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We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…
Monotone learning describes learning processes in which expected performance consistently improves as the amount of training data increases. However, recent studies challenge this conventional wisdom, revealing significant gaps in the…
The subspace identification method (SIM) has become a widely adopted approach for the identification of discrete-time linear time-invariant (LTI) systems. In this paper, we derive finite sample high-probability error bounds for the system…
Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for…
Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…
This paper studies attack-resilient estimation of a class of switched nonlinear systems subject to stochastic noises. The systems are threatened by both of signal attacks and switching attacks. The problem is formulated as the joint…
Available methods for identification of stochastic dynamical systems from input-output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability…
The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) based on a testing dataset. Whereas, these algorithms are optimized through the…
In this paper, we present an optimal filter for linear time-varying continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. We first show that the unknown inputs…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
Identifying controlled safety invariant sets (CSISs) is essential for safety-critical systems. This paper addresses the problem of computing CSISs for black-box discrete-time systems, where the dynamics are unknown and only limited…
This paper deals with the problem of covariance stabilization for a class of linear stochastic discrete-time systems in the Stochastic Model Predictive Control (SMPC) framework. The considered systems are affected by independent and…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
This paper considers the problem of set-based state estimation for linear time-invariant (LTI) systems under time-varying sensor attacks. Provided that the LTI system is stable and observable via every single sensor and that at least one…
We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…
Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…