CDC2000 Probabilistic Approaches to Robust Control

Probabilistic Approaches to Robust Control
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 Worst-Case Estimate of Stability Probability for Polynomials with Multilinear Uncertainty Structure Authors: Sheila R. Ross, B. Ross Barmish, Volume: 1, Page 2756 Paper number 1914 Abstract: The main result in this paper is a worst-case estimate of the probability of stability for an uncertain polynomial which has as coefficients multilinear functions of real, random, independent parameters q_i. The result requires little apriori information about the probability distributions of these uncertain parameters. We only require that the distributions are symmetric about zero, non-increasing as \|q_i\| increases, and supported on a given interval [-r_i,r_i]. The probability estimate is sharp in the sense that the estimated probability of stability is ^p^*=1 when the uncertainty bounds r_i are below the deterministic robustness radius r_map obtained with the Mapping Theorem. To obtain the probabilistic estimate, we recast the problem so that the following characterization of stability is applicable: If the Nyquist curve for a proper plant lies to the right of a frequency-dependent separating line through -1+j0 at each frequency, then stability is guaranteed. The result is applied in a numerical example, illustrating a common amplification phenomenon: Even when the magnitude of uncertainty is significantly greater than the deterministic robustness bound, the risk of instability is small. CD001914.PDF (From Author) TOP A Probabilistic Approach To Robust Control Design Authors: Shinji Hara, Tomoki Miyazato, Volume: 1, Page 2761 Paper number 9061 Abstract: A new probabilistic approach to disturbance attenuation problem for LTI discrete-time systems is proposed. The performance is measured by a probability with respect to the stochastic noise of which the worst case 2-norm of the output against a class of deterministic signals with bounded 2-norm is less than a specified level. We first provides a matrix inequality characterization of the probability based on the Toeplitz form of the system and derive a lower bound of the probability. We then show that a guaranteed performance level can be computed by solving an LMI convex optimization problem. CD009061.PDF (From Author) TOP Multiobjective Control Design via Successive Over-Bounding of Quadratic Terms Authors: Takashi Shimomura, Takao Fujii, Volume: 1, Page 2763 Paper number 1581 Abstract: This paper addresses less conservative control design for multiple design specifications. Although problems are described by a set of LMIs, they are solved with non-common LMI solutions to reduce the conservatism arising from seeking a common LMI solution. Noticing that completing the square can split two variables in BMI terms into two different LMI ones, we propose iterative algorithms while replacing non-positive quadratic terms by their upper bounds. A suitable choice of the parameters in these upper bounds guarantees convergence property. An illustrated example is included. CD001581.PDF (From Author) TOP Guaranteed Cost Inequalities for Robust Stability and Performance Analysis Authors: Scot L. Osburn, Dennis S. Bernstein, Volume: 1, Page 2769 Paper number 2177 Abstract: In this paper we formulate robust stability and performance bounds in terms of guaranteed cost inequalities. We derive new guaranteed cost bounds for plants with real structured uncertainty, and we reformulate them as LMI's. In particular, we obtain a shifted linear bound and a shifted inverse bound, and give LMI forms for a shifted bounded real bound, a shifted Popov bound, a shifted linear bound and a shifted inverse bound. Several examples are used to compare the shifted bounds with their unshifted counterparts and to make comparisons among these new bounds and bounds based on standard LMI techniques. CD002177.PDF (From Author) TOP Estimation of Perturbation Bounds for Finite Trajectories Authors: Ulf T. Jönsson, Volume: 1, Page 2775 Paper number 1892 Abstract: The problem of estimating perturbation bounds for finite trajectories of non-autonomous systems is considered. A worst case sensitivity derivative of the trajectory with respect to the uncertainty is used to verify that the perturbed trajectory is within a given neighborhood of the nominal. This gives rise to a robust control problem for linear time-varying systems. It is shown that relaxation using integral quadratic constraints and the solution to a linear quadratic optimal control problem can be used to find bounds on the robust control problem. CD001892.PDF (From Author) TOP A Convexifying Algorithm for the Design of Structured Linear Controllers Authors: Mauricio C. de Oliveira, Juan F. Camino, Robert E. Skelton, Volume: 1, Page 2781 Paper number 2101 Abstract: This paper addresses the design of linear controllers with special structure imposed on the gain matrix. This problem is called a SLC (Structured Linear Control) problem. The SLC problem includes fixed order output feedback control, decentralized control, joint plant and control design, and many other linear control problems. A theoretical framework that allows one to pursue the solution of SLC problems is provided. Although the obtained conditions are nonconvex, it is shown that solving a SLC problem involving standard control objectives such as stability, bounds on the H_2 or H_(infinity) norms, and real positiveness is not harder than solving a standard unstructured static output feedback problem. A convexifying algorithm that might be used to solve the SLC problem is also developed. At each iteration a certain function is added to the constraints in order to make them convex. At convergence, the artificially introduced convexifying functions reduce to zero, guaranteeing the feasibility of the original problem. Local optimality can be guaranteed. Some examples illustrate how the SLC framework and the convexifying algorithm can improve the solutions of control problem with suboptimal solutions available. CD002101.PDF (From Author) TOP Gain-Scheduling Through Continuation of Observer-Based Realizations - Applications to H_(infinity) and µ Controllers Authors: Paulo C. Pellanda, Pierre Apkarian, Daniel Alazard, Volume: 1, Page 2787 Paper number 1151 Abstract: The dynamic behavior of gain-scheduling controllers is highly depending on the state-space representations adopted for the family of linear controllers designed on a set of operating conditions. In this paper, a technique for determining a set of consistent and physically motivated linear state-space transformations to be applied to the original set of linear controllers is proposed. After transformation, these controllers exhibit an observer-based structure and are therefore easily interpolated and implemented. This method is applicable to discrete- or continuous-time and full- or augmented-order compensators, particularly including H_(infinity) and µ controllers, which do not generally enjoy ease of implementation. CD001151.PDF (From Author) TOP