New algorithm learns linear dynamical systems from measurements.
problem Learning system dynamics from linear measurements efficiently and accurately.
method Method of moments estimator to directly estimate Markov parameters.
result First polynomial time algorithm for learning linear dynamical systems.
dynoNet learns dynamical systems using linear operators.
problem Learning complex dynamical systems.
method dynoNet uses linear dynamical operators for sequence modeling and system identification.
result dynoNet effectively identifies systems on benchmarks.
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work shows that the eigenspectrum of unknown linear dynamics can be identified without…
New method controls linear systems with partial info and disturbances.
problem Controlling linear dynamical systems under partial observation and adversarial disturbances.
method Double Spectral Control (DSC) using two-level spectral approximation strategy.
result Matches best known regret guarantees with exponential runtime improvement.
We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
Paper connects dynamics of mechanical systems to Reeb dynamics.
problem Understanding dynamics in mechanical systems with Poisson structures.
method Using Jacobi bundle metrics and linear Poisson structures.
result Extends classical results on Reeb dynamics to mechanical systems.
Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement map…
New method for accurately predicting linear dynamical systems.
problem Forecasting and estimating system matrices of linear dynamical systems.
method Non-convex polynomial optimization approach with global convergence guarantee.
result Global convergence of numerical solutions to a least-squares estimator.
SSL framework identifies non-linear systems without labeled data.
problem System identification in non-linear environments without labeled data.
method Dynamics contrastive learning framework.
result SSL can identify non-linear dynamics in latent space.
Paper proposes variational inference for piecewise-linear systems.
problem Intractability of switching dynamical systems.
method Variational approximation and expectation-maximization algorithms.
result Parameters can be estimated off-line, including the number of linear modes.
Study absolute equivalence for Pfaffian systems, applying to control systems.
problem Absolute equivalence of Pfaffian systems with specific independence conditions.
method Structural results for Pfaffian systems of corank 3, applied to control systems.
result Dynamic feedback linearization of control systems with 2 inputs.
Greedy policy maximizes information in unknown linear systems.
problem Exploration in unknown linear dynamical systems.
method Online greedy policy maximizing information.
result Competitive performance compared to gradient-based methods.
We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
Geometrically transforms nonconservative dynamics to linearize Kepler and Manev systems.
problem Regularizing and linearizing nonconservative central force dynamics.
method Projective transformation and conformal scaling in configuration and phase spaces.
result Full linearization of Kepler and Manev dynamics in any finite dimension.
Review of algorithms for linear system approximations.
problem Linear approximation of high-dimensional dynamical systems.
method State-of-the-art algorithms for low-rank DMD.
result Provides additional details for comprehensive understanding.
New approach learns mixtures of linear dynamical systems without separation conditions.
problem Learning mixtures of linear dynamical systems with better fit or understanding.
method Tensor decompositions to learn mixtures of linear dynamical systems.
result Algorithm succeeds without strong separation conditions and can compete with Bayes optimal clustering.
AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.
problem Adaptive control in partially observable linear dynamical systems.
method AdaptOn algorithm that estimates system dynamics through online learning and gradient descent.
result AdaptOn achieves a logarithmic regret bound of polylog(T) after T steps.
New method controls linear systems with adversarial disturbances.
problem Controlling linear dynamical systems under adversarial conditions.
method Novel convex relaxation using spectral filters from Hankel matrix eigenvectors.
result Polylogarithmic running time improvement over prior methods.
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments that are each explained by simpler dynamic units. Building on switching linear dy…
Algorithm optimally estimates linear dynamical systems with active input selection.
problem Estimating parameters of linear dynamical systems efficiently.
method Active learning with adaptive input selection.
result Finite time bound and asymptotic optimality proven.
Study learns dynamics of linear systems from multiple short trajectories.
problem Learning dynamics of autonomous linear systems from multiple short trajectories.
method Finite sample analysis for stable and unstable systems, adjusting trajectory length for marginally stable systems.
result Learning rate of O ( 1 N ) \mathcal{O}(\frac{1}{\sqrt{N}}) O ( N 1 ) for both stable and unstable systems. Test for linearizing 2-input systems with 2D feedback.
problem Linearizability of two-input systems by feedback.
method Algorithmic test for 2D endogenous feedback.
result Systematic derivation of flat outputs.
dynoGP uses deep Gaussian processes for dynamic system identification.
problem System identification for complex dynamical systems.
method Interconnecting linear dynamic GPs and static GPs to model dynamic and static nonlinearities.
result Demonstrates effectiveness of the approach using both simulated and real-world data.
Efficient algorithm for unknown linear systems with convex costs.
problem Controlling an unknown linear system with stochastic convex costs.
method Optimism in the Face of Uncertainty paradigm.
result Achieves optimal T \sqrt{T} T regret-rate. This paper improves system identification by reducing sample complexity for high-dimensional linear dynamical systems.
problem High sample complexity for learning partially observed linear dynamical systems in high dimensions.
method Introduces an ℓ 1 \ell_1 ℓ 1 -regularized estimation method that reduces sample complexity from linear to logarithmic with system dimension. result Markov parameters can be learned with logarithmic number of samples relative to system dimension, improving sample complexity.
