Results 1  10
of
61
The Complex Structures Singular Value
, 1993
"... A tutorial introduction to the complex structured singular value (µ) is presented, with an emphasis on the mathematical aspects of µ. The µbased methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests ..."
Abstract

Cited by 119 (10 self)
 Add to MetaCart
A tutorial introduction to the complex structured singular value (µ) is presented, with an emphasis on the mathematical aspects of µ. The µbased methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
Abstract

Cited by 116 (21 self)
 Add to MetaCart
The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
A Global Optimization Method, αBB, for General TwiceDifferentiable Constrained NLPs: I  Theoretical Advances
, 1997
"... In this paper, the deterministic global optimization algorithm, αBB, (αbased Branch and Bound) is presented. This algorithm offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twicedifferentiable NLPs. The key idea is the constru ..."
Abstract

Cited by 52 (3 self)
 Add to MetaCart
In this paper, the deterministic global optimization algorithm, αBB, (αbased Branch and Bound) is presented. This algorithm offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twicedifferentiable NLPs. The key idea is the construction of a converging sequence of upper and lower bounds on the global minimum through the convex relaxation of the original problem. This relaxation is obtained by (i) replacing all nonconvex terms of special structure (i.e., bilinear, trilinear, fractional, fractional trilinear, univariate concave) with customized tight convex lower bounding functions and (ii) by utilizing some α parameters as defined by Maranas and Floudas (1994b) to generate valid convex underestimators for nonconvex terms of generic structure. In most cases, the calculation of appropriate values for the α parameters is a challenging task. A number of approaches are proposed, which rigorously generate a set of α par...
Rigorous Convex Underestimators for General TwiceDifferentiable Problems
 Journal of Global Optimization
, 1996
"... . In order to generate valid convex lower bounding problems for nonconvex twicedifferentiable optimization problems, a method that is based on second order information of general twicedifferentiable functions is presented. Using interval Hessian matrices, valid lower bounds on the eigenvalues ..."
Abstract

Cited by 35 (15 self)
 Add to MetaCart
. In order to generate valid convex lower bounding problems for nonconvex twicedifferentiable optimization problems, a method that is based on second order information of general twicedifferentiable functions is presented. Using interval Hessian matrices, valid lower bounds on the eigenvalues of such functions are obtained and used in constructing convex underestimators. By solving several nonlinear example problems, it is shown that the lower bounds are sufficiently tight to ensure satisfactory convergence of the ffBB, a branch and bound algorithm which relies on this underestimation procedure [3]. Key words: convex underestimators; twicedifferentiable; interval anlysis; eigenvalues 1. Introduction The mathematical description of many physical phenomena, such as phase equilibrium, or of chemical processes generally requires the introduction of nonconvex functions. As the number of local solutions to a nonconvex optimization problem cannot be predicted a priori, the identifi...
Branch and Bound Algorithm for Computing the Minimum Stability Degree of Parameterdependent Linear Systems
, 1991
"... We consider linear systems with unspecified parameters that lie between given upper and lower bounds. Except for a few special cases, the computation of many quantities of interest for such systems can be performed only through an exhaustive search in parameter space. We present a general branch and ..."
Abstract

