Output Feedback H∞ Control for a Class of Nonlinear Stochastic Systems

This paper deals with the output feedback H∞ control problem for a class of nonlinear stochastic systems. Based on the latest developed theory of stochastic dissipation, a notable result about the nonlinear H∞ output feedback control of deterministic system is generalized to the stochastic case. Finally, in the cases of state feedback and output feedback, two families of controllers are provided respectively.     

On Absorbing Cycles in Min–Max Digraphs

We consider smooth finite dimensional optimization problems with a compact, connected feasible set M and objective function f. The basic problem, on which we focus, is: how to get from one local minimum to all the other ones. To this aim we introduce a bipartite digraph as follows. Its nodes are formed by the set of local minima and maxima of f|_M, respectively. Given a smooth Riemannian (i.e. variable) metric, there is an arc from a local minimum x to a local maximum y if the ascent (semi-)flow induced by the projected gradients of f connects points from a neighborhood of x with points from a neighborhood of y. The existence of an arc from y to x is defined with the aid of the descent (semi-)flow. Strong connectedness of ensures that, starting from one local minimum, we may reach any other one using ascent and descent trajectories in an alternating way. In case that no inequality constraints are present or active, it is well known that for a generic Riemannian metric the resulting min-max digraph is indeed strongly connected. However, if inequality constraints are active, then there might appear obstructions. In fact, we show that may contain absorbing two-cycles. If one enters such a cycle, one cannot leave it anymore via ascent and descent trajectories. Moreover, the cycles being constructed are stable with respect to small perturbations (in the C¹-topology) of the Riemannian metric.     

Min–Max vs. Min–Sum Vehicle Routing: A worst-case analysis

The classical objective function of the Vehicle Routing Problem (VRP) is to minimize the total distance traveled by all vehicles (Min–Sum). In several situations, such as disaster relief efforts, computer networks, and workload balance, the minimization of the longest route (Min–Max) is a better objective function. In this paper, we compare the optimal solution of several variants of the Min–Sum and the Min–Max VRP, from the worst-case point of view. Our aim is two-fold. First, we seek to motivate the design of heuristic, metaheuristic, and matheuristic algorithms for the Min–Max VRP, as even the optimal solution of the classical Min–Sum VRP can be very poor if used to solve the Min–Max VRP. Second, we aim to show that the Min–Max approach should be adopted only when it is well-justified, because the corresponding total distance can be very large with respect to the one obtained by optimally solving the classical Min–Sum VRP.     

An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays

In this paper, the problem of stability analysis for uncertain dynamic systems with time-varying delays is considered. The parametric uncertainties are assumed to be bounded in magnitude. Based on the Lyapunov stability theory, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities, which can be solved easily by various efficient convex optimization algorithms. Two numerical examples are illustrated to show the effectiveness of proposed method.     

The Partial Stability for Linear Discrete Systems

In this paper, we study the partial stability of linear discrete systems by means of Liapunov's functions of quadratic form. We obtain a necessary and sufficient condition for the system being stable with respect to part of variables and generalize Liapunov's equation to the partial stability of linear discrete systems. A method of constructing Liapunov's function of quadratic form for the stability of the systems is given.     

Input–Output Identifiability of Continuous-Time Linear Systems

In time-domain identification of linear systems the aim is to estimate the impulse response or transfer function of a linear system to within a given tolerance using a finite number of noisy observations of the output. Whether this is possible depends on the model set, that is, a given set to which the system is assumed to belong a priori. We give necessary and sufficient conditions on the model set to ensure that such identification is possible in the continuous-time case.     

Robust Averaged Control of Vibrations for the Bernoulli–Euler Beam Equation

This paper proposes an approach for the robust averaged control of random vibrations for the Bernoulli–Euler beam equation under uncertainty in the flexural stiffness and in the initial conditions. The problem is formulated in the framework of optimal control theory and provides a functional setting, which is so general as to include different types of random variables and second-order random fields as sources of uncertainty. The second-order statistical moment of the random system response at the control time is incorporated in the cost functional as a measure of robustness. The numerical resolution method combines a classical descent method with an adaptive anisotropic stochastic collocation method for the numerical approximation of the statistics of interest. The direct and adjoint stochastic systems are uncoupled, which permits to exploit parallel computing architectures to solve the set of deterministic problem that arise from the stochastic collocation method. As a result, problems with a relative large number of random variables can be solved with a reasonable computational cost. Two numerical experiments illustrate both the performance of the proposed method and the significant differences that may occur when uncertainty is incorporated in this type of control problems.     

