We consider the problem of joint estimation of the parameters of $m$ linear dynamical systems, given access to single realizations of their respective trajectories, each of length $T$. The linear systems are assumed to reside on the nodes of an undirected and connected graph $G = ([m], \mathcal{E})$, and the system matrices are assumed to either vary smoothly or exhibit small number of ``jumps'' across the edges. We consider a total variation penalized least-squares estimator and derive non-asymptotic bounds on the mean squared error (MSE) which hold with high probability. In particular, the bounds imply for certain choices of well connected $G$ that the MSE goes to zero as $m$ increases, even when $T$ is constant. The theoretical results are supported by extensive experiments on synthetic and real data.

This work introduces a learning-enhanced observer (LEO) for linear time-invariant systems with uncertain dynamics. Rather than relying solely on nominal models, the proposed framework treats the system matrices as optimizable variables and refines them through gradient-based minimization of a steady-state output discrepancy loss. The resulting data-informed surrogate model enables the construction of an improved observer that effectively compensates for moderate parameter uncertainty while preserving the structure of classical designs. Extensive Monte Carlo studies across diverse system dimensions show systematic and statistically significant reductions, typically exceeding 15\%, in normalized estimation error for both open-loop and Luenberger observers. These results demonstrate that modern learning mechanisms can serve as a powerful complement to traditional observer design, yielding more accurate and robust state estimation in uncertain systems. Codes are available at https://github.com/Hao-B-Shu/LTI_LEO.

Online change detection (OCD) aims to rapidly identify change points in streaming data and is critical in applications such as power system monitoring, wireless network sensing, and financial anomaly detection. Existing OCD methods typically assume precise system knowledge, which is unrealistic due to estimation errors and environmental variations. Moreover, existing OCD methods often struggle with efficiency in large-scale systems. To overcome these challenges, we propose RoS-Guard, a robust and optimal OCD algorithm tailored for linear systems with uncertainty. Through a tight relaxation and reformulation of the OCD optimization problem, RoS-Guard employs neural unrolling to enable efficient parallel computation via GPU acceleration. The algorithm provides theoretical guarantees on performance, including expected false alarm rate and worst-case average detection delay. Extensive experiments validate the effectiveness of RoS-Guard and demonstrate significant computational speedup in large-scale system scenarios.

In this paper, the problem of distributed state estimation of human-driven vehicles (HDVs) by connected autonomous vehicles (CAVs) is investigated in mixed traffic transportation systems. Toward this, a distributed observable state-space model is derived, which paves the way for estimation and observability analysis of HDVs in mixed traffic scenarios. In this direction, first, we obtain the condition on the network topology to satisfy the distributed observability, i.e., the condition such that each HDV state is observable to every CAV via information-exchange over the network. It is shown that strong connectivity of the network, along with the proper design of the observer gain, is sufficient for this. A distributed observer is then designed by locally sharing estimates/observations of each CAV with its neighborhood. Second, in case there exist faulty sensors or unreliable observation data, we derive the condition for redundant distributed observability as a $q$-node/link-connected network design. This redundancy is achieved by extra information-sharing over the network and implies that a certain number of faulty sensors and unreliable links can be isolated/removed without losing the observability. Simulation results are provided to illustrate the effectiveness of the proposed approach.

Dynamical systems modeling is a core pillar of scientific inquiry across natural and life sciences. Increasingly, dynamical system models are learned from data, rendering identifiability a paramount concept. For systems that are not identifiable from data, no guarantees can be given about their behavior under new conditions and inputs, or about possible control mechanisms to steer the system. It is known in the community that "linear ordinary differential equations (ODE) are almost surely identifiable from a single trajectory." However, this only holds for dense matrices. The sparse regime remains underexplored, despite its practical relevance with sparsity arising naturally in many biological, social, and physical systems. In this work, we address this gap by characterizing the identifiability of sparse linear ODEs. Contrary to the dense case, we show that sparse systems are unidentifiable with a positive probability in practically relevant sparsity regimes and provide lower bounds for this probability. We further study empirically how this theoretical unidentifiability manifests in state-of-the-art methods to estimate linear ODEs from data. Our results corroborate that sparse systems are also practically unidentifiable. Theoretical limitations are not resolved through inductive biases or optimization dynamics. Our findings call for rethinking what can be expected from data-driven dynamical system modeling and allows for quantitative assessments of how much to trust a learned linear ODE.

XX, XXXX 2017 1 Direct Data Driven Control Using Noisy Measurements Ramin Esmzad, Gokul S. Sankar, T eawon Han, Hamidreza Modares, Senior, IEEE Abstract -- This paper presents a novel direct data-driven control framework for solving the linear quadratic regulator (LQR) under disturbances and noisy state measurements. The system dynamics are assumed unknown, and the LQR solution is learned using only a single trajectory of noisy input-output data while bypassing system identification. Our approach guarantees mean-square stability (MSS) and optimal performance by leveraging convex optimization techniques that incorporate noise statistics directly into the controller synthesis. First, we establish a theoretical result showing that the MSS of an uncertain data-driven system implies the MSS of the true closed-loop system. Building on this, we develop a robust stability condition using linear matrix inequalities (LMIs) that yields a stabilizing controller gain from noisy measurements. Finally, we formulate a data-driven LQR problem as a semidefinite program (SDP) that computes an optimal gain, minimizing the steady-state covariance. Extensive simulations on benchmark systems--including a rotary inverted pendulum and an active suspension system--demonstrate the superior robustness and accuracy of our method compared to existing data-driven LQR approaches. The proposed framework offers a practical and theoretically grounded solution for controller design in noise-corrupted environments where system identification is infeasible. I NTRODUCTION D IRECT data-driven control has recently gained a surge of interest due to its control-oriented approach to solving control design problems [1]-[3]. That is, controller parameters are learned directly using input-output or input-state trajectories, without explicitly constructing a predictive model of the system. Bypassing system identification allows for leveraging the collected data to achieve what is best for the control objectives rather than using the data to fit a predictive model.

