On a class of optimization-based robust estimators

We consider in this paper the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and a dense and bounded noise sequence of "moderate" amount. This is termed a robust regression problem. To tackle it, a quite general optimization-based framework is proposed and analyzed. When only the sparse noise is present, a sufficient bound is derived on the number of nonzero elements in the sparse noise sequence that can be accommodated by the estimator while still returning the true parameter matrix. While almost all the restricted isometry-based bounds from the literature are not verifiable, our bound can be easily computed through solving a convex optimization problem. Moreover, empirical evidence tends to suggest that it is generally tight. If in addition to the sparse noise sequence, the training data are affected by a bounded dense noise, we derive an upper bound on the estimation error.Comment: To appear in IEEE Transactions on Automatic Contro

Robustness analysis of a Maximum Correntropy framework for linear regression

In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based correntropy estimators as special cases. An analysis of the robustness properties is then provided. The analysis includes a quantitative characterization of the informativity degree of the regression which is appropriate for studying the stability of the estimator. Using this tool, a sufficient condition is expressed under which the parametric estimation error is shown to be bounded. Explicit expression of the bound is given and discussion on its numerical computation is supplied. For illustration purpose, two special cases are numerically studied.Comment: 10 pages, 5 figures, To appear in Automatic

Analysis of A Nonsmooth Optimization Approach to Robust Estimation

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault detection, state estimation in lossy networks, hybrid system identification, robust estimation, etc. The problem is hard because it exhibits some intrinsic combinatorial features. Therefore, obtaining an effective solution necessitates relaxations that are both solvable at a reasonable cost and effective in the sense that they can return the true parameter vector. The current paper discusses a nonsmooth convex optimization approach and provides a new analysis of its behavior. In particular, it is shown that under appropriate conditions on the data, an exact estimate can be recovered from data corrupted by a large (even infinite) number of gross errors.Comment: 17 pages, 9 figure

Optimal control of discrete-time switched linear systems via continuous parameterization

The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly minimize a quadratic performance index. State-of-art methods for solving such a control problem suffer in general from a high computational requirement due to the fact that an exponential number of switching sequences must be explored. The method of this paper addresses the challenge of the switching law design by introducing auxiliary continuous input variables and then solving a non-smooth block-sparsity inducing optimization problem.Comment: 6 pages, 2 figures, 2 tables; To appear in the Proceedings of IFAC World Congress, 201

Adaptive output feedback control based on neural networks: application to flexible aircraft control

One of the major challenges in aeronautical flexible structures control is the uncertain for the non stationary feature of the systems. Transport aircrafts are of unceasingly growing size but are made from increasingly light materials so that their motion dynamics present some flexible low frequency modes coupled to rigid modes. For reasons that range from fuel transfer to random flying conditions, the parameters of these planes may be subject to significative variations during a flight. A single control law that would be robust to so large levels of uncertainties is likely to be limited in performance. For that reason, we follow in this work an adaptive control approach. Given an existing closed-loop system where a basic controller controls the rigid body modes, the problem of interest consists in designing an adaptive controller that could deal with the flexible modes of the system in such a way that the performance of the first controller is not deteriorated even in the presence of parameter variations. To this purpose, we follow a similar strategy as in Hovakimyan (2002) where a reference model adaptive control method has been proposed. The basic model of the rigid modes is regarded as a reference model and a neural network based learning algorithm is used to compensate online for the effects of unmodelled dynamics and parameter variations. We then successfully apply this control policy to the control of an Airbus aircraft. This is a very high dimensional dynamical model (about 200 states) whose direct control is obviously hard. However, by applying the aforementioned adaptive control technique to it, some promising simulation results can be achieved

Data Informativity for the Identication of MISO FIR Systems with Filtered White Noise Excitation

For Prediction Error Identication, there are two main ingredients to get a consistent estimate: one of them is the data informativity with respect to (w.r.t.) the considered model structure. One common criterion used for the informativity is the positive deniteness of the input density spectral power (DSP) matrix at all frequencies. This criterion is not appropriate for multisine excitation but can be used for ltered white noise excitation for many identication problems. However, this criterion is not necessary and its application for some identication problems might not be possible. In this paper, we propose a necessary and sucient condition for the data informativity in the case of multiple-inputs single-output (MISO) nite impulse response (FIR) model structure in open-loop