The Experts below are selected from a list of 32229 Experts worldwide ranked by ideXlab platform
Ian R Petersen - One of the best experts on this subject based on the ideXlab platform.
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Brief paper: A notion of possible controllability for uncertain linear systems with Structured Uncertainty
Automatica, 2009Co-Authors: Ian R PetersenAbstract:This paper introduces a notion of possible controllability for a class of uncertain linear systems with Structured Uncertainty described by averaged integral quadratic constraints. This notion relates to the question of when a state is controllable for some possible value of the Uncertainty. The notion of possible controllability is motivated by a desire to extend the theory of minimal realization for linear time invariant systems to the case of uncertain systems with Structured Uncertainty.
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Robust unobservability for uncertain linear systems with Structured Uncertainty
IEEE Transactions on Automatic Control, 2007Co-Authors: Ian R PetersenAbstract:This correspondence introduces a notion of robust unobservability for a class of uncertain linear systems with Structured Uncertainty described by averaged integral quadratic constraints. This notion relates to the question of when a state is unobservable for all possible values of the Uncertainty. This question may arise which considering modeling and realization theory for uncertain systems. The correspondence presents an algorithm for finding the robust unobservability function and corresponding unobservable cone.
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Notions of Observability for Uncertain Linear Systems with Structured Uncertainty
SIAM Journal on Control and Optimization, 2002Co-Authors: Ian R PetersenAbstract:This paper introduces a notion of observability for a class of uncertain linear systems with Structured Uncertainty. In the uncertain systems under consideration, the Uncertainty is described by averaged integral quadratic constraints. In order to define a notion of observability for uncertain linear systems, the paper introduces a robust observability function which extends the usual definition of the observability Gramian to the case of uncertain systems. Using this observability function, a corresponding unobservable cone is defined, and an uncertain system is said to be robustly observable if this cone contains only the origin. The paper presents an algorithm for finding the robust observability function and corresponding unobservable cone. This algorithm involves solving a parameterized Riccati differential equation.
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Robust H∞ Filtering with Structured Uncertainty
Robust Kalman Filtering for Signals and Systems with Large Uncertainties, 1999Co-Authors: Ian R Petersen, Andrey V SavkinAbstract:In this chapter, we present another approach to the problem of robust filtering for uncertain systems with Structured Uncertainty. In particular, we take a H∞ filtering approach rather than the set-valued state estimation approach taken in Chapters 4–7.
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set valued state estimation with Structured Uncertainty
1999Co-Authors: Ian R Petersen, Andrey V SavkinAbstract:In this chapter, we will present a new formulation of the robust set-valued state estimation problem which enables us to present set-valued state estimation results for a class of uncertain systems with Structured uncertainties. This class of uncertain systems is one in which the Uncertainty is described by an “Averaged Integral Quadratic Constraint”(AIQC). This Uncertainty description extends the standard integral quadratic constraint Uncertainty description given in Chapter 4. The standard integral quadratic constraint defines a class of uncertainties which is extremely rich and allows for nonlinear time-varying dynamic uncertainties.Our new Uncertainty description also allows for such a rich Uncertainty class. Furthermore, it enables a tractable solution to be obtained for the set-valued state estimation problem in the case of Structured Uncertainty. Such problems have been found to be intractable using other representations of Structured Uncertainty.
G Stein - One of the best experts on this subject based on the ideXlab platform.
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Structured Uncertainty analysis of robust stability for multidimensional array systems
IEEE Transactions on Automatic Control, 2003Co-Authors: Dimitry Gorinevsky, G SteinAbstract:This paper considers one of the fundamental issues in design and analysis of sampled multidimensional systems - that of Uncertainty modeling and robust stability analysis. Methods of Structured Uncertainty analysis (/spl mu/-analysis) are extended toward systems with dynamical and noncausal spatial coordinates. The stability is understood in a broad sense and includes decay (localization) of system response along the noncausal spatial coordinates. Robustness of dynamical stability and spatial localization of response and boundary effects are addressed in a unified way. The main technical condition enabling the technical results of the paper is that the feedback loop including a multidimensional plant and controller does not have a feedthrough in the dynamical (time) coordinate sense. As an example, this paper applies the multidimensional Structured Uncertainty analysis to closed-loop control of a cross-directional paper machine process. The paper formulates multidimensional models of the process, its controller, and a Structured Uncertainty. The Uncertainty corresponds to a combination of errors in the actuator mapping, the cross-directional response gain, and the response width.
