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…
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48 results for “Linear System Identification”
The paper explores when linear system identification is hard or easy, especially for under-actuated systems.
problem Statistical hardness of learning linear systems, especially under-actuated or under-excited systems.
method Using tools from minimax theory and recent statistical tools for finite sample analysis of system identification.
result The controllability index of linear systems affects the sample complexity of identification, making some systems hard to learn.
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.
The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.
problem System identification for linear systems with nonlinear and/or time-varying policies under i.i.d. random excitation noises.
method Least square estimation with non-asymptotic error bound for bounded state and action trajectories.
result The error bound is consistent with linear policies and generalizes existing guarantees.
Study identifies and validates a method for system identification of Markov jump linear systems.
problem System identification for autonomous Markov jump linear systems with complete state observations.
method Proposes switched least squares method for identification and derives rates of convergence.
result Data-independent rate of convergence is , showing strong consistency.
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.
The paper tackles long-context linear system identification with improved sample complexity bounds.
problem Identifying dynamical systems with long dependencies over fixed context windows.
method Established sample complexity bounds for systems with linear dependencies over a context window of length p.
result The learning process is not hindered by slow mixing properties in extended context windows.
Optimal noise excitation for linear system identification reduces sample complexity.
problem Efficiently identifying linear systems with minimal data.
method Active learning algorithm using ordinary least squares and semidefinite programming.
result The proposed algorithm matches lower bounds on sample complexity for any active learning method.
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.
Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Datastat.ML
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.
A tutorial on non-asymptotic system identification methods.
problem Identifying system parameters in linear models.
method Covering technique, Hanson-Wright Inequality, method of self-normalized martingales.
result Streamlined proofs of least-squares based estimator performance.
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…
A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of regularization/Bayesian techniques. This approach guarantees the identification of stab…
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.
Solves parameter non-identifiability in Bayesian LTI system identification.
problem Parameter non-identifiability in standard Bayesian approaches for LTI system identification.
method Embedding canonical forms of LTI systems within the Bayesian framework.
result Unlocking the use of meaningful priors and robust uncertainty estimates.
In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of basis functions. We reconstruct the …
The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and variance. Recently, a different approach to linear system identification has been…
Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. T…
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…
Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not robust with respect to outliers. In this paper, we introduce a novel method to robust…
A distributed system identification method for LTI systems using reverse experience replay.
problem Online system identification of LTI systems over multi-agent networks.
method DSGD-RER, a distributed variant of SGD-RER with backward updates.
result The estimation error decreases as the network size grows.
New algorithm optimizes linear system estimation from single trajectory.
problem Estimating LTI systems from a single trajectory.
method SGD with Reverse Experience Replay ()
result Optimal guarantees for parameter and prediction errors.
Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regressionstat.ML
Bayesian approach tackles collinearity in large-scale linear system identification.
problem Collinearity in large-scale linear system identification.
method Bayesian regularization framework with Gaussian process and stable spline kernel. Novel Markov chain Monte Carlo scheme.
result Efficiently reconstructs impulse responses posterior by dealing with collinearity.
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.
We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design of the cost function promotes a model with either a continuous change in dynamic…
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 -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.
New bounds quantify estimation error in kernel-based system identification with unknown hyperparameters.
problem Inaccurate error bounds for kernel-based system identification with unknown hyperparameters.
method Construct a high-probability set for true hyperparameters from marginal likelihood, then find worst-case posterior covariance.
result Proposed bounds contain true model with high probability and verified in simulations.
New nonconvex methods improve SysID efficiency and accuracy.
problem Efficiently identify low-order linear systems from limited data.
method Proposes two nonconvex reformulations of Hankel-rank minimization for SysID.
result Nonconvex methods achieve lower statistical error rates and sample complexities.
