We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems - with a reasonable expectation of suc…
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48 results for “Nonlinear systems”
Paper accelerates nonlinear mapping in online systems with lower time complexity.
problem Speeding up nonlinear mapping in online systems.
method Integrates an acceleration module into Dendrite Net (DD) to reduce time complexity.
result DD with AC has lower time complexity while maintaining nonlinear mapping and system identification properties.
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.
Develops VAEs for learning complex physical systems from data.
problem Learning low-dimensional representations of nonlinear physical systems.
method Variational Autoencoders with manifold latent spaces.
result Effective in learning nonlinear Burgers equation and constrained mechanical systems.
Introduces nonlinear splittings on fibre bundles for generalizing connections.
problem Generalizing connections on fibre bundles.
method Definition and properties of nonlinear splittings, including affine, homogeneous, and principal splittings.
result Curvature map defined for nonlinear splittings, linking to nonholonomic systems and magnetic Lagrangian 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.
Unified framework identifies nonlinear systems using characteristic curves and neural networks.
problem Balancing interpretability and flexibility in nonlinear system identification.
method Combines differential equation structure with neural networks, using characteristic curves as modular components.
result NN-CC approach outperforms other methods in complex nonlinear systems.
We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only proper, the reduced nonlinear control system need not be smooth. Using the smooth …
Metric nonlinear connectionsmath.DG
For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange struc…
New method identifies key genes affecting phenotypes in biological systems.
problem Identifying genes that drive specific phenotypes in complex biological systems.
method Data-driven observability decomposition using Koopman operators.
result Koopman operator representation identifies genes that drive phenotypes.
Our objective is to estimate the unknown compositional input from its output response through an unknown system after estimating the inverse of the original system with a training set. The proposed methods using artificial neural networks (ANNs) can compete with the optimal bounds for linear systems, where convex optim…
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.
The paper introduces reservoir computing models for complex systems.
problem Modeling complex engineering systems using nonlinear autoregression.
method Introduces reservoir computing with output feedback as stationary and ergodic infinite-order nonlinear autoregressive models.
result Demonstrates versatility of classical and quantum reservoir computers in modeling synthetic and real data.
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where ba…
Optimizes exploration for nonlinear systems to learn controllers efficiently.
problem Learning optimal controllers for unknown nonlinear systems.
method Formally quantifies which parameters are most critical, and develops an algorithm to efficiently explore these parameters.
result Proves a near-instance-optimal rate for learning controllers.
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space wh…
Semi-parametric framework for nonlinear system identification
problem Nonlinear system identification
method Orthogonal Gaussian process regression
result Interpretable models from incomplete physics
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.
Modeling financial systemic risk with optimal control theory for stability.
problem Analyzing and stabilizing systemic risk in interconnected financial entities.
method Developed a theoretical model using optimal control theory, including steps for synthesizing stabilizing controllers.
result The model ensures that the norms of the mappings from disturbance to output are less than a predefined constant, stabilizing the system.
Uncertainty Quantification of Locally Nonlinear Dynamical Systems using Neural Networksphysics.comp-ph
Neural networks simplify uncertainty quantification of locally nonlinear systems.
problem Estimating statistics of responses in large-scale locally nonlinear dynamical systems.
method Decomposes response into nominal linear system and a neural network-estimated pseudoforce.
result Neural networks can efficiently estimate pseudoforce containing nonlinear and uncertain information.
Method estimates parameters of complex nonlinear systems.
problem Parameter estimation for nonlinear systems with derivative states.
method Regularized linear regression using differentiation filtering and least squares.
result Finite-sample bound on mean absolute error of estimation.
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.
QENDy learns quadratic dynamics from nonlinear systems data.
problem Identifying governing equations of highly nonlinear dynamical systems.
method QENDy embeds nonlinear dynamics into a quadratic feature space, requiring trajectory data and preselected basis functions.
result QENDy accurately identifies quadratic dynamics and outperforms SINDy and deep learning methods.
Deep SSMs use neural networks to identify complex systems.
problem Identifying nonlinear systems with high uncertainty.
method Deep state space models with neural networks.
result Deep SSMs outperform traditional methods on benchmarks.
The new business paradigms originate a strong necessity to re-think the theory of the firm with the aim to get a better understanding on the organizational and functional principles of the firm, operating in the investment economies in the prosperous societies. In this connection, we make the innovative research to adv…
New techniques improve the accuracy of identifying nonlinear systems from noisy data.
problem Identifying nonlinear dynamical systems from noisy state measurements.
method Comparative study of local and global smoothing techniques to denoise state measurements and improve sparse regression methods.
result Global smoothing methods outperform local methods in improving the accuracy of governing equation recovery.
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.
Modern control theories such as systems engineering approaches try to solve nonlinear system problems by revelation of causal relationship or co-relationship among the components; most of those approaches focus on control of sophisticatedly modeled white-boxed systems. We suggest an application of actor-critic reinforc…
Algorithm learns dynamics from past observations.
problem Learning a nonlinear dynamical system.
method Spectral filtering, online convex optimization.
result Vanishing prediction error for marginally stable systems.
DeepRSCN models nonlinear systems using stochastic configurations.
problem Modeling nonlinear dynamic systems efficiently.
method Incrementally constructed deep reservoir computing framework with random parameters and online weight updates.
result DeepRSCN outperforms single-layer networks in efficiency, learning, and generalization.
In this paper we develop a method for learning nonlinear systems with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood principle we derive a criterion for learning the model. The resulting optimization…
Extended Koopman Modelseess.SY
Two new Koopman models improve nonlinear system prediction.
problem Predicting nonlinear, nonconvex dynamic systems.
method Convex and Extended Koopman Models using deep learning.
result Significantly improved predictive performance.
Proposes a Koopman operator method for time-dependent reliability analysis of nonlinear systems.
problem Challenges in time-dependent reliability analysis of nonlinear dynamical systems.
method Koopman operator approach for transforming nonlinear systems into linear ones, combined with deep learning for intrinsic coordinates.
result Robust and generalizable approach for time-dependent reliability analysis, superior to purely data-driven methods.
Algorithm learns weight matrix from single trajectory of nonlinear dynamical system.
problem Learning weight matrix from a single trajectory of nonlinear dynamical system.
method Algorithm uses global stability and well-conditioned covariance to recover weight matrix.
result Algorithm recovers weight matrix with optimal sample complexity and linear running time.
KCRL learns stable policies for nonlinear systems with formal guarantees.
problem Lack of stabilization guarantees in RL methods for safety-critical systems.
method KCRL uses Krasovskii's Lyapunov functions as a stability constraint and a primal-dual approach to learn stabilizing policies.
result KCRL guarantees learning a stabilizing policy in a finite number of interactions.
Policy Gradient Converges to the Globally Optimal Policy for Nearly Linear-Quadratic Regulatorscs.LG
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
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 …
Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.
Physics-guided model improves deep learning for nonlinear systems.
problem Intractable inference of nonlinear dynamical systems from data.
method Physics-guided Deep Markov Model (PgDMM) using neural networks.
result Improved performance on nonlinear systems with structured latent space.
Examines multiagent systems for complex learning tasks.
problem Achieving cohesive learning behavior in multiagent networks.
method General formulation for multiagent dynamics and conditions for learning.
result Conditions for achieving cohesive learning behavior in multiagent networks.
We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully …
Data-Efficient Non-Gaussian Semi-Nonparametric Density Estimation for Nonlinear Dynamical Systemsmath.OC
This paper presents a method for efficient density estimation in nonlinear systems.
problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.
Study optimal control in unknown nonlinear systems with near-optimal regret bound.
problem Sequential control in unknown, nonlinear dynamical systems.
method LC^3 algorithm, based on information theory.
result Near-optimal regret bound for episodic settings.
Energy-Based Control of Nonlinear Infinite-Dimensional Port-Hamiltonian Systems with Dissipationmath.OC
In this paper, we consider nonlinear PDEs in a port-Hamiltonian setting based on an underlying jet-bundle structure. We restrict ourselves to systems with 1-dimensional spatial domain and 2nd-order Hamiltonian including certain dissipation models that can be incorporated in the port- Hamiltonian framework by means of a…
The accurate characterization of the business cycles in the nonlinear dynamic financial and economic systems in the time of globalization represents a formidable research problem. The central banks and other financial institutions make their decisions on the minimum capital requirements, countercyclical capital buffer …
A novel model uses ODE-based random features to model nonlinear dynamical systems.
problem Modeling highly nonlinear dynamical systems with uncertainty quantification.
method Compositions of physics-informed random features derived from ODEs, combined with deep Gaussian processes and approximate Bayesian inference.
result The model effectively captures nonlinear behavior in real-world multivariate time series data and achieves comparable performance to other models on benchmark tasks.
The paper tackles data-driven optimal control of unknown nonlinear systems using RKHS.
problem Unknown nonlinear dynamics and stage cost functions.
method Embed state densities into RKHS, learn Markov operators, solve Hamilton-Jacobi-Bellman recursions.
result Solves a wide range of nonlinear control problems, including depth regulation.
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.