Nonlinear Optimal Approach to Spacecraft Formation Flying Using Lorentz and Impulsive Actuation

Journal of Optimization Theory and Applications - This paper proposes an optimal control design framework for hybrid nonlinear time-dependent dynamical systems involving an interacting mixture of...     

Gerrymander-proof representative democracies

International Journal of Game Theory - This article is devoted to the analysis of electoral systems involving two step procedures. It appears that designers are able to manipulate the result of...     

Impulsive control of multiple Lotka–Volterra systems

In this work, we consider the control problem of multiple Lotka–Volterra system. Our means to control the population dynamics is via impulses not only in a single species, but also in multiple species, that is, some members of these populations are added to or removed from the environment impulsively at the same time. We establish the strategies for preventing all the species from going extinct by stabilizing some special positive points, which may not be the equilibrium points of the system. We give several Lotka–Volterra systems to illustrate our results by drawing their time-series graphs.     

Multistage reverse logistics of assembly systems in extended MRP Theory consisting of all material flows

In this paper we will address the issue of environmental problems in connection with extended MRP Theory. It is based on Grubbstr?m??s well developed MRP Theory (Grubbstr?m in Z für BetrWirthsch 77(3):297?C324, 2007). A major advantage of this theory is that timing and its impact on net present value can be easily calculated even for extended multilevel, multistage production-inventory systems and also for perturbed production systems consisting of many production cells. Theory has recently been extended by including reverse logistics of final and used products (Grubbstr?m et?al. in A compact representation of distribution and reverse logistics in the value chain. Faculty of Economics, Ljubljana, 2007). At each activity cell a certain percentage of scrapes is produced and sent for recycling after quality control. Here we present an input?Coutput model which includes all possible flows into a recycling sub-process with several stages of recycling. This model is presented in a generalized form of input and output matrices which has not been developed before. The model will be presented in two different ways which differ in the level of detailed information they contain. Contribution of recycling to the net present value of all activities in a supply chain is expressed and can be compared to environmental damage that could occur if reverse processes are not introduced. Using this approach, the losses and gains in both the economy and the environment could be evaluated more accurately considering all individual flows in the system. No other approaches besides input?Coutput analysis and Laplace transforms have been found so successful in compound supply systems.     

The general behavior of pull production systems: The allocation problems

The design of tandem production systems has been well studied in the literature with the primary focus being on how to improve their efficiency. Considering the large costs associated, a slight improvement in efficiency can lead to very significant savings over its life. Division of work and allocation of buffer capacities between workstations are two critical design problems that have attracted the attention of many researchers. In this study, first an understanding into how the system works is to be provided. Except for the integration of two allocation problems, the basic model utilized here is essentially the same as the previous studies. Theoretical results that characterize the dynamics of these systems may also provide some heuristic support in the analysis of large-scale pull production systems.     

Random-Direction Optimization Algorithms with Applications to Threshold Controls

This work develops a class of stochastic optimization algorithms. It aims to provide numerical procedures for solving threshold-type optimal control problems. The main motivation stems from applications involving optimal or suboptimal hedging policies, for example, production planning of manufacturing systems including random demand and stochastic machine capacity. The proposed algorithm is a constrained stochastic approximation procedure that uses random-direction finite-difference gradient estimates. Under fairly general conditions, the convergence of the algorithm is established and the rate of convergence is also derived. A numerical example is reported to demonstrate the performance of the algorithm.     

A necessary and sufficient condition for input identifiability for linear time-invariant systems

A necessary and sufficient condition for input identifiability for linear autonomous systems is given. The result is based on a finite iterative process and its proof relies on elementary arguments involving matrices, finite dimensional linear spaces, Gronwall’s lemma, and linear differential systems. Our condition is equivalent to the classical condition involving the geometrical concept of controlled invariant [V. Basile, G. Marro, Controlled and Conditioned Invariants in Linear System Theory, Prentice Hall, Englewood Cliffs, NJ, 1992, p. 237] and the dimension reduction algorithm that we propose seems to be useful in designing deconvolution methods.     

与(p,q)-Laplace算子相关的非线性Dirichlet椭圆系解的存在性及其迭代构造(英文)

利用变分不等式解的存在性的结论,研究了一类与(p,q)-Laplace算子相关的非线性Dirichlet椭圆系解的存在性的抽象结论.然后,利用极大单调算子零点的结论,构造了一种迭代格式强收敛到上述椭圆系的解.本文所研究的椭圆系及所用方法是对以往一些工作的推广和补充.     

A survey of solved problems and applications on bandwidth,edgesum, and profile of graphs

This article provides a survey of results on the exact bandwidth, edgesum, and profile of graphs. A bibliography of work in these areas is provided. The emphasis is on composite graphs. This may be regarded as an update of the original survey of solved bandwidth problems by Chinn, Chvátalová, Dewdney, and Gibbs [10] in 1982. Also several of the application areas involving these graph parameters are described. © John & Sons, Inc. Graph Theory 31: 75–94, 1999     

From extended regular variation to regular variation with application in extreme value statistics

This paper aims to provide a study of a variety of concepts involving power behavior of eventually positive functions which, falling under the umbrella of the Theory of Regular Variation and its second order refinements, are prone to application in Extreme Value Theory. To this extent, some well-known properties shall be resumed, others will be designed with the ultimate purpose of establishing a relation between regular variation and extended regular variation of second order. As a by-product, new ways of looking at some common estimators for the extreme value index, in particular the maximum likelihood estimator, will be unveiled.     

