CDC2000 Linear Matrix Inequalities in Design

Linear Matrix Inequalities in Design
Home Full List of Titles 1: Proceedings of CDC2000 Discrete Event Systems Control in Communication Systems Optimal Control and Applications I Optimisation Approaches and Methods Model Predictive Control Advances in Linear Estimation Stochastic and Uncertain Systems Nonlinear Control and Applications Nonlinear Estimation and Filtering Formation Control and its Applications New Approaches to Fuzzy Control Manufacturing Systems Automotive Applications Stability Issues in Hybrid Control Recent Advances in Stochastic Networks Optimal Control and Applications II Robust Controller Design - mu, L1 and H2 Constrained and Receding Horizon Control Identification and Control around the World Markov Decision Processes Nonlinear Optimisation Observers for Nonlinear Systems Motion Planning Neural / Fuzzy Stability and Control Motor Control Control of Quantum Phenomena I Hybrid Systems Methods Control in Communication Networks Robustness and Optimisation Bumpless Transfer, Antiwindup and Saturation Adaptive Control: Linear Systems Estimation and Closed Loop Identification Control of Markov Processes Nonlinear Filtering and Control Modelling, Identification and Validation of Nonlinear Systems Differential Geometric Control Theory for Mechanical Systems Nonlinear Output Feedback Control Pneumatics and Compression Systems Control of Quantum Phenomena II Stability of Hybrid Systems Performance Analysis in Communication Networks Adaptive Control of Nonlinear Systems LMI Methods in Design Robust Control of Time Delay Systems Subspace Identification Methods Nonlinear Stochastic Filtering and Estimation Bifurcations, Chaos and Control I New Progress in Synthesis of Nonlinear Systems I Implementation Issues of Sliding Mode Control Theory Control of Mixing in Shear Flows Novel Neural Network Control Techniques for Industrial Motion Control Systems Physiological Control Systems Optimal Control of Hybrid Systems Stochastic Models for Communication Networks Control and Stabilisation of Nonlinear Systems New Directions in Robust Control Linear Systems Theory Advanced Topics in Systems Theory Estimation in Action Bifurcations, Chaos and Control II New Progress in Synthesis of Nonlinear Systems II Numerical Design and Analysis Techniques for Nonlinear Systems Analysis and Control of Underactuated Systems Sliding Mode Control I Challenges in the Application of Control to Computer Systems Estimation and Diagnosis of Discrete Event Systems Communications and Games Optimal Control Stochastic Systems Model Reduction Methodologies Identification and Subspace Methods Applications of Nonlinear Adaptive Control Advances in Nonlinear Output Feedback Design The Behavioural Approach to Systems and Control Vision Based Estimation and Control: Recent Advances and Open Problems Agile Control of Military Operations Sliding Mode Control II Model-based Fault Diagnosis of Industrial Processes Discrete Event Systems / Petri Nets System Identification and Confidence Estimation New Approaches to H-Infinity Control I Probabilistic Approaches to Robust Control Time Delay System Stabilisation Identification Methods Controlled Stochastic Processes Output Feedback of Nonlinear Systems Topics in Nonlinear Stabilisation Mobile Robots: Tracking Control Robust Control of Nonlinear Systems Power Systems Stabilisation and Control Disk Drive Control Hybrid Control Applications Discrete Time Systems New Approaches to H-Infinity Control II Linear Systems with Saturating Actuators New Theories in Distributed Parameter Systems Applications of Estimation and Identification Stochastic Control and Tuning Methodologies Control of Nonlinear Systems Iterative Learning and Control Coordinating Robot Systems Nonlinear Time Varying Systems Novel Applications of Neural Networks Aerospace Applications Switched Systems Implicit and Descriptor Systems LQG Periodic Systems and Disturbances New Horizons for Distributed Parameter Systems State Estimation Learning and Neuro-Control Nonlinear Control and Stabilisation I Tracking Vision Servoing Controllability of Nonlinear Systems Control of Flexible Systems Electro-Mechanical Systems Robust Control Methods and Applications Fault Detection and Diagnosis Optimisation and Applications Robust Stability Analysis Numerical Methods in Control Filtering in Continuous Time Stochastic Systems Interplay between Control and Signal Processing Fault Detection and Analysis Nonlinear Dynamical Systems Nonlinear Time Delay Systems Computational Issues in Nonlinear Control Disturbance Rejection Process Control Industry Applications Linear Parameter Varying Systems Linear Control Systems Dynamic and Nonlinear Programming Model Reduction Applications New Techniques for Control and Systems: Numerical Linear Algebra Estimation and Identification using Hidden Markov Models Applications of Stochastic Control Topics in Linear Design Nonlinear Control and Stabilisation II Ambulatory Robot Systems Chaotic and Oscillatory Systems Biomedical System Control Integrated Control and CPU Scheduling Linear Design Techniques Adaptive Disturbance / Noise Compensation Nonlinear Model Predictive Control Sensitivity Design, Analysis and Limitations Analysis of Linear Systems Linear Matrix Inequalities in Design Lyapunov's 2nd Method Robotics: Tracking Control Lagrangian and Hamiltonian Theory Variable Structure Control Machine Vision Signal Processing Methods in Control Applied Nonlinear Control Author Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z	A Symbolic Algorithm For Determining Convexity