Third-Order Continuous-Discrete Filtering for a Nonlinear Dynamical System

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Hiren G. Patel ◽  
Shambhu N. Sharma
Keyword(s):  
Numerical Solutions ◽  
Nonlinear Dynamical System ◽  
Planck Equation ◽  
Extended Kalman Filtering ◽  
Third Order ◽  
Nonlinear Dynamical ◽  
Stochastic Filtering ◽  
Systems And Control ◽  
Backward Equation ◽  
And Control

Approximate higher-order filters are more attractive and popular in control and signal processing literature in contrast to the exact filter, since the analytical and numerical solutions of the nonlinear exact filter are not possible. The filtering model of this paper involves stochastic differential equation (SDE) formalism in combination with a nonlinear discrete observation equation. The theory of this paper is developed by adopting a unified systematic approach involving celebrated results of stochastic calculus. The Kolmogorov–Fokker–Planck equation in combination with the Kolmogorov backward equation plays the pivotal role to construct the theory of this paper “between the observations.” The conditional characteristic function is exploited to develop “filtering” at the observation instant. Subsequently, the efficacy of the filtering method of this paper is examined on the basis of its comparison with extended Kalman filtering and true state trajectories. This paper will be of interest to applied mathematicians and research communities in systems and control looking for stochastic filtering methods in theoretical studies as well as their application to real physical systems.

scholarly journals Analysis of Large-Amplitude Pulses in Short Time Intervals: Application to Neuron Interactions

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Gianni Mattioli ◽  
Massimo Scalia ◽  
Carlo Cattani
Keyword(s):  
Dynamical System ◽  
Order Approximation ◽  
Nonlinear Dynamical System ◽  
High Amplitude ◽  
Time Dependent ◽  
Third Order ◽  
Time Intervals ◽  
Nonlinear Dynamical ◽  
Short Time ◽  
Third Order Approximation

This paper deals with the analysis of a nonlinear dynamical system which characterizes the axons interaction and is based on a generalization of FitzHugh-Nagumo system. The parametric domain of stability is investigated for both the linear and third-order approximation. A further generalization is studied in presence of high-amplitude (time-dependent) pulse. The corresponding numerical solution for some given values of parameters are analyzed through the wavelet coefficients, showing both the sensitivity to local jumps and some unexpected inertia of neuron's as response to the high-amplitude spike.

Chaos Behavior and Control of Stay-Cables

2012 ◽  
Vol 446-449 ◽  
pp. 1109-1114
Author(s):  
Jin Hai Li ◽  
Qing Li Yan ◽  
Jin Shuan Liu
Keyword(s):  
Dynamic Behavior ◽  
Chaotic Motion ◽  
Nonlinear Dynamical System ◽  
Melnikov Method ◽  
Periodic Excitation ◽  
Stay Cable ◽  
Nonlinear Dynamical ◽  
Infinite Dimensional ◽  
First Order ◽  
And Control

Stay-cable is infinite dimensional nonlinear dynamical system with a very complex vibration types and mechanism which are not described reasonably yet. In order to better control its dynamic behavior, it is necessary to study complex dynamic behavior carefully. Fistly, partial differential equation of the cable motion is established based on the parabolic initial configuration and is simplified into n Duffing-equations by using Galerkin method. Secondly, the chaos behaviors of the first order Duffing-equation under periodic excitation are studied by taking advantage of Melnikov method. At last , parameters may lead to chaotic motion of a true cable in laboratory are calculated and the methods of chaos control are discussed briefly. The study shows that: 1. First order vibration of cable under periodic excitation has much more complex behaviors than the freedom vibration; 2. The Melnikov method can be very effective and convenient for the analysis of chaotic motion of cable.

