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Let's Get Real
 In Robust Control Theory, IMA Proceedings
, 1995
"... This paper gives an overview of promising new developments in robust stability and performance analysis of linear control systems with real parametric uncertainty. The goal is to develop a practical algorithm for medium size problems, where medium size means less than 100 real parameters, and "pr ..."
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Cited by 8 (2 self)
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This paper gives an overview of promising new developments in robust stability and performance analysis of linear control systems with real parametric uncertainty. The goal is to develop a practical algorithm for medium size problems, where medium size means less than 100 real parameters, and "practical" means avoiding combinatoric (nonpolynomial) growth in computation with the number of parameters for all of the problems which arise in engineering applications. We present an algorithm and experimental evidence to suggest that this goal has, for the first time, been achieved. We also place these results in context by comparing with other approaches to robustness analysis and considering potential extensions, including controller synthesis. 1 Introduction Robust stability and performance analysis with real parametric uncertainty can be naturally formulated as a Structured Singular Value, or , problem, where the block structured uncertainty description is allowed to contain both...
An Efficient Algorithm for Performance Analysis of Nonlinear Control Systems
 In Proc. American Control Conference
, 1995
"... A numerical algorithm for computing necessary conditions for performance specifications is developed for nonlinear uncertain systems. The algorithm is similar in nature and behavior to the power algorithm for the ¯ lower bound, and doesn't rely on a descent method. The algorithm is applied to a prac ..."
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Cited by 5 (3 self)
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A numerical algorithm for computing necessary conditions for performance specifications is developed for nonlinear uncertain systems. The algorithm is similar in nature and behavior to the power algorithm for the ¯ lower bound, and doesn't rely on a descent method. The algorithm is applied to a practical example. 1 Introduction Theoretical and computational tools for analysis and synthesis of robust controllers for linear systems are well developed in a variety of instances. Controllers generated with these tools can provide guaranteed performance in the presence of structured uncertainty, and the worst case disturbances for a given controller can be determined. A recent description of this approach is given by Packard and Doyle [7]. For linear time invariant (LTI) systems with complex, structured uncertainty, analysis of robust performance can be reduced to searching for the solution of a set of algebraic equations which give bounds on the achievable performance. One is thus able to ...
Optimal H2/Popov Controller Design Using Linear Matrix Inequalities
, 1996
"... The purpose of this thesis is to develop an efficient scheme for the design of controllers that guarantee H 2 performance in view of linear or nonlinear real parametric uncertainties. To begin, dissipation techniques are used to design parameterdependent Lyapunov functions that impose constraints o ..."
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The purpose of this thesis is to develop an efficient scheme for the design of controllers that guarantee H 2 performance in view of linear or nonlinear real parametric uncertainties. To begin, dissipation techniques are used to design parameterdependent Lyapunov functions that impose constraints on the magnitude and the timevariation of the uncertainties. This approach reduces the conservatism of the robustness criteria. The robust stability problem is formulated in terms of a linear matrix inequality problem that constitutes a convex constraint and can be solved in polynomial time. The robust performance problem is obtained by the introduction of a performance metric that bounds the H 2 cost of the closedloop system and is shown to be equivalent to the robust performance problem obtained by the \Omega\Gammah ound framework and the use of Popov multipliers. Although the resulting robust performance criteria are in matrix inequality form, they are not linear in the scaling matrices ...
The Rank One Mixed µ Problem and "KharitonovType" Analysis
 Manuscript in Preparation
"... The general mixed problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed problem. We show ..."
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The general mixed problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed problem. We show that for this case the mixed problem is equivalent to its upper bound (which is convex), and it can in fact be computed easily (and exactly). This special case is shown to be equivalent to the so called "affine parameter variation" problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated "Kharitonovtype" results have been proven. 1 Introduction It is now known that the general mixed problem is NP hard, and this strongly suggests that the exact solution of the general problem is computationally intractable, except for small problems [3]. In this paper we consider not the general problem, but a particular ...
Numerically Efficient Robustness Analysis of
, 1995
"... this paper is to extend the robustness analysis techniques of linear systems, and in particular the associated computational methods, to nonlinear systems. Given the diversity of nonlinear behavior, it is clear that this cannot be done in complete generality and still maintain the efficiency and usa ..."
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this paper is to extend the robustness analysis techniques of linear systems, and in particular the associated computational methods, to nonlinear systems. Given the diversity of nonlinear behavior, it is clear that this cannot be done in complete generality and still maintain the efficiency and usability of the methods. In this paper we will develop analysis methods for a specific nonlinear robust performance problem. We will show that an efficient numerical algorithm can be developed to compute a lower bound on the corresponding performance index. The problem, and the corresponding algorithm, share the characteristics of current industrial practice mentioned earlier
JOURNAL OF AIRCRAFT Vol. 47, No. 4, July–August 2010 Evaluation of Aeroelastic Uncertainty Analysis Methods
"... Flutter is a destructive and potentially explosive phenomenon that is the result of the simultaneous interaction of aerodynamic, elastic, and inertial forces. The nature of flutter mandates that flutter flight testing be cautious and conservative. Because of this, further investigation of uncertaint ..."
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Flutter is a destructive and potentially explosive phenomenon that is the result of the simultaneous interaction of aerodynamic, elastic, and inertial forces. The nature of flutter mandates that flutter flight testing be cautious and conservative. Because of this, further investigation of uncertainty analysis with respect to the flutter problem is desired and warranted. Prediction of flutter in the transonic regime requires computationally expensive highfidelity simulation models. Because of the computational demands, traditional uncertainty analysis is not often applied to transonic flutter prediction, resulting in reduced confidence in the results. The work described herein is aimed at exploring various methods to reduce the existing computational time limitations of traditional uncertainty analysis. Specifically, the coupling of design of experiment and response surface methods and the application of analysis are applied to a validated aeroelastic model of the AGARD 445.6 wing. From a highfidelity nonlinear aeroelastic model, a linear reducedorder model is produced that captures the essential dynamic characteristics. Using reducedorder models, the design of experiment, response surface methods, andanalysis approaches are compared with traditional Monte Carlobased stochastic simulation. All of these approaches to uncertainty analysis have advantages and drawbacks. Results from these methods and their robustness are compared and evaluated. I.