. We consider least-squares problems where the coefficient matrices A; b are unknown-butbounded. We minimize the worst-case residual error using (convex) second-order cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact bound on the robustness of solution, and a rigorous way to compute the regularization parameter. When the perturbation has a known (e.g., Toeplitz) structure, the same problem can be solved in polynomial-time using semidefinite programming (SDP). We also consider the case when A; b are rational functions of an unknown-but-bounded perturbation vector. We show how to minimize (via SDP) upper bounds on the optimal worst-case residual. We provide numerical examples, including one from robust identification and one from robust interpolation. Key Words. Least-squares, uncertainty, robustness, second-order cone...

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In this paper a framework for an iterative procedure of identification and robust control design is introduced wherein the robust performance is monitored during the subsequent steps of the iterative scheme. By monitoring the performance via a mode-lbased approach, the possibility to guarantee performance improvement in the iterative scheme is being employed. In order to monitor achieved performance (for a present controller) and to guarantee robust performance (for a future controller), an uncertainty set is used where the uncertainty structure is chosen in terms of model perturbations in the dual Youla parametrization. This uncertainty structure is shown to be particularly suitable for the control performance measure that is considered. The model uncertainty set can be identified by an uncertainty estimation procedure on the basis of closed-loop experimental data. To obtain performance robustness, robust control design tools are used to synthesise controllers on the basis of ...

Given measurement data, a nominal model and a linear fractional transformation uncertainty structure with an allowance on unknown but bounded exogenous disturbances, easily computable tests for the existence of a model validating uncertainty set are given. Under mild conditions, these tests are necessary and su#cient for the case of complex, nonrepeated, block-diagonal structure. For the more general case which includes repeated and#or real scalar uncertainties, the tests are only necessary but become su#cient if a collinearity condition is also satis#ed. With the satisfaction of these tests, it is shown that a parameterization of all model validating sets of plant models is possible. The new parameterization is used as a basis for a systematic way to construct or perform uncertainty tradeo# with model validating uncertainty sets whichhave speci#c linear fractional transformation structure for use in robust control design and analysis. An illustrative example which includes a compariso...

. This paper presents analysis of a scheme for iterated identification and control design. The approach is based on least squares identification in closed loop and pole placement design. It has previously been shown that the criteria for control and identification are the same provided that the data filters are chosen properly. The iterated scheme may be viewed as a recursion in model parameters. Each step consists of system identification and control design. Interesting questions are then: What are the fix points? Are the fix points stable? These questions are investigated for some simple examples. Relations to other problems like model reduction and adaptive control are also discussed. Keywords. Adaptive Control, Control Design, Identification, Least Squares Estimation, Model reduction, Pole Placement Control, Prediction Error Methods. 1. INTRODUCTION A sensible formulation of an identification problem should consider the ultimate use of the model. In control system design we are in...

Recent hardware developments have rendered controlled active vision a viable option for a broad range of practical problems. However, realizing this potential requires having a framework for synthesizing robust active vision systems, capable of moving beyond carefully controlled environments. Recent work has shown that this can be achieved by combining robust computer vision and control techniques. However, in some cases robustness is achieved at the expense of performance. In this paper we show that this performance loss can be avoided by recasting the problem into a Linear Parameter Varying (LPV) form and using recently developed robust identification and control tools for this class of problems. These results are experimentally validated using a Bisight robotic head. 1 Introduction and Motivation Recent hardware advances have rendered visual feedback a viable option for a very diverse spectrum of applications ranging from MEMS manufacture[7] to assisting individuals with disabilit...

This paper addresses the problem of model (in)validation of linear discrete–time (LTI) models subject to unstructured LTI uncertainty, using frequency–domain data corrupted by additive noise. Contrary to the case usually considered in the (deterministic) invalidation literature, here the input to the system has an unknown phase. This problem arises naturally for instance in the context of validating systems subject to unknown time–delays, or in cases where only the spectral power density of the (in this case stochastic) input is known. It can be shown that this leads to a generically NP hard minimization problem. The main result of this paper is an efficient, LMI based convex relaxation of the problem. These results are illustrated with a non–trivial problem: classification of textured images.

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: Very frequently the same biological system is described by several, sometimes competing mathematical models. This usually creates confusion around their validity, ie, which one is correct. However, this is unnecessary since validity of a model cannot be established; model validation is actually a misnomer. In principle the only statement that one can make about a system model is that it is incorrect, ie, invalid, a fact which can be established given appropriate experimental data. Nonlinear models of high dimension and with many parameters are impossible to invalidate through simulation and as such the invalidation process is often overlooked or ignored. Results: We develop different approaches for showing how competing ordinary differential equation (ODE) based models of the same biological phenomenon containing nonlinearities and parametric uncertainty can be invalidated using experimental data. We first emphasize the strong interplay between system identification and model invalidation and we describe a method for obtaining a lower bound on the error between candidate model predictions and data. We then turn

This paper introduces a general and powerful framework for the analysis of uncertain systems, encompassing linear fractional transformations, the behavioral approach for system theory and the integral quadratic constraint formulation. In this approach, a system is defined by implicit equations, and the central analysis question is to test for solutions of these equations. In Part I, the general properties of this formulation are developed, and computable necessary and sufficient conditions are derived for a robust performance problem posed in this framework. 1 Introduction In the predominant viewpoint in systems and control theory, a system is an input-output (I/O) entity, where the variables are clearly separated in two groups, and a cause-effect relationship is established between them. This approach entails a "signal flow" conception, adequate for systems which are deliberately built to match the I/O philosophy, such as computers and amplifiers. For many other physical systems this...

In previous work, the determination of uncertainty models via minimum norm model validation is based on a single set of input and output measurement data. Since uncertainty bounds at each frequency is directionally dependent for multivariable systems, this will lead to optimistic uncertainty levels. In addition, the design freedom in the uncertainty model has not been utilized to further reduce uncertainty levels. The above issues are addressed by formulating a minmax problem. An analytical solution to the min-max problem is given to within a generalized eigenvalue problem, thus avoiding a direct numerical approach. This result will lead to less conservative and more realistic uncertainty models for use in robust control. 1 Introduction In applying multivariable robust control analysis and synthesis techniques to linear, time-invariant systems, as in for example [1], a set of plants as defined by a nominal and uncertainty model are required a priori. Nominal models are usually associa...