mainly done via numerical experiments and can only show local synchronization in the neighborhood of the synchronization manifold. On the other hand, Lyapunov's direct method is more rigorous and can give global results. The coupling topology is generally expressed in matrix form and the first class of methods mainly deals with symmetric matrices whereas the second class of methods can work with all diagonalizable matrices. The purpose of this brief is to bridge the gap in the applicability of the two classes of methods by considering the nonsymmetric case-for the first class of methods. We derive a synchronization criterion for nonreciprocal coupling related to a numerical quantity that depends on the coupling topology and we present methods for computing this quantity.
Simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation. This paper modifies the Hooke-Jeeves alternating...
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Simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation. This paper modifies the Hooke-Jeeves alternating variable method used in deterministic optimization to suit the stochastic environment in simulation response optimization. The basic idea underlying the proposed method is to conduct several different replications at each trial point to obtain a reliable estimate of the theoretical response. To avoid misjudging the real difference between two points due to the stochastic nature, a t-test instead of a simple comparison of the mean responses is performed. Empirical results from a stochastic Watson function with nine variables, a queueing problem with two variables, and an inventory problem with two variables indicate that the alternating variable method modified in this paper is superior to the Nelder-Mead simplex method, two stochastic approximation methods, and Fu and Healy's hybrid method. It is also robust with respect to the parameter for deciding the number of replications conducted at each trial point.
In robust system analysis and robust controller design, the parameters of the nominal system and admissible perturbation classes are usually assumed to be known. In many cases, these classes are described by constrain...
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In robust system analysis and robust controller design, the parameters of the nominal system and admissible perturbation classes are usually assumed to be known. In many cases, these classes are described by constraints on perturbation norms and weight filters. Model validation consists in verifying whether the nominal model and the a priori assumptions on measurement perturbations are consistent. A far more difficult problem is the estimation of norms or weights of perturbations from measurement data. In this paper, model verification and perturbation weight estimation are investigated within the framework the l(1)-theory of robust control corresponding to the fundamental signal space l(infinity). For any model in the form of a linear stationary discrete system with structured uncertainty, model validation is reduced to verifying, whether a system of inequalities generated by measurements holds or riot. For a model with unstructured uncertainty and diagonal weighted perturbations, optimization of perturbation weights is reduced a fractional quadratic programming problem. For a model with perturbations of irreducible multipliers of the transfer matrix of the nominal system, optimization of perturbation weights is reduced a linear programming problem.
The algorithm presented in this article incorporates the trust region method (TR) into the restricted decomposition algorithm for convex-constrained nonlinear problems (RSDCC) to solve the master problem of RSDCC. The...
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The algorithm presented in this article incorporates the trust region method (TR) into the restricted decomposition algorithm for convex-constrained nonlinear problems (RSDCC) to solve the master problem of RSDCC. The global convergence is proved. The computational comparison between the presented algorithm and RSDCC is given. The results show that the former is much better than the latter.
An overview is given on the application of the covector mapping theorem (CMT) to the verification of the first-order optimality conditions arising in the path-constrained trajectory optimization of reentry vehicles. T...
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An overview is given on the application of the covector mapping theorem (CMT) to the verification of the first-order optimality conditions arising in the path-constrained trajectory optimization of reentry vehicles. The problem chosen for this purpose is the standard benchmark problem of maximizing cross range.
Under F-convexity, F-concavity/F-pseudoconvexity, F-pseudoconcavity, appropriate duality results for a pair of Wolfe and Mond-Weir type symmetric dual nonlinear programming problems in complex spaces are established. ...
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Under F-convexity, F-concavity/F-pseudoconvexity, F-pseudoconcavity, appropriate duality results for a pair of Wolfe and Mond-Weir type symmetric dual nonlinear programming problems in complex spaces are established. These results are then used to develop second order F-convexity, F-concavity, second order F-pseudoconvexity, F-pseudoconcavity, and appropriate second order symmetric dual nonlinear programming problems in complex spaces. (C) 2003 Elsevier Inc. All rights reserved.
We present a learning-oriented interactive reference direction algorithm for solving multi-objective convex nonlinear integer programming problems. At each iteration the decision-maker (DM) sets his/her preferences as...
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We present a learning-oriented interactive reference direction algorithm for solving multi-objective convex nonlinear integer programming problems. At each iteration the decision-maker (DM) sets his/her preferences as aspiration levels of the objective functions. The modified aspiration point and the solution found at the previous iteration define the reference direction. Based on the reference direction, we formulate a mixed-integer scalarizing problem with specific properties. By solving this problem approximately, we find one or more integer solutions located close to the efficient surface. At some iteration (usually at the last iteration), the DM may want to solve the scalarizing problem to obtain an exact (weak) efficient solution. Based on the proposed algorithm, we have developed a research-decision support system that includes one exact and one heuristic algorithm. Using this system, we illustrate the proposed algorithm with an example, and report some computational results. International Federation of Operational Research Societies 2001.
A transportation problem is a linear programming problem based on a network structure consisting of a finite numbers of nodes and arcs attached to them. In real world applications, the supply and demand quantities in ...
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A transportation problem is a linear programming problem based on a network structure consisting of a finite numbers of nodes and arcs attached to them. In real world applications, the supply and demand quantities in the transportation problem are sometimes hardly specified precisely because of changing economic conditions. This paper investigates the transportation problem when the demand and supply quantities are varying. A pair of mathematical programs is formulated to calculate the objective value. The derived result is also in range, where the total transportation cost would appear. In addition to allowing for simultaneous changes in supply and demand values, the total cost bounds are calculated directly. Due to the structure of the transportation problem, the largest total transportation cost may not occur at the highest total quantities shipped. Since the total cost bounds are derived, it would be beneficial to decision-making. (C) 2003 Elsevier Science Ltd. All rights reserved.
This paper describes how the use of monadic second-order logic for specifying regular languages can be extended for specifying regular relations, providing a declarative description language for finite state transduct...
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This paper describes how the use of monadic second-order logic for specifying regular languages can be extended for specifying regular relations, providing a declarative description language for finite state transductions of the sort used in NLP. We discuss issues arising in the integration into an automaton toolkit of an implementation of the conversion from logic formulas to automata. The utility of the logic of regular relations is demonstrated by showing how it can be used to define the family of replacement operators in a way that lends itself to straightforward proofs of correctness.
Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability, and design are discussed. One of them is the still challenging problem of ...
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Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability, and design are discussed. One of them is the still challenging problem of producing dynamically stable gaits. The generation of fast walking or running motions requires methods and algorithms adept at handling the nonlinear dynamical effects and stability issues which arise. Reduced, recursive multibody algorithms, a numerical optimal control method, and new stability and energy performance indices are presented which are well-suited for this purpose. Difficulties and open problems are discussed along with numerical investigations into the proposed gait generation scheme. Our analysis considers both bipedal and quadrupedal gaits. (C) 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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