Optimal nonlinear dynamic sparse model selection and Bayesian parameter estimation for nonlinear systems
Not provided.
Computer Science↗
SEARCH · Engineering Papers
Results for “nonlinear systems”
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Data-driven Minimum Entropy Control for Stochastic Nonlinear Systems using the Cumulant-Generating Function
Here, we present a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.
42 ENGINEERING↗
The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations
We propose a new class of method for solving nonlinear systems of equations, which, among other things, has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extension to the Newton-Raphson (NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.
97 MATHEMATICS AND COMPUTING↗
Investigating Shaker-System Stability for Strong and Weak Nonlinear Systems.
Abstract not provided.
Robbins, Eric↗
Decentralized Filtering Adaptive Neural Network Control for Uncertain Switched Interconnected Nonlinear Systems
This article presents a novel decentralized filtering adaptive neural network control framework for uncertain switched interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, the nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF) neural network incorporated with a piecewise constant adaptive law, where the adaptive law will update adaptive parameters from the error dynamics between the host system and the decentralized state predictor by discarding the unknowns, whereas a decentralized filtering control law is derived to cancel both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. The matched uncertainties are canceled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. By exploiting the average dwell time principle, the error bounds between the real system and the virtual reference system, which defines the best performance that can be achieved by the closed-loop system, are derived. A numerical example is given to illustrate the effectiveness of the decentralized filtering adaptive neural network control architecture by comparing against the model reference adaptive control (MRAC).
Average dwell time, decentralized, filtering adapt↗
Neural Ordinary Differential Equations for Nonlinear System Identification
Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art nonlinear and classical linear methods. In particular, we present a quantitative study comparing NODE's performance against neural state-space models and classical linear system identification methods and evaluate their inference speed and prediction performance on open-loop errors across eight different dynamical systems. The experiments show that NODEs can consistently improve the prediction accuracy by order of magnitude compared to benchmark methods. Besides improved accuracy, we also observed that NODEs are less sensitive to hyperparameters compared to neural state-space models by paying the cost of increased computation at the inference time.
machine leaning, system identification, physics in↗
Gradient-Descent-Based Learning Gain for Backstepping Controller and Disturbance Observer of Nonlinear Systems
This paper proposes a gradient-descent-based learning (GL) gain for backstepping controller and disturbance observer (DOB) of nonlinear system. The proposed method consists of the GL gain update law, controller, and DOB. The GL gain update law is proposed to adapt the control gain and DOB gain according to the direction that minimizes the cost function. The mathematical analysis reveals that the GL gain always has a positive sign and upper bound. The controller is designed via a backstepping procedure to track the desired output with GL control gain. The DOB is designed to estimate the unknown external disturbance with the GL DOB gain. Because the control and DOB gains are simultaneously tuned to achieve improved performance, the time consumption for tuning can be reduced. In addition, the peaking phenomenon can be avoided initially by a small initial value of GL gains. The stability of the closed-loop system is guaranteed using the input-to-state stability property. The performance of the proposed method was validated via simulations and experiments using a DC motor.
42 ENGINEERING↗
Propagating Parameter Uncertainty in Power System Nonlinear Dynamic Simulations Using a Koopman Operator-Based Surrogate Model
In this work, we propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment a priori known state-space model by reformulating parameters deemed uncertain as pseudo-state variables. Then, we apply the Koopman operator theory to the resulting state-space model and obtain a linear dynamical system model. This transformation allows us to analyze the evolution of the system dynamics through its Koopman eigenfunctions, eigenvalues, and modes. Of particular importance for this letter, the obtained linear dynamical system is a surrogate that enables the evaluation of parameter uncertainties by simply perturbing the initial conditions of the Koopman eigenfunctions associated with the pseudo-state variables. Simulations carried out on the New England test system reveal the excellent performance of the proposed method in terms of accuracy and computational efficiency.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Multi-modality deep learning for pulse prediction in homogeneous nonlinear systems via parametric conversion
In this Letter, we introduce FusionNet, a multi-modality deep learning framework designed to predict and analyze output pulses in high-power rare-earth-doped laser systems driving parametric conversion in homogeneous guided nonlinear media. FusionNet integrates temporal, spectral, and physical experimental conditions to model ultrafast nonlinear phenomena, including parametric nonlinear frequency conversion, self-phase modulation, and cross-phase modulation in homogeneous guided systems such as gas-filled hollow-core fibers. These systems bridge physical models with experimental data, advancing our understanding of light-guiding principles and nonlinear interactions while expediting the design and optimization of on-demand high-power, high-brightness systems. Our results demonstrate a 73% reduction in prediction error and an 83% improvement in computational efficiency compared to conventional neural networks. This work establishes a new paradigm for accelerating parametric simulations and optimizing experimental designs in high-power laser systems, with further implications for high-precision spectroscopy, quantum information science, and distributed entangled interconnects.
47 OTHER INSTRUMENTATION↗
Resilient Consensus State Observer for Nonlinear Systems and Against Attacks
Herein, we investigate the design of a resilient consensus observer that yields correct and continuous state estimates of a nonlinear control system whose state observations are subject to attacks. The observations are assumed to be obtained from multiple sensors and/or communication channels employed to provide redundancy. It is shown that, in an attack-free setting, individual globally convergent observers can be designed for each sensor/channel using the corresponding state-dependent Jacobian system. To counter attacks, a resilient consensus observer is then designed by merging the observers estimates to produce a smooth consensus estimate. Resilient convergence of the consensus estimate to the true state is ensured under the condition that the sparsity of the attacks being less than a half of the number of redundant channels. As an illustrative example, the proposed scheme is successfully applied to the chaotic circuit synchronization problem in which their synchronization has been attacked.
97 MATHEMATICS AND COMPUTING↗
IOTA Run 2 Beam Dynamics Studies in Nonlinear Integrable Systems
Nonlinear integrable optics is a promising design approach for suppressing fast collective instabilities. To study it experimentally, a new storage ring, the Integrable Optics Test Accelerator (IOTA), was built at Fermilab. IOTA has recently completed its second scientific run, incorporating many hardware and instrumentation improvements. This report presents the results of the two integrable optics experiments - the quasi-integrable Henon-Heiles octupole system and the fully integrable Danilov-Nagaitsev system. We demonstrate tune spread and dynamic aperture in agreement with tracking simulations, and a stable crossing of the integer resonance. Based on recovered single-particle phase space dynamics, we show improved invariant jitter consistent with intended effective Hamiltonian. We conclude by outlining future plans and efforts towards proton studies and larger designs.
43 PARTICLE ACCELERATORS↗
Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.
Data-driven model reduction↗
VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems
Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.
Conditional VAEs↗
Differentiable predictive control: Deep learning alternative to explicit model predictive control for unknown nonlinear systems
Not Available
97 MATHEMATICS AND COMPUTING↗
A Simple Linearization Method of Nonlinear Systems Based on Fuzzy Logic
Not Available
Perdukova, Daniela↗
Nonlinear System Identification of a Fixture-Pylon Assembly using Stepped Sine Testing.
Abstract not provided.
Robbins, Eric↗
Nonlinear System Identification of a Fixture-Pylon Assembly using Stepped Sine Testing.
Abstract not provided.
Robbins, Eric↗
Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems
Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.
PDE systems↗