Parametric identification of the dynamics of inter-sectoral balance: modelling and forecastingmath.DS
This work is devoted to modelling and identification of the dynamics of the inter-sectoral balance of a macroeconomic system. An approach to the problem of specification and identification of a weakly formalized dynamical system is developed. A matching procedure for parameters of a linear stationary Cauchy problem wit…
New mathematical foundations for stable RKHSs improve system identification.
problem Improving stability tests and modeling of impulse responses.
method Providing new structural properties and stability conditions for stable RKHSs.
result Any stable kernel admits feature maps induced by orthogonal eigenvectors in l2.
We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the theories of large-deviations and self-normalized martingales, and provide both d…
In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This s…
New model stabilizes asynchronous LTI systems, independent of synchronous stability.
problem Stability of asynchronous LTI systems under randomization and asynchrony.
method Introduced a new model for random asynchronous LTI systems and developed a method for system identification.
result Stability of random asynchronous LTI systems is independent of synchronous stability.
We prove that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory. Our upper bound relies on a generalization of Mendelson's small-ball method to dependent data, eschewing the use of standard mixing-ti…
This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for conf…
The paper tackles system identification via Hankel nuclear norm regularization, improving estimation rates and singular value gaps.
problem Identifying low-order linear systems from limited data.
method Hankel nuclear norm regularization to encourage low-rankness of the Hankel matrix.
result Hankel regularization enables optimal system recovery with fewer observations and better estimation rates.
Physics-informed Gaussian Process Regression in Solving Eigenvalue Problem of Linear Operatorsstat.ML
Physics-informed GP regression solves eigenvalue problems by identifying non-trivial eigenspaces.
problem Solving eigenvalue problems of linear operators with trivial solutions.
method Constructing a transfer function-type indicator using physics-informed Gaussian Process posterior.
result The posterior covariance is non-trivial only for eigenvalues of the operator, indicating non-trivial eigenspaces.
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to …
Unified Bayesian framework for LTV system identification using neural networks and Gaussian Processes.
problem Identifying Linear Time-Varying systems from input-output data.
method Bayesian modeling of impulse response as a stochastic process, using neural networks and Gaussian Processes for inference.
result Framework can infer LTI system properties from a single noisy input-output pair, achieving lower error than classical methods.
In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This s…
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
problem Identification of nonlinear dynamic systems in engineering.
method Modeling the nonlinear restoring force as a Gaussian process, converting it to a state-space model, and inferring internal states and the nonlinear restoring force through filtering and smoothing.
result The approach effectively identifies nonlinear restoring forces in both simulated and experimental datasets.
The paper tackles joint learning of linear systems, improving accuracy with pooled data.
problem Estimating transition matrices of multiple related linear systems more accurately.
method Developed novel techniques to bound estimation errors and establish high probability bounds for singular values.
result Significant gains in accuracy achieved by pooling data across systems.
Active learning method estimates nonlinear systems efficiently.
problem Identifying nonlinear dynamical systems with continuous states and actions.
method Repeating three steps: trajectory planning, tracking, and re-estimation.
result Estimates nonlinear dynamical systems at a parametric rate.
Learning from examples is one of the key problems in science and engineering. It deals with function reconstruction from a finite set of direct and noisy samples. Regularization in reproducing kernel Hilbert spaces (RKHSs) is widely used to solve this task and includes powerful estimators such as regularization network…
Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimatormath.ST
The OLS estimator optimally identifies stable linear systems with a finite number of samples.
problem Identifying stable linear systems with a finite number of samples.
method Finite-time analysis of the Ordinary Least Squares (OLS) estimator for stable linear systems.
result The OLS estimator achieves optimal sample complexity for stable systems, matching existing lower bounds up to universal factors.
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.
COSMIC identifies LTV systems from large data sets efficiently.
problem Identification of discrete-time linear time-variant systems from large-scale data.
method Formulates as regularized least squares problem, develops closed-form algorithm with linear complexity.
result Achieves optimal results even with large data volumes, significantly faster than general solvers.
CNN identifies nonlinear human posture control models efficiently.
problem Identifying nonlinear human posture control models.
method Convolutional Neural Networks (CNN) for model identification.
result Efficiently identifies nonlinear human posture control models.