Geometric framework for dynamic feedback linearization of control systems with symmetry.
problem Dynamic feedback linearization of control systems with symmetry.
method Geometric framework based on Lie symmetry, systematic procedure for all smooth, generic system trajectories.
result Sufficient condition for dynamic feedback linearizability obtained.
Develops a method to model neural dynamics with flexible yet interpretable latent states.
problem Capturing complex nonlinear dynamics in neural time series while maintaining interpretability.
method Gaussian Process Switching Linear Dynamical System (gpSLDS) that balances expressiveness and interpretability.
result Favorable performance in comparison to rSLDS on synthetic and real neuroscience data.
Paper models non-linear dynamics from time series data.
problem Modeling non-linear dynamical systems from time series data.
method Introduces latent state modeling and a novel alternating minimization algorithm.
result LaNoLem achieves competitive performance in dynamics estimation and prediction.
Improved RL algorithm stabilizes unknown linear systems with polynomial regret.
problem Learning and stabilizing unknown linear dynamical systems.
method Proposes an algorithm with an improved exploration strategy for fast stabilization.
result Achieves i l d e O ( T ) ilde{\mathcal{O}}(\sqrt{T}) i l d e O ( T ) regret after T T T time steps. Transformers can learn noisy linear systems with depth and IID data.
problem Learning noisy linear dynamical systems with transformers.
method Theoretical analysis of multi-layer and single-layer transformers with respect to L 2 L^2 L 2 -testing loss. result Single-layer transformers have a non-diminishing lower bound on approximation error, suggesting depth separation.
Improved robust latent variable estimation for neural dynamics.
problem Inconsistent results due to noise and nonlinearity in existing models.
method Probabilistic approach to latent variable estimation in decomposed models.
result More accurate latent variable inference in nonlinear systems with diverse noise conditions.
This work extends identifiability analysis to sequential latent variable models, focusing on Switching Dynamical Systems.
problem Identifying latent variables in sequential data models.
method Proved identifiability of Markov Switching Models and established conditions for Switching Dynamical Systems.
result Identifiability of latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations.
New insights into cascade feedback linearization of control systems.
problem Obtaining a cascade feedback linearization for invariant control systems.
method Introducing truncated versions of operators from the calculus of variations to prove new theorems.
result Established new geometry and foundational theorems for future work.
Develops CLDS models to model neural activity with nonlinear dynamics.
problem Complex, nonlinear dynamics in neural population activity.
method Conditionally Linear Dynamical System (CLDS) models using Gaussian Process (GP) priors.
result CLDS models can perform well even in data-limited conditions.
We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied only to systems with a…
Analog forecasting uses local dynamics to predict chaotic systems.
problem Theoretical connections between analog forecasting and dynamical systems are overlooked.
method Local approximations of the system's dynamics, linear regression, and estimation of analog forecasting errors.
result Analog forecasting performances are highly linked to the local Jacobian matrix of the flow map.
We develop algorithms to learn non-linear dynamical systems without mixing assumptions.
problem Learning non-linear dynamical systems from dependent data.
method We introduce an offline algorithm and a one-pass streaming method with SGD-RER.
result Our methods achieve optimal or near-optimal performance for learning non-linear systems.
New algorithm reduces learning regret in multi-agent systems with unknown dynamics.
problem Challenges in decentralized learning due to unknown dynamics and lack of communication.
method Proposed MARL algorithm for two-agent LQ systems with unknown dynamics and one-directional communication.
result Achieved O ( T ) O(\sqrt{T}) O ( T ) regret bound for multi-agent LQ systems with certain communication patterns. Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, exist…
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when …
Proposes a new model for better speech segmentation.
problem Improving speech segmentation accuracy.
method Integrates recurrent explicit duration variables into rSLDS and uses Pólya-gamma augmentation for inference.
result Demonstrates improved segmentation on various datasets.
Estimates parameters of interconnected linear systems using total variation penalization.
problem Joint estimation of parameters in interconnected linear dynamical systems.
method Total variation penalized least-squares estimator.
result The MSE goes to zero as the number of systems increases, even with constant trajectory length.
Many real-valued stochastic time-series are locally linear (Gassian), but globally non-linear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents muscle actions. We present a mixed-state dynamic graphical model in which a hid…
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running …
Breaks down complex nonlinear dynamics into simpler components.
problem Control of nonlinear dynamical systems remains challenging.
method Inspired by hybrid switching systems, decomposes dynamics into simpler stochastic switching linear dynamical systems.
result Extracts hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts.
Easy conditions found for simplifying complex systems.
problem Linearizing complex two-input systems.
method Endogenous dynamic feedback with a dimension of at most two.
result Necessary and sufficient conditions for linearizability.
Use simplified layerwise linear models to understand neural dynamics.
problem Complex neural network dynamics are hard to grasp.
method Apply simplified layerwise linear models to explain neural phenomena.
result Simplified models explain neural collapse, emergence, etc.
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged…