Maria Cecilia Mazzaro

An LMI approach to control-oriented identification and model (In) validation of LPV systems

This note proposes a control-oriented identification framework for a class of linear parameter varying systems that takes into account both the dependence of part of the model on time-varying parameters as well as the possible existence of a nonparametric component. The main results of the note show that the problems of obtaining and validating a model for these systems can be recast as linear matrix inequality feasibility problems. Moreover, as the information is completed, the algorithm is shown to converge in the l/sub 2/-induced topology to the actual plant. Additional results include deterministic bounds on the identification error. These results are illustrated with a practical example arising in the context of active vision.

A model (in)validation approach to gait classification

This paper addresses the problem of human gait classification from a robust model (in)validation perspective. The main idea is to associate to each class of gaits a nominal model, subject to bounded uncertainty and measurement noise. In this context, the problem of recognizing an activity from a sequence of frames can be formulated as the problem of determining whether this sequence could have been generated by a given (model, uncertainty, and noise) triple. By exploiting interpolation theory, this problem can be recast into a nonconvex optimization. In order to efficiently solve it, we propose two convex relaxations, one deterministic and one stochastic. As we illustrate experimentally, these relaxations achieve over 83 percent and 86 percent success rates, respectively, even in the face of noisy data.

An algorithm for sampling subsets of H/sub /spl infin// with applications to risk-adjusted performance analysis and model (in)validation

In spite of their potential to reduce computational complexity, the use of probabilistic methods in robust control has been mostly limited to parametric uncertainty, since the problem of sampling causal bounded operators is largely open. In this note, we take steps toward removing this limitation by proposing a computationally efficient algorithm aimed at uniformly sampling suitably chosen subsets of H/sub /spl infin//. As we show in the note, samples taken from these sets can be used to carry out model (in)validation and robust performance analysis in the presence of structured dynamic linear time-invariant uncertainty, problems known to be NP-hard in the number of uncertainty blocks.

Convex necessary and sufficient conditions for frequency domain model (in)validation under SLTV structured uncertainty

This paper deals with the problem of model (in)validation of discrete time, causal, linear time-invariant (LTI) stable models subject to slowly linear time-varying structured uncertainty, using frequency domain data corrupted by additive noise. It is well known that in the case of structured LTI uncertainty the problem is NP hard in the number of uncertainty blocks. The main contribution of this paper shows that, on the other hand, if one considers arbitrarily slowly time varying uncertainty and noise in L/sub 2/, then tractable, convex necessary and sufficient conditions for (in)validation can be obtained. Additional results include a discussion of the case where the noise is characterized in terms of the L/sub /spl infin// norm.

Semi–Blind Model (In) Validation with Applications to Texture Classification

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.

Sampling random transfer functions

Recently, considerable attention has been paid to the use of probabilistic algorithms for analysis and design of robust control systems. However, since these algorithms require the generation of random samples of the uncertain parameters, their application has been mostly limited to the case of parametric uncertainty. Notable exceptions to this limitation are the algorithm for generating FIR transfer functions in Lagoa et al. and the algorithm for generating random fixed order state space representations in Calafiore et al. In this paper, we provide the means for further extending the use of probabilistic algorithms for the case of dynamic causal uncertain parameters. More precisely, we exploit both time and frequency domain characterizations to develop efficient algorithms for generation of random samples of causal, linear time-invariant uncertain transfer functions. The usefulness of these tools are illustrated by developing an algorithm for solving some multi-disk problems arising in the context of synthesizing robust controllers for systems subject to structured dynamic uncertainty.

A risk-adjusted approach to model (in)validation

This paper presents a risk-adjusted approach to the problem of model (in)validation of LTI systems subject to structured dynamic uncertainty entering the model in LFT form. The proposed method proceeds by sampling the set of admissible uncertainties, with the aim of finding at least one element that together with the candidate model can reproduce the experimental data. If so, the model is not invalidated by experimental evidence. Otherwise, if no such element exists, the model is invalidated by the data with a certain probability. As we show in the paper, give /spl epsiv/ >0, it is possible to determine a priori the number of samples so that the probability a valid model is below /spl epsiv/. Thus, by introducing a relaxation in terms of this risk /spl epsiv/, we can overcome the computational complexity associated with model invalidation in the presence of structured uncertainties.

Convex necessary and sufficient conditions for model (in)validation under SLTV structured uncertainty

This paper deals with the problem of model (in)validation of discrete-time, causal, LTI stable models subject to slowly linear time varying structured uncertainty, using frequency-domain data corrupted by additive noise. It is well known that in the case of structured LTI uncertainty the problem is NP hard in the number of uncertainty blocks. The main contribution of this paper shows that, on the other hand, if one considers arbitrarily slowly time varying uncertainty and noise in L/sub 2/ then tractable, convex necessary and sufficient conditions for (in)validation can be obtained.