Discrete Abstractions of Continuous Systems – an Input/Output Point of View

This contribution proposes a hierarchy of discrete ions for a given continuous model. It adopts an input/output point of view, and starts from the continuous system behaviour B _c (i.e., 'the set of all pairs of input and output signals which are compatible with the continuous model equations). The first step is to construct a sequence of behaviours B _l , l =0, 1,..., such that B ₀ ? B ₁ ?... ? B _c. In a second step, nondeterministic Moore automata A_l are generated as minimal realizations for the behaviours B _l . Hence, the continuous base system and its discrete abstractions A l form a totally ordered set of models, where ordering is in the sense of set inclusion of model behaviours or, equivalently, in terms of approximation accuracy. Within this set, there exists a uniquely defined “coarsest” (and therefore least complex) model which allows a given set of specifications to be enforced by discrete feedback. The ordering property implies that this discrete feedback also forces the continuous base system to obey the specifications.     

Control Synthesis for Čaplygin Polynomial Systems

This paper discusses new control synthesis for certain cascade type polynomial systems addressed in the paper as aplygin systems. A numerical control synthesis as well as characterization of reachability set are presented. The results of the paper are important for various branches of system theory, where the control synthesis is concerned.     

A Min–Max Property of Chordal Bipartite Graphs with Applications

We show that if G is a bipartite graph with no induced cycles on exactly 6 vertices, then the minimum number of chain subgraphs of G needed to cover E(G) equals the chromatic number of the complement of the square of line graph of G. Using this, we establish that for a chordal bipartite graph G, the minimum number of chain subgraphs of G needed to cover E(G) equals the size of a largest induced matching in G, and also that a minimum chain subgraph cover can be computed in polynomial time. The problems of computing a minimum chain cover and a largest induced matching are NP-hard for general bipartite graphs. Finally, we show that our results can be used to efficiently compute a minimum chain subgraph cover when the input is an interval bigraph.     

Discrete approximations for complex Kac–Moody groups

We construct a map from the classifying space of a discrete Kac–Moody group over the algebraic closure of the field with p elements to the classifying space of a complex topological Kac–Moody group and prove that it is a homology equivalence at primes q different from p. This generalizes a classical result of Quillen, Friedlander and Mislin for Lie groups. As an application, we construct unstable Adams operations for general Kac–Moody groups compatible with the Frobenius homomorphism. Our results rely on new integral homology decompositions for certain infinite dimensional unipotent subgroups of discrete Kac–Moody groups.     

Robust regression for mixed Poisson–Gaussian model

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson–Gaussian noise, and when there are additional outliers in the measured data. The Poisson–Gaussian noise leads to a weighted minimization problem, with solution-dependent weights. To address outliers, the standard least squares fit-to-data metric is replaced by the Talwar robust regression function. Convexity, regularization parameter selection schemes, and incorporation of non-negative constraints are investigated. A projected Newton algorithm is used to solve the resulting constrained optimization problem, and a preconditioner is proposed to accelerate conjugate gradient Hessian solves. Numerical experiments on problems from image deblurring illustrate the effectiveness of the methods.     

Adaptive Control Model and Algorithms for the Dynamic Flowshop Scheduling Problem

1.IntroductionProductionschedulingcanbedefinedgenerallyastheallocationoftheresourcesinaproductionsystemovertimetoperformtheoperationsneededtotransformrawmaterialsilltoproducts.Aneffectiveandefficientschedulingsystemisnecessarytowellachievethepotentialsofaproductionfacility.Productionschedulingproblemsareextremelycomplex.Thecomplexityismainlyduetothefollowingtwofeaturesoftheproblem(Liu,1995).InterconnectedDecisions:Thecomponentsofaproductionsystem,e.g.,machines,ma-tenalhandlingdevicesandstora…