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Structured Uncertainty analysis of spatially distributed paper machine process control
Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), 2001Co-Authors: Dimitry Gorinevsky, G SteinAbstract:Demonstrates an application of multidimensional Structured Uncertainty analysis (/spl mu/-analysis) to closed-loop control of cross-directional paper machine process. A multidimensional model of a cross-directional control process and a multidimensional Structured Uncertainty model are formulated. The analysis allows including the influence of the edge effects.
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Structured Uncertainty analysis of robust stability for spatially distributed systems
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 1Co-Authors: Dimitry Gorinevsky, G SteinAbstract:Considers one of the fundamental issues in design and analysis of sampled multidimensional systems-that of Uncertainty modeling and robust stability analysis. The paper extends methods of Structured Uncertainty analysis (/spl mu/-analysis) towards spatially distributed system with dynamical and spatial coordinates. The main contribution with respect to earlier work in this area is in clarification of stability issues for multidimensional systems with noncausal coordinates. Here stability is understood in a broad sense and includes decay (localization) of system response along noncausal spatial coordinates. The presented framework allows to address such practically important issues as robustness of dynamical stability and spatial localization of multidimensional closed-loop feedback system response and boundary effects in a unified way.
Andrey V Savkin - One of the best experts on this subject based on the ideXlab platform.
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Robust H∞ Filtering with Structured Uncertainty
Robust Kalman Filtering for Signals and Systems with Large Uncertainties, 1999Co-Authors: Ian R Petersen, Andrey V SavkinAbstract:In this chapter, we present another approach to the problem of robust filtering for uncertain systems with Structured Uncertainty. In particular, we take a H∞ filtering approach rather than the set-valued state estimation approach taken in Chapters 4–7.
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set valued state estimation with Structured Uncertainty
1999Co-Authors: Ian R Petersen, Andrey V SavkinAbstract:In this chapter, we will present a new formulation of the robust set-valued state estimation problem which enables us to present set-valued state estimation results for a class of uncertain systems with Structured uncertainties. This class of uncertain systems is one in which the Uncertainty is described by an “Averaged Integral Quadratic Constraint”(AIQC). This Uncertainty description extends the standard integral quadratic constraint Uncertainty description given in Chapter 4. The standard integral quadratic constraint defines a class of uncertainties which is extremely rich and allows for nonlinear time-varying dynamic uncertainties.Our new Uncertainty description also allows for such a rich Uncertainty class. Furthermore, it enables a tractable solution to be obtained for the set-valued state estimation problem in the case of Structured Uncertainty. Such problems have been found to be intractable using other representations of Structured Uncertainty.
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Minimax Optimal Control of Discrete-Time Uncertain Systems With Structured Uncertainty
Dynamics and Control, 1997Co-Authors: S. O. Reza Moheimani, Andrey V Savkin, Ian R PetersenAbstract:Inthis paper we consider a guaranteed cost control problem fora class of uncertain discrete-time systems which contain Structureduncertainties. The uncertainties are assumed to satisfy a certainsum quadratic constraint. The controller will be a minimax controllerin the sense that it minimizes the maximum value of a cost function.For a given initial condition, the minimax optimal controlleris constructed by solving a parameter dependent Riccati equation.This controller guarantees absolute stability of the closed loopsystem.
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nonlinear versus linear control in the absolute stabilizability of uncertain systems with Structured Uncertainty
IEEE Transactions on Automatic Control, 1995Co-Authors: Andrey V Savkin, Ian R PetersenAbstract:This note considers a stabilization problem for a class of uncertain linear systems containing Structured Uncertainty described by a certain integral quadratic constraint. The notion of stabilizability considered is that of absolute stabilizability. The main result gives a necessary and sufficient condition for the absolute stabilizability of this class of uncertain systems in terms of the existence of a solution to a corresponding "diagonally scaled" H/sup /spl infin// control problem. It follows from this result that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control. >
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An Uncertainty averaging approach to optimal guaranteed cost control of uncertain systems with Structured Uncertainty
Automatica, 1995Co-Authors: Andrey V Savkin, Ian R PetersenAbstract:This paper presents an optimal state feedback guaranteed cost control result for a class of uncertain linear time-varying systems with Structured Uncertainty. The cost function considered is a quadratic cost function defined over a finite time interval. The solution of the optimal control problem is obtained by solving a parametrized Riccati differential equation of the game type.