Dimarogonas Abstract --Recent years have witnessed the rapid advancement of understanding the control mechanism of networked dynamical systems (NDSs), which are governed by components such as nodal dynamics and topology. This paper reveals that the critical components in continuous-time state feedback cooperative control of NDSs can be inferred merely from discrete observations. In particular, we advocate a bi-level inference framework to estimate the global closed-loop system and extract the components, respectively. The novelty lies in bridging the gap from discrete observations to the continuous-time model and effectively decoupling the concerned components. Specifically, in the first level, we design a causality-based estimator for the discrete-time closed-loop system matrix, which can achieve asymptotically unbiased performance when the NDS is stable. In the second level, we introduce a matrix logarithm based method to recover the continuous-time counterpart matrix, providing new sampling period guarantees and establishing the recovery error bound. By utilizing graph properties of the NDS, we develop least square based procedures to decouple the concerned components with up to a scalar ambiguity. Furthermore, we employ inverse optimal control techniques to reconstruct the objective function driving the control process, deriving necessary conditions for the solutions. Numerical simulations demonstrate the effectiveness of the proposed method. I NTRODUCTION In the last decades, networked dynamical systems (NDSs) have played a crucial role in many engineering and biological fields, e.g., multi-robot formation [1], power grids [2], human brain [3], and immune cell network [4]. An NDS, comprising multiple interconnected nodes, is characterized by not only the self-dynamics of a single node (nodal dynamics) but also the interaction structure (topology) between nodes, and can achieve various cooperative behaviors such as synchronization. However, the prior information about the nodal dynamics and topology is not always accessible in practice, and needs to be inferred from observations. This inference enhances our ability to understand, predict, and intervene with the NDS [5]. A. Motivations This paper focuses on the continuous-time linear state-feedback cooperative control of NDSs, where only discrete and noisy observations on a single round of the system's trajectory are available. In particular, we aim to provide a: Y ushan Li and Dimos V . Dimarogonas are with the Division of Decision and Control Systems, KTH Royal Institute of Technology, Stockholm, Sweden. The motivation for addressing this problem stems from two main aspects.

We study the problem of learning to stabilize (LTS) a linear time-invariant (LTI) system. Policy gradient (PG) methods for control assume access to an initial stabilizing policy. However, designing such a policy for an unknown system is one of the most fundamental problems in control, and it may be as hard as learning the optimal policy itself. Existing work on the LTS problem requires large data as it scales quadratically with the ambient dimension. We propose a two-phase approach that first learns the left unstable subspace of the system and then solves a series of discounted linear quadratic regulator (LQR) problems on the learned unstable subspace, targeting to stabilize only the system's unstable dynamics and reduce the effective dimension of the control space. We provide non-asymptotic guarantees for both phases and demonstrate that operating on the unstable subspace reduces sample complexity. In particular, when the number of unstable modes is much smaller than the state dimension, our analysis reveals that LTS on the unstable subspace substantially speeds up the stabilization process. Numerical experiments are provided to support this sample complexity reduction achieved by our approach.

We derive a finite-sample probabilistic bound on the parameter estimation error of a system identification algorithm for Linear Switched Systems. The algorithm estimates Markov parameters from a single trajectory and applies a variant of the Ho-Kalman algorithm to recover the system matrices. Our bound guarantees statistical consistency under the assumption that the true system exhibits quadratic stability. The proof leverages the theory of weakly dependent processes. To the best of our knowledge, this is the first finite-sample bound for this algorithm in the single-trajectory setting.

This paper studies the linear quadratic regulation (LQR) problem of unknown discrete-time systems via dynamic output feedback learning control. In contrast to the state feedback, the optimality of the dynamic output feedback control for solving the LQR problem requires an implicit condition on the convergence of the state observer. Moreover, due to unknown system matrices and the existence of observer error, it is difficult to analyze the convergence and stability of most existing output feedback learning-based control methods. To tackle these issues, we propose a generalized dynamic output feedback learning control approach with guaranteed convergence, stability, and optimality performance for solving the LQR problem of unknown discrete-time linear systems. In particular, a dynamic output feedback controller is designed to be equivalent to a state feedback controller. This equivalence relationship is an inherent property without requiring convergence of the estimated state by the state observer, which plays a key role in establishing the off-policy learning control approaches. By value iteration and policy iteration schemes, the adaptive dynamic programming based learning control approaches are developed to estimate the optimal feedback control gain. In addition, a model-free stability criterion is provided by finding a nonsingular parameterization matrix, which contributes to establishing a switched iteration scheme. Furthermore, the convergence, stability, and optimality analyses of the proposed output feedback learning control approaches are given. Finally, the theoretical results are validated by two numerical examples.