Optimal nonlinear dynamic sparse model selection and Bayesian parameter estimation for nonlinear systems
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Computer Science↗
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Results for “NONLINEAR SYSTEM”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Composite Robust $H_\infty$ Control for Uncertain Stochastic Nonlinear Systems with State Delay via Disturbance Observer
Here in this note, the robust stochastic stabilization and robust H_infinity control problems are investigated for uncertain stochastic time-delay systems with nonlinearity and multiple disturbances. By estimating the disturbance, which can be described by an exogenous model, a composite hierarchical control scheme is proposed that integrates the output of the disturbance observer with state feedback control law. Sufficient conditions for the existence of the disturbance observer and composite hierarchical controller are established in terms of linear matrix inequalities, which ensure the mean-square asymptotic stability of the resulting closed-loop system and the disturbance attenuation. It has been shown that the disturbance rejection performance can also be achieved. A numerical example is provided to show the potential of the proposed techniques and encouraging results have been obtained.
42 ENGINEERING↗
Nonlinear phase field model for electrodeposition in electrochemical systems
A nonlinear phase-field model has been developed for describing the electrodeposition process in electrochemical systems that are highly out of equilibrium. Main thermodynamic driving forces for the electrode-electrolyte interface (EEI) evolution are limited to local variations of overpotential and ion concentration. Application of the model to Li-ion batteries describes the electrode interface motion and morphology change caused by charge mass transfer in the electrolyte, an electrochemical reaction at the EEI and cation deposition on the electrode surface during the charging operation. The Li electrodeposition rate follows the classical Butler-Volmer kinetics with exponentially and linearly depending on local overpotential and cation concentration at the electrode surface, respectively. Simulation results show that the Li deposit forms a fiber-like shape and grows parallel to the electric field direction. The longer and thicker deposits are observed both for higher current density and larger rate constant where the surface reaction rate is expected to be high. The proposed diffuse interface model well captures the metal electrodeposition phenomena in plenty of non-equilibrium electrochemical systems.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.
In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratio variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.
36 MATERIALS SCIENCE↗
Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation
A numerical method for solving systems of nonlinear one-dimensional balance laws, based on multivariate sigmoidal functions approximation, is developed. Constructive approximation theorems are first established in both, uniform and L{sup p} norms. A priori as well as a posteriori error estimates are derived for the numerical solutions, when various kinds of sigmoidal functions, such as unit step, logistic and Gompertz functions, are chosen. The residual of the numerical method is also estimated. Numerical examples are given to test the performance of the algorithm, a comparison with the Godunov method is made concerning accuracy and computational cost. Finally, the numerical stability of the method is analyzed.
97 MATHEMATICS AND COMPUTING↗
Koopman Operators for Generalized Persistence of Excitation Conditions for Nonlinear Systems
It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the capacity to generate extremely large datasets. We seek to develop generalized identifiability conditions for informing the design of automated experiments to discover predictive nonlinear biological models. For linear systems, identifiability is characterized by persistence of excitation conditions. For nonlinear systems, no such persistence of excitation conditions exist. We use the input-Koopman operator method to model nonlinear systems and derive identifiability conditions for openloop systems initialized from a single initial condition. We show that nonlinear identifiability is intrinsically tied to the rank of a given dataset’s power spectral density, transformed through the lifted Koopman observable space. We illustrate these identifiability conditions with a simulated synthetic gene circuit model, the repressilator. We illustrate how rank degeneracy in datasets results in overfitted nonlinear models of the repressilator, resulting in poor predictive accuracy. Our findings provide novel experimental design criteria for discovery of globally predictive nonlinear models of biological phenomena.
Boddupalli, Nibodh↗
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↗
Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs
This paper proposes an unscented Kalman filter (UKF)-based unbiased minimum-variance estimation (UMV) method for the nonlinear system with unknown inputs. By utilizing the statistical linerization, the nonlinear system and measurement functions are transformed into a “linear-like” regression form. The latter preserves the nonlinearity of the system and the measurement models. To this end, the unknown inputs can be estimated by the weighted least-squares. This “linear-like” regression form also allows us to resort to the UMV state estimation framework for the development of new nonlinear filter to handle unknown inputs. Specifically, two approaches have been developed: 1) given the estimated inputs, we derive a filter by minimizing the trace of the state error covariance matrix; 2) without input estimation, we derive the filter by minimizing the trace of the state error covariance matrix subject to a constraint imposed on the gain matrix. We prove that these two approaches provide the same results. Numerical results validate the effectiveness of the proposed method.
Unscented Kalman filter, unbiased minimumvariance ↗
Filtering adaptive output feedback control for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics
This article synthesizes a filtering adaptive output feedback controller for multivariable nonlinear systems with mismatched uncertainties and unmodeled dynamics. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The unmodeled dynamics are bounded-input bounded-output stable. By adopting an estimation/cancellation strategy, a piecewise constant adaptive law drives the estimation error to zero at every time instant, which yields the adaptive parameters; a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, while a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. A feedforward control law is designed to track a given command. Since the virtual reference system defines the best performance that can be achieved by the closed-loop system, the uniform performance bounds are derived for the states and control signals via comparison. Both numerical and practical examples are provided to illustrate the effectiveness of the proposed filtering adaptive output feedback control architecture, comparisons with the model reference adaptive control demonstrates the superiority of the proposed control method.
filtering adaptive control, mismatched uncertainit↗
On LPMHSS-based iteration methods for a class of weakly nonlinear systems
In this paper, for a class of the large sparse system of weakly nonlinear equations, combining separable property of the linear and nonlinear terms with the lopsided Hermitian and skew-Hermitian splitting (LHSS) of the coefficient matrix, the Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are presented. Theoretical analysis shows that these methods are locally convergent under suitable conditions. Numerical results show that both Picard-LPMHSS and nonlinear LPMHSS-like iteration methods are feasible and effective for the large-scale system of weakly nonlinear equations.
97 MATHEMATICS AND COMPUTING↗
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↗
The Influence of Switching between Chaotic Regimes on the Correlation Characteristics of Nonlinear Systems
The problem of dynamic regime diagnostics in nonlinear systems using their experimental time series is studied in the presence of switching between various oscillatory processes. Interpretation of such data can be affected by errors in the calculated correlation characteristics caused by the presence of fragments corresponding to different dynamic regimes. It is shown that the switching between various regimes more significantly influences the diagnostics of anticorrelated dynamics.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Investigating Shaker-System Stability for Strong and Weak Nonlinear Systems.
Abstract not provided.
Robbins, Eric↗
RBFNN-based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems
This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using RBF neural network while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be included as 1) an output entropy model is presented using neural network; 2) a nonlinear filter design algorithm is developed as the main result and 3) a solution of entropy assignment problem is obtained which is an extension of the presented framework.
42 ENGINEERING↗
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↗
Response of MDOF strongly nonlinear systems to fractional Gaussian noises
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Probability Density Function Control for Stochastic Nonlinear Systems using Monte Carlo Simulation
This paper presents a fast implementation framework of output probability density function (PDF) control for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. The statistical properties of the system outputs can be adjusted by shaping the dynamic output probability density function to track the reference stochastic distribution. However, the dynamic probability density function evolution is very difficult to obtain analytically even if the system model and the stochastic distributions of the noises are known. Motivated by Monte Carlo simulation, the dynamic probability density function can be estimated by sampling data which forms the contribution of this paper. In particular, the sampling points are generated following the stochastic distribution of the noise for each instant. These points go through the system would generate the histogram for system outputs, then the dynamic model can be established based on the dynamic histogram which reflects the randomness and the nonlinear dynamics of the investigated system. Based on the established model, the output probability density function tracking can be achieved and the simulation results and discussions show the effectiveness and benefits of the presented framework.
Zhang, Qichun↗