DIRECT ADAPTIVE TYPE-2 FUZZY CONTROL FOR NONLINEAR SYSTEMS

2006 ◽  
Vol 06 (03) ◽  
pp. 389-411 ◽  
Author(s):  
KHEIREDDINE CHAFAA ◽  
LAMIR SAIDI ◽  
MOUNA GHANAI ◽  
KHIER BENMAHAMMED
Keyword(s):  
Fuzzy Controller ◽  
Tracking Error ◽  
Nonlinear Dynamical System ◽  
Reference Trajectory ◽  
Oscillation System ◽  
Control Effort ◽  
Nonlinear Dynamical ◽  
Supervisory Controller ◽  
And Control

A new direct adaptive type-2 fuzzy controller for a nonlinear dynamical system is developed in this paper. The parameters of the membership functions characterizing the linguistic terms in the type-2 fuzzy IF–THEN rules change according to some adaptive law for the purpose of controlling a plant to track a reference trajectory. A supervisory controller is appended to the type-2 fuzzy controller to force the state to be within the constraint set. Stability of this adaptive scheme is established using Lyapunov stability tools, where we guarantee the global stability of the resulting closed-loop system, in the sense that all signals involved are uniformly bounded. The simulation results for a Duffing forced-oscillation system show better performances, i.e. tracking error and control effort can be made smaller.

scholarly journals Neural Networks-Based Identification and Control of a Large Flexible Antenna

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Minoru Sasaki ◽  
Takuya Murase ◽  
Yoshihiro Inoue ◽  
Nobuharu Ukita
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Nonlinear Dynamical System ◽  
Inverse Model ◽  
Nonlinear Dynamical ◽  
The Neural Network ◽  
Network Output ◽  
Flexible Antenna ◽  
Angle Encoder ◽  
And Control

This paper presents identification and control of a 10-m antenna via accelerometers and angle encoder data. Artificial neural networks can be used effectively for the identification and control of nonlinear dynamical system such as a large flexible antenna with a friction drive system. Some identification results are shown and compared with the results of conventional prediction error method. And we use a neural network inverse model to control the large flexible antenna. In the neural network inverse model, a neural network is trained, using supervised learning, to develop an inverse model of the antenna. The network input is the process output, and the network output is the corresponding process input. The control results show the validation of the ANN approach for identification and control of the 10-m flexible antenna.

scholarly journals Maximum Entropy Probability Density Principle in Probabilistic Investigations of Dynamic Systems

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 790
Author(s):  
Jiří Náprstek ◽  
Cyril Fischer
Keyword(s):  
Probability Density ◽  
Maximum Entropy ◽  
Gaussian White Noise ◽  
Nonlinear Dynamical System ◽  
Planck Equation ◽  
Continuous Systems ◽  
Nonlinear Dynamical ◽  
Polynomial Type ◽  
Mdof Systems ◽  
Density Principle

In this study, we consider a method for investigating the stochastic response of a nonlinear dynamical system affected by a random seismic process. We present the solution of the probability density of a single/multiple-degree of freedom (SDOF/MDOF) system with several statically stable equilibrium states and with possible jumps of the snap-through type. The system is a Hamiltonian system with weak damping excited by a system of non-stationary Gaussian white noise. The solution based on the Gibbs principle of the maximum entropy of probability could potentially be implemented in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker–Planck equation (FPE) for the system considered or from the system of ordinary differential equations for the stochastic moments of the response derived from the relevant FPE. In terms of the application type, this strategy is most suitable for SDOF/MDOF systems containing polynomial type nonlinearities. Thus, the solution links up with the customary formulation of the finite elements discretization for strongly nonlinear continuous systems.

scholarly journals Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Control

2019 ◽  
Author(s):  
Jeremy Morton ◽  
Freddie D. Witherden ◽  
Mykel J. Kochenderfer
Keyword(s):  
Nonlinear Dynamical System ◽  
Effective Control ◽  
Dynamics Modeling ◽  
Dynamical Models ◽  
Nonlinear Dynamical ◽  
Modeling And Control ◽  
Koopman Operator ◽  
Control Framework ◽  
And Control ◽  
Long Term Prediction

Koopman theory asserts that a nonlinear dynamical system can be mapped to a linear system, where the Koopman operator advances observations of the state forward in time. However, the observable functions that map states to observations are generally unknown. We introduce the Deep Variational Koopman (DVK) model, a method for inferring distributions over observations that can be propagated linearly in time. By sampling from the inferred distributions, we obtain a distribution over dynamical models, which in turn provides a distribution over possible outcomes as a modeled system advances in time. Experiments show that the DVK model is effective at long-term prediction for a variety of dynamical systems. Furthermore, we describe how to incorporate the learned models into a control framework, and demonstrate that accounting for the uncertainty present in the distribution over dynamical models enables more effective control.

Sign in / Sign up

Export Citation Format

Share Document