Cited by 21 (5 self)
 Add to MetaCart
We consider linear systems with unspecified parameters that lie between given upper and lower bounds. Except for a few special cases, the computation of many quantities of interest for such systems can be performed only through an exhaustive search in parameter space. We present a general branch and bound algorithm that implements this search in a systematic manner and apply it to computing the minimum stability degree. 1 Introduction 1.1 Notation R (C) denotes the set of real (complex) numbers. For c 2 C, Re c is the real part of c. The set of n \Theta n matrices with real (complex) entries is denoted R n\Thetan (C n\Thetan ). P T stands for the transpose of P , and P , the complex conjugate transpose. I denotes the identity matrix, with size determined from context. For a matrix P 2 R n\Thetan (or C n\Thetan ), i (P ); 1 i n denotes the ith eigenvalue of P (with no particular ordering). oe max (P ) denotes the maximum singular value (or spectral norm) of P , define...
Robust Stability of Linear Systems Described By Higher Order Dynamic Equations
, 1993
"... In this note we study the stability radius of higher order differential and difference systems with respect to various classes of complex affine perturbations of the coefficient matrices. Different perturbation norms are considered. The aim is to derive robustness criteria which are expressed direct ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
In this note we study the stability radius of higher order differential and difference systems with respect to various classes of complex affine perturbations of the coefficient matrices. Different perturbation norms are considered. The aim is to derive robustness criteria which are expressed directly in terms of the original data. Previous results on robust stability of Hurwitz and Schur polynomials [13] are extended to monic matrix polynomials. For disturbances acting via a uniform input matrix, computable formulae are obtained whereas for perturbations with multiple input matrices structured singular values are involved. 1 Introduction If the equations of a physical system are written down, they will often not be in statespace form but involve higher order derivatives of some variables, see [18], [21]. In these cases it is useful to have results available which can be directly applied without prior transformation into state space form. In a recent paper [20] Fuhrmann and Willems ...
WorstCase Properties of the Uniform Distribution and Randomized Algorithms for Robustness Analysis
, 1996
"... Motivated by the current limitations of the existing algorithms for robustness analysis and design, in this paper we take a different direction which follows the socalled probabilistic approach. That is, we aim to estimate the probability that a control system with uncertain parameters q restricted ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
Motivated by the current limitations of the existing algorithms for robustness analysis and design, in this paper we take a different direction which follows the socalled probabilistic approach. That is, we aim to estimate the probability that a control system with uncertain parameters q restricted to a box Q attains a given level of performance fl. Since this probability depends on the underlying distribution, we address the following question: What is a "reasonable" distribution so that the estimated probability makes sense? To answer this question, we define two worstcase criteria and prove that the uniform distribution is optimal in both cases. In the second part of the paper, we turn our attention to a subsequent problem. That is, we estimate the sizes of both the socalled "good" and "bad" sets via sampling. Roughly speaking, the good set contains the parameters q 2 Q with performance level better than or equal to fl while the bad set is the set of parameters q 2 Q with perform...
Global Optimization in Control System Analysis and Design
 CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS
, 1992
"... Many problems in control system analysis and design can be posed in a setting where a system with a fixed model structure and nominal parameter values is affected by parameter variations. An example is parametric robustness analysis, where the parameters might represent physical quantities that are ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
Many problems in control system analysis and design can be posed in a setting where a system with a fixed model structure and nominal parameter values is affected by parameter variations. An example is parametric robustness analysis, where the parameters might represent physical quantities that are known only to within a certain accuracy, or vary depending on operating conditions etc. Frequently asked questions here deal with performance issues: "How bad can a certain performance measure of the system be over all possible values of the parameters?" Another example is parametric controller design, where the parameters represent degrees of freedom available to the control system designer. A typical question here would be: "What is the best choice of parameters, one that optimizes a certain design objective?" Many of the questions above may be directly restated as optimization problems: If q denotes the vector of parameters, Q
Path planning for permutationinvariant multirobot formations
, 2002
"... In many multirobot applications, the specific assignment of goal configurations to robots is less important than the overall behavior of the robot formation. In such cases, it is convenient to define a permutationinvariant multirobot formation as a set of robot configurations, without assigning ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
In many multirobot applications, the specific assignment of goal configurations to robots is less important than the overall behavior of the robot formation. In such cases, it is convenient to define a permutationinvariant multirobot formation as a set of robot configurations, without assigning specific configurations to specific robots. For the case of robots that translate in the plane, we can represent such a formation by the coefficients of a complex polynomial whose roots represent the robot configurations. Since these coefficients are invariant with respect to permutation of the roots of the polynomial, they provide an effective representation for permutationinvariant formations. In this paper, we extend this idea to build a full representation of a permutationinvariant formation space. We describe the properties of the representation, and show how it can be used to construct collisionfree paths for permutationinvariant formations.