of A Matrix Function: How To Get Schur Complements Out of Your Life Authors: Juan F. Camino, J. William Helton, Robert E. Skelton, Volume: 1, Page 5023 Paper number 1776 Abstract: Inequalities involving polynomials in matrices and their inverses and associated optimization problems have become very important in engineering. When these polynomials are ``matrix convex'' interior point methods apply directly. A difficulty is that often an engineering problem presents a matrix polynomial problem whose convexity takes considerable skill, time, and luck to determine. Typically this is done by looking at a formula and recognizing complicated patterns involving Schur complements; a tricky hit or miss procedure. Certainly computer assistance in determining convexity would be valuable. This paper describes some symbolic methods and software which represent a beginning along these lines. Our procedure proceeds automatically and completely avoids Schur complement wizardry. [New Paragraph] The paper presents an algorithm which takes in a noncommutative rational function F(X,Y) of X,Y and puts out a family of inequalities which determine a domain G of X and Y on which F is ``matrix convex''. Somewhat surprising and decidedly non-trivial is our main theorem showing that when the variable X is symmetric the domain G determined by our algorithm is, in a certain sense, the ``largest'' possible domain of matrix convexity for G. [New Paragraph] Of possible independent interest in this article is a theory of positivity of noncommutative quadratic functions and a noncommutative LDU algorithm. The algorithms described here have been implemented under Mathematica and the noncommutative algebra package NCAlgebra. They are available at www.math.ucsd.edu/~ncalg. Examples presented in this article illustrate some of this software. CD001776.PDF (From Author) TOP Solving Large Structured Semidefinite Programs Using an Inexact Spectral Bundle Method Authors: Scott A. Miller, Roy S. Smith, Volume: 1, Page 5027 Paper number 9704 Abstract: Semidefinite programs have received a great deal of attention because of the variety of problems that they can model and the rich theory that leads to polynomial-time algorithms to solve them. However, large practical problems are still hard to solve because most algorithms ignore the structure of the problem. In this paper we present an algorithm for solving semidefinite programs that exploits structure yet is not tailored a priori to any particular structure. It adapts a bundle method designed to solve structured LMI feasibility problems. Duality provides a tight lower bound for the optimal cost for use in a termination criterion. A numerical experiment demonstrates that the complexity is comparable to that of structured interior-point methods, and unlike those methods it applies to a general class of structures. CD009704.PDF (From Author) TOP Efficient Solution Of Linear Matrix Inequalities For Integral Quadratic Constraints Authors: Anders Hansson, Lieven Vandenberghe, Volume: 1, Page 5033 Paper number 9042 Abstract: In this article is discussed how to implement an efficient interior-point algorithm for the semi-definite programs that result from integral quadratic constraints. The algorithm is a primal-dual potential reduction method, and the computational effort is dominated by a least-squares system that has to be solved in each iteration. The key to an efficient implementation is to utilize iterative methods and the specific structure of integral quadratic constraints. The algorithm has been implemented in Matlab. To give a rough idea of the efficiencies obtained, it is possible to solve problems resulting in a linear matrix inequality of dimension 130x130 with approximately 5000 variables in about 10 minutes on a lap-top. Problems with approximately 20000 variable and a linear matrix inequality of dimension 230x230 are solved in a few hours. It is not assumed that the system matrix has no eigenvalues on the imaginary axis, nor is it assumed that it is Hurwitz. CD009042.PDF (From Author) TOP Fast Algorithms for Exact and Approximate Feasibility of Robust LMIs Authors: Giuseppe Calafiore, Boris T. Polyak, Volume: 1, Page 5035 Paper number 1415 Abstract: In this paper, we discuss fast randomized algorithms for determining an admissible solution for robust linear matrix inequalities (LMIs) of the form F(x,(Delta)) (preceq) 0, where x is the optimization variable and (Delta) is the uncertainty, which belongs to a given set (Delta). The proposed algorithm is based on uncertainty randomization: it finds a solution in a finite number of iterations with probability one, if a strong feasibility condition holds. Otherwise, it computes a candidate solution which minimizes the expected value of a suitably selected feasibility indicator function. The theory is illustrated by examples of application to uncertain linear inequalities and quadratic stability of interval matrices. CD001415.PDF (From Author) TOP Convergent LMI Relaxations For Nonconvex Quadratic Programs Authors: Jean B. Lasserre, Volume: 1, Page 5041 Paper number 1111 Abstract: We consider the general nonconvex quadratic programming problem and provide a series of convex positive semidefinite programs (or LMI relaxations) whose sequence of optimal values is monotone and converges to the optimal value of the original problem. It improves and includes as a special case the well-known Shor's relaxation. Often the optimal value is obtained at some particular early relaxation as shown on some nontrivial test problems. CD001111.PDF (From Author) TOP