相关论文: Realization Theory for LPV State-Space Representat…

In this paper, we investigate a continuous-time linear quadratic control problem for systems with unknown matrices, where only input-output data are available. We propose an output-feedback learning framework based on a canonical nonminimal…

In this work we approach the dual optimal reach-safe control problem using sparse approximations of Koopman operator. Matrix approximation of Koopman operator needs to solve a least-squares (LS) problem in the lifted function space, which…

High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…

We study the optimal control of path-dependent McKean-Vlasov equations valued in Hilbert spaces motivated by non Markovian mean-field models driven by stochastic PDEs. We first establish the well-posedness of the state equation, and then we…

The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…

State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

Inferring latent dynamics from multivariate time-series defined over topological cell complexes is crucial for capturing the complex, higher-order interactions inherent in real-world systems such as in water, sensor, and transportation…

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…

We investigate the use of matrix completion methods for time-series imputation. Specifically we consider low-rank completion of the block-Hankel matrix representation of a time-series. Simulation experiments are used to compare the method…

Koopman linear representations have become a popular tool for control design of nonlinear systems, yet it remains unclear when such representations are exact. In this paper, we establish sufficient and necessary conditions under which a…

Using the framework of the quantum separation of variables (SoV) for higher rank quantum integrable lattice models [1], we introduce some foundations to go beyond the obtained complete transfer matrix spectrum description, and open the way…

This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…

The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…

A promising step from linear towards nonlinear data-driven control is via the design of controllers for linear parameter-varying (LPV) systems, which are linear systems whose parameters are varying along a measurable scheduling signal.…

Modern state-space models (SSMs) often utilize transition matrices which enable efficient computation but pose restrictions on the model's expressivity, as measured in terms of the ability to emulate finite-state automata (FSA). While…

Modeling and inference with multivariate sequences is central in a number of signal processing applications such as acoustics, social network analysis, biomedical, and finance, to name a few. The linear-Gaussian state-space model is a…

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for parameterizing physical fields, yet they often suffer from spectral bias and the computational expense of non-convex optimization. We introduce the Vekua Layer…

This paper studies the performative prediction problem which optimizes a stochastic loss function with data distribution that depends on the decision variable. We consider a setting where the agent(s) provides samples adapted to the…

Koopman operator theory yields powerful tools for modeling, analysis, and control of nonlinear dynamical systems. Prominently, linear time-invariant (LTI) Koopman representations have been proposed to enable the application of linear…