Yongfang Cheng

A convex optimization approach to model (in)validation of switched ARX systems with unknown switches

This paper considers the problem of (in)validating switched affine models from noisy experimental data, in cases where the mode-variable is not directly observable. This problem, the dual of identification, is a crucial step when designing controllers using models identified from experimental data. Our main results are convex certificates, obtained by exploiting a combination of sparsification and polynomial optimization tools, for a given model to either be consistent with the observed data or be invalidated by it. These results are illustrated using both academic examples and a non-trivial application: detecting abnormal activities using video data.

Hankel based maximum margin classifiers: A connection between machine learning and Wiener systems identification

This paper considers the problem of nonparametric identification of Wiener systems in cases where there is no a-priori available information on the dimension of the output of the linear dynamics. Thus, it can be considered as a generalization to the case of dynamical systems of non-linear manifold embedding methods recently proposed in the machine learning community. A salient feature of this framework is its ability to exploit both positive and negative examples, as opposed to classical identification techniques where usually only data known to have been produced by the unknown system is used. The main result of the paper shows that while in principle this approach leads to challenging non-convex optimization problems, tractable convex relaxations can be obtained by exploiting a combination of recent developments in polynomial optimization and matrix rank minimization. Further, since the resulting algorithm is based on identifying kernels, it uses only information about the covariance matrix of the observed data (as opposed to the data itself). Thus, it can comfortably handle cases such as those arising in computer vision applications where the dimension of the output space is very large (since each data point is a frame from a video sequence with thousands of pixels).

Subspace Clustering with Priors via Sparse Quadratically Constrained Quadratic Programming

This paper considers the problem of recovering a subspace arrangement from noisy samples, potentially corrupted with outliers. Our main result shows that this problem can be formulated as a convex semi-definite optimization problem subject to an additional rank constrain that involves only a very small number of variables. This is established by first reducing the problem to a quadratically constrained quadratic problem and then using its special structure to find conditions guaranteeing that a suitably built convex relaxation is indeed exact. When combined with the standard nuclear norm relaxation for rank, the results above lead to computationally efficient algorithms with optimality guarantees. A salient feature of the proposed approach is its ability to incorporate existing a-priori information about the noise, co-ocurrences, and percentage of outliers. These results are illustrated with several examples.

A convex optimization approach to robust fundamental matrix estimation

This paper considers the problem of estimating the fundamental matrix from corrupted point correspondences. A general nonconvex framework is proposed that explicitly takes into account the rank-2 constraint on the fundamental matrix and the presence of noise and outliers. The main result of the paper shows that this non-convex problem can be solved by solving a sequence of convex semi-definite programs, obtained by exploiting a combination of polynomial optimization tools and rank minimization techniques. Further, the algorithm can be easily extended to handle the case where only some of the correspondences are labeled, and, to exploit co-ocurrence information, if available. Consistent experiments show that the proposed method works well, even in scenarios characterized by a very high percentage of outliers.

A convex optimization approach to semi-supervised identification of switched ARX systems

This paper proposes a general convex framework for robustly identifying discrete-time affine hybrid systems from measurements contaminated by noise (both process and measurement) and outliers. Our main result shows that this problem can be formulated as a constrained polynomial optimization, for which a monotonically convergent sequence of tractable convex relaxations can be obtained by exploiting recent developments in sparse polynomial optimization. A salient feature of the proposed framework is its ability to incorporate existing a-priori information about the noise, co-ocurrences, or the switching sequence. These results are illustrated with several examples showing the ability of the proposed approach to make effective use of this additional information.

Identification of switched wiener systems based on local embedding

This paper considers the problem of switched Wiener system identification from a Kernel based manifold embedding perspective. Our goal is to identify both the Kernel mapping and the dynamics governing the evolution of the data on the manifold from noisy output measurements and with minimal assumptions about the nonlinearity and the affine portion of the systems. While in principle this is a very challenging problem, the main result of the paper shows that a computationally efficient solution can be obtained using a polynomial optimization approach that allows for exploiting the underlying sparse structure of the problem and provides optimality certificates. As an alternative, we provide a low complexity algorithm for the case where the affine part of the system switches only between 2 sub models.

Identification of LPV systems with LFT parametric dependence via convex optimization

This paper considers the identification of Linear Parameter Varying (LPV) systems in Linear Fractional Transformation (LFT) form, where the “forward” part is a Linear Time Invariant (LTI) system, while the “feedback” part is given by a single scheduling variable available for measurement. Our main result shows that, despite the nonlinear dependence on the scheduling parameter, the system can be identified using convex optimization, provided that this parameter can be suitably manipulated. These results are illustrated with examples showing the effectiveness of the proposed method.

ℓ ∞ worst-case optimal estimators for switched ARX systems

This paper considers the problem of worst-case estimation for switched piecewise linear models, in cases where the mode-variable is not directly observable. Our main result shows that worst case point wise optimal estimators can be designed by solving a constrained polynomial optimization problem. In turn, this problem can be relaxed to a sequence of convex optimizations by exploiting recent results on moments-based semi-algebraic optimization. Theoretical results are provided showing that this approach is guaranteed to find the optimal filter in a finite number of steps, bounded above by a constant that depends only on the number of data points available and the parameters of the model. Finally, we briefly show how to extend these results to accommodate parametric uncertainty.