The chromatic connectivity of graphs

A graphG ischromatically k-connected if every vertex cutset induces a subgraph with chromatic number at leastk. This concept arose in some work, involving the third author, on Ramsey Theory. (For the reference, see the text.) Here we begin the study of chromatic connectivity for its own sake. We show thatG is chromaticallyk-connected iff every homomorphic image of it isk-connected. IfG has no triangles then it is at most chromatically 1-connected, but we prove that the Kneser graphs provide examples ofK ₄-free graphs with arbitrarily large chromatic connectivity. We also verify thatK ₄-free planar graphs are at most chromatically 2-connected.This work was supported by grants from NSERC of Canada.     

On the Ambrosetti‐Prodi problem for a system involving p‐Laplacian operator

In this work we study an Ambrosetti‐Prodi type problem for an elliptic system involving p‐Laplacian operator. The sub and supersolution method and the Leray‐Schauder Degree Theory are used in order to prove our result.     

Introductory Statement

This work continues the account given in Part I of the paper¹ by presenting a short summary of some of the mathematical techniques employed in the wave front analysis of quasi‐linear hyperbolic partial differential equations. Starting from a number of important physical examples, the classification of quasi‐linear first‐order systems is discussed and followed by a simple account of the theory of characteristics for systems involving n dependent and two independent variables. A special example is discussed showing how discontinuities arise in solutions, and the paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics.     

A note on the ‘underadjustment phenomenon’

In recent work in the area of employment discrimination statistics we have noticed that a basic formula quantifying the degree of underadjustment bias in regression coefficients seems not to have been clearly stated and proved. We believe the underadjustment phenomenon to be of great importance in assessing the validity of multiple regression studies of wage disparities in equal employment litigation, and of observational studies involving two populations in general. Since the argument is based entirely on some simple mathematical features of the linear model, the result should be of interest in other fields of application as well.     

Description of complex dynamics in a class of impulsive differential equations

Dynamical evolutions involving from equilibrium state to complex motion are prevalent not only in systems depicted by either continuous equations or discrete iterations but also in models governed by hybrid systems. In particular, chaotic motion could be found in hybrid systems whose dimension is even less than three. In this paper, we attempt to provide some concepts to describe various dynamics that occur in the simulations of a class of impulsive differential equations. Furthermore, some specific examples are also provided to illustrate these established concepts.     

A radial basis function method for solving PDE-constrained optimization problems

In this article, we apply the theory of meshfree methods to the problem of PDE-constrained optimization. We derive new collocation-type methods to solve the distributed control problem with Dirichlet boundary conditions and also discuss the Neumann boundary control problem, both involving Poisson’s equation. We prove results concerning invertibility of the matrix systems we generate, and discuss a modification to guarantee invertibility. We implement these methods using Matlab, and produce numerical results to demonstrate the methods’ capability. We also comment on the methods’ effectiveness in comparison to the widely-used finite element formulation of the problem, and make some recommendations as to how this work may be extended.     

线性常微分方程系统的稳定性

本文用矩阵的Lozinskii测度的方法,得到了线性常微分方程系统的某些稳定性准则.导出了关于线性系统χ'=A(t)χ稳定性的充要条件.对于A是常数或周期矩阵的情形,我们的结果与从Jordan标准型和Floquet理论得到的经典结论相同.     

A Bliss-Type Multiplier Rule for Constrained Variational Problems with Time Delay

This paper gives a Bliss-type multiplier rule for general constrained variational problems with time delay. Our formulation allows the time delay terms and their derivatives to be present in both the objective functional and the equality and inequality constraint equations. Our major results include a Lagrange Multiplier Rule involving Euler–Lagrange equations for delay differential equations and transversality conditions. Of special note is that these results will be used in later work by the authors to obtain new analytical techniques to solve general constrained problems involving delay differential equations for the Calculus of Variations and for Optimal Control Theory. They will also lead to new general, accurate, and efficient numerical methods to solve these important problems where no such methods exist at this time. Thus, for the first time, we will be able to solve this important class of problems obtaining analytic solutions for simpler problems and accurate numerical results for more complex problems when such a solution exists.     

Algebraic and multiple integral identities

In this paper we develop some identities involving symmetric products in an abstract algebra which was formerly introduced by Rimark Ree to investigate the shuffle product and relations with skew symmetric (Lie) products. His motivation was partially the characterization of homogeneous Lie polynomials in noncommuting variables, while our motivation is derived from problems in systems theory. The main link in these applications is the need for identities involving multiple integrals of functions of many variables. The relation between these identities and some of the abstract identities developed here is also worked out and some of the applications to systems theory reviewed.     

Inverse Optimal Control Via Diagonal Stabilization Applied to Attitude Tracking of a Reusable Launch Vehicle

Journal of Optimization Theory and Applications - In this work, a novel strategy for the inverse optimal control of a class of affine nonlinear systems is proposed. The proposed strategy involves...