Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to nonfederal websites. Their policies may differ from this site.

Inspired by the work of Tsiamis et al. [1], in this paper we study the statistical hardness of learning to stabilize linear timeinvariant systems. Hardness is measured by the number of samples required to achieve a learning task with a given probability. The work in [1] shows that there exist system classes that are hard to learn to stabilize with the core reason being the hardness of identification. Here we present a class of systems that can be easy to identify, thanks to a nondegenerate noise process that excites all modes, but the sample complexity of stabilization still increases exponentially with the system dimension. We tie this result to the hardness of costabilizability for this class of systems using ideas from robust control.more » « lessFree, publiclyaccessible full text available December 13, 2024

Free, publiclyaccessible full text available November 1, 2024

While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a modereduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality.more » « less

While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a modereduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality. Keywords: Markov Jump Systems, System Reduction, Clusteringmore » « less

While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a modereduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality.more » « less

AutoRegressive eXogenous (ARX) models form one of the most important model classes in control theory, econometrics, and statistics, but they are yet to be understood in terms of their finite sample identification analysis. The technical challenges come from the strong statistical dependency not only between data samples at different time instances but also between elements within each individual sample. In this work, for ARX models with potentially unknown orders, we study how ordinary least squares (OLS) estimator performs in terms of identifying model parameters from data collected from either a single lengthT trajectory or N i.i.d. trajectories. Our main results show that as long as the orders of the model are chosen optimistically, i.e., we are learning an overparameterized model compared to the ground truth ARX, the OLS will converge with the optimal rate O(1/√T) (or O(1/√N)) to the true (loworder) ARX parameters. This occurs without the aid of any regularization, thus is referred to as selfregularization. Our results imply that the oracle knowledge of the true orders and usage of regularizers are not necessary in learning ARX models — overparameterization is all you need.more » « less

AutoRegressive eXogenous (ARX) models form one of the most important model classes in control theory, econometrics, and statistics, but they are yet to be understood in terms of their finite sample identification analysis. The technical challenges come from the strong statistical dependency not only between data samples at different time instances but also between elements within each individual sample. In this work, for ARX models with potentially unknown orders, we study how ordinary least squares (OLS) estimator performs in terms of identifying model parameters from data collected from either a single lengthT trajectory or N i.i.d. trajectories. Our main results show that as long as the orders of the model are chosen optimistically, i.e., we are learning an overparameterized model compared to the ground truth ARX, the OLS will converge with the optimal rate O(1/√T) (or O(1/√N)) to the true (loworder) ARX parameters. This occurs without the aid of any regularization, thus is referred to as selfregularization. Our results imply that the oracle knowledge of the true orders and usage of regularizers are not necessary in learning ARX models — overparameterization is all you needmore » « less