Dimitry Gorinevsky - One of the best experts on this subject based on the ideXlab platform.
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Structured Uncertainty analysis of robust stability for multidimensional array systems
IEEE Transactions on Automatic Control, 2003Co-Authors: Dimitry Gorinevsky, G SteinAbstract:This paper considers one of the fundamental issues in design and analysis of sampled multidimensional systems - that of Uncertainty modeling and robust stability analysis. Methods of Structured Uncertainty analysis (/spl mu/-analysis) are extended toward systems with dynamical and noncausal spatial coordinates. The stability is understood in a broad sense and includes decay (localization) of system response along the noncausal spatial coordinates. Robustness of dynamical stability and spatial localization of response and boundary effects are addressed in a unified way. The main technical condition enabling the technical results of the paper is that the feedback loop including a multidimensional plant and controller does not have a feedthrough in the dynamical (time) coordinate sense. As an example, this paper applies the multidimensional Structured Uncertainty analysis to closed-loop control of a cross-directional paper machine process. The paper formulates multidimensional models of the process, its controller, and a Structured Uncertainty. The Uncertainty corresponds to a combination of errors in the actuator mapping, the cross-directional response gain, and the response width.
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Structured Uncertainty analysis of spatially distributed paper machine process control
Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), 2001Co-Authors: Dimitry Gorinevsky, G SteinAbstract:Demonstrates an application of multidimensional Structured Uncertainty analysis (/spl mu/-analysis) to closed-loop control of cross-directional paper machine process. A multidimensional model of a cross-directional control process and a multidimensional Structured Uncertainty model are formulated. The analysis allows including the influence of the edge effects.
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Structured Uncertainty analysis of robust stability for spatially distributed systems
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 1Co-Authors: Dimitry Gorinevsky, G SteinAbstract:Considers one of the fundamental issues in design and analysis of sampled multidimensional systems-that of Uncertainty modeling and robust stability analysis. The paper extends methods of Structured Uncertainty analysis (/spl mu/-analysis) towards spatially distributed system with dynamical and spatial coordinates. The main contribution with respect to earlier work in this area is in clarification of stability issues for multidimensional systems with noncausal coordinates. Here stability is understood in a broad sense and includes decay (localization) of system response along noncausal spatial coordinates. The presented framework allows to address such practically important issues as robustness of dynamical stability and spatial localization of multidimensional closed-loop feedback system response and boundary effects in a unified way.
J. B. Pearson - One of the best experts on this subject based on the ideXlab platform.
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Robust Control System Design.
1995Co-Authors: J. B. PearsonAbstract:Abstract : This research was concerned with the robust optimal control of systems subjected to Structured Uncertainty. The design objective was to minimize the induced system norm (i.e. maximum gain) in the cases of l2/L2 and l(inf)/L(inf) inputs. Major results were obtained in the case of linear discrete-time systems with nonlinear/time-varying Uncertainty and for continuous systems controlled by digital computers (sampled-data systems). The sampled-data results are now a part of the MATLAB u-tools toolbox and the Structured Uncertainty results for discrete-time systems has led to an efficient 'D-K-type' synthesis procedure for minimizing the l(inf) induced system norm. (AN)
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analysis and design for robust performance with Structured Uncertainty
Systems & Control Letters, 1993Co-Authors: Mustafa Khammash, J. B. PearsonAbstract:Abstract Necessary and sufficient conditions for stability and performance robustness of discrete-time systems are provided in terms of the spectral radius of a certain nonnegative matrix. The conditions are easily computable and provide a simple and efficient method for computation of the robustness conditions for SISO as well MIMO perturbations. The problem of robust controller synthesis is explored, and an iteration scheme for controller synthesis is introduced.
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performance robustness of discrete time systems with Structured Uncertainty
IEEE Transactions on Automatic Control, 1991Co-Authors: Mustafa Khammash, J. B. PearsonAbstract:Given an interconnection of a nominal discrete-time plant and a stabilizing controller together with Structured, norm-bounded, nonlinear/time-varying perturbations, necessary and sufficient conditions for robust stability and performance of the system are provided. It is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem. The resulting stability robustness problem is shown to be equivalent to a simple algebraic one, the solution of which provides the desired necessary and sufficient conditions for performance/stability robustness. These conditions provide an effective tool for robustness analysis and can be applied to a large class of problems. In particular, it is shown that some known results can be obtained immediately as special cases of these conditions. >
