NEURAL ADAPTIVE CONTROL OF NONLINEAR MULTIVARIABLE SYSTEMS WITH APPLICATION TO A CLASS OF INVERTED PENDULUMS

2002 ◽  
Vol 12 (05) ◽  
pp. 411-424
Author(s):  
SHOULING HE
Keyword(s):  
Neural Networks ◽  
Control System ◽  
Control Algorithm ◽  
Learning Algorithm ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Base Point ◽  
Upper Body ◽  
Model Parameters ◽  
State Variables

In this paper multilayer neural networks (MNNs) are used to control the balancing of a class of inverted pendulums. Unlike normal inverted pendulums, the pendulum discussed here has two degrees of rotational freedom and the base-point moves randomly in three-dimensional space. The goal is to apply control torques to keep the pendulum in a prescribed position in spite of the random movement at the base-point. Since the inclusion of the base-point motion leads to a non-autonomous dynamic system with time-varying parametric excitation, the design of the control system is a challenging task. A feedback control algorithm is proposed that utilizes a set of neural networks to compensate for the effect of the system's nonlinearities. The weight parameters of neural networks updated on-line, according to a learning algorithm that guarantees the Lyapunov stability of the control system. Furthermore, since the base-point movement is considered unmeasurable, a neural inverse model is employed to estimate it from only measured state variables. The estimate is then utilized within the main control algorithm to produce compensating control signals. The examination of the proposed control system, through simulations, demonstrates the promise of the methodology and exhibits positive aspects, which cannot be achieved by the previously developed techniques on the same problem. These aspects include fast, yet well-maintained damped responses with reasonable control torques and no requirement for knowledge of the model or the model parameters. The work presented here can benefit practical problems such as the study of stable locomotion of human upper body and bipedal robots.

Quaternionic Neural Networks

2009 ◽  
pp. 411-439 ◽  
Author(s):  
Teijiro Isokawa ◽  
Nobuyuki Matsui ◽  
Haruhiko Nishimura
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Network Models ◽  
Recurrent Network ◽  
Affine Transformations ◽  
Neural Network Models ◽  
Fundamental Properties ◽  
Modern Physics ◽  
The Stability

Quaternions are a class of hypercomplex number systems, a four-dimensional extension of imaginary numbers, which are extensively used in various fields such as modern physics and computer graphics. Although the number of applications of neural networks employing quaternions is comparatively less than that of complex-valued neural networks, it has been increasing recently. In this chapter, the authors describe two types of quaternionic neural network models. One type is a multilayer perceptron based on 3D geometrical affine transformations by quaternions. The operations that can be performed in this network are translation, dilatation, and spatial rotation in three-dimensional space. Several examples are provided in order to demonstrate the utility of this network. The other type is a Hopfield-type recurrent network whose parameters are directly encoded into quaternions. The stability of this network is demonstrated by proving that the energy decreases monotonically with respect to the change in neuron states. The fundamental properties of this network are presented through the network with three neurons.

scholarly journals A Fractional-Order Discrete Noninvertible Map of Cubic Type: Dynamics, Control, and Synchronization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang ◽  
Dafeng Tang
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
State Variables ◽  
Discrete Maps ◽  
The Stability ◽  
Control And Synchronization ◽  
Simultaneous Variation

In this paper, a new fractional-order discrete noninvertible map of cubic type is presented. Firstly, the stability of the equilibrium points for the map is examined. Secondly, the dynamics of the map with two different initial conditions is studied by numerical simulation when a parameter or a derivative order is varied. A series of attractors are displayed in various forms of periodic and chaotic ones. Furthermore, bifurcations with the simultaneous variation of both a parameter and the order are also analyzed in the three-dimensional space. Interior crises are found in the map as a parameter or an order varies. Thirdly, based on the stability theory of fractional-order discrete maps, a stabilization controller is proposed to control the chaos of the map and the asymptotic convergence of the state variables is determined. Finally, the synchronization between the proposed map and a fractional-order discrete Loren map is investigated. Numerical simulations are used to verify the effectiveness of the designed synchronization controllers.

Neural Networks Based Attitude Decoupling Control for AUV with X-Shaped Fins

2013 ◽  
Vol 819 ◽  
pp. 222-228 ◽  
Author(s):  
Xiu Jun Sun ◽  
Jian Shi ◽  
Yan Yang
Keyword(s):  
Neural Networks ◽  
Attitude Control ◽  
Autonomous Underwater Vehicle ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mathematic Model ◽  
On Line ◽  
The Neural Networks ◽  
Vehicle Motion ◽  
Three Dimensional Space

Attitude control in three-dimensional space for AUV (autonomous underwater vehicle) with x-shaped fins is complicated but advantageous. Yaw, pitch and roll angles of the vehicle are all associated with deflection angle of each fin while navigating underwater. In this paper, a spatial motion mathematic model of the vehicle is built by using theorem of momentum and angular momentum, and the hydrodynamic forces acting on x-shaped fins and three-blade propeller are investigated to clarify complex principle of the vehicle motion. In addition, the nonlinear dynamics equation which indicates the coupling relationship between attitude angles of vehicle and rotation angles of x-shaped fins is derived by detailed deduction. Moreover, a decoupling controller based on artificial neural networks is developed to address the coupling issue exposed in attitude control. The neural networks based controller periodically calculates and outputs deflection angles of fins according to the attitude angles measured with magnetic compass, thus the vehicles orientation can be maintained. By on-line training, twenty four weights in this controller converged according to index function.

Active Noise Control Using Multi-Layered Perceptron Neural Networks

1997 ◽  
Vol 16 (2) ◽  
pp. 109-144 ◽  
Author(s):  
M.O. Tokhi ◽  
R. Wood
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Noise Control ◽  
Learning Algorithm ◽  
Free Field ◽  
Active Noise Control ◽  
Three Dimensional ◽  
Broadband Noise ◽  
Active Noise

This paper presents the development of a neuro-adaptive active noise control (ANC) system. Multi-layered perceptron neural networks with a backpropagation learning algorithm are considered in both the modelling and control contexts. The capabilities of the neural network in modelling dynamical systems are investigated. A feedforward ANC structure is considered for optimum cancellation of broadband noise in a three-dimensional propagation medium. An on-line adaptation and training mechanism allowing a neural network architecture to characterise the optimal controller within the ANC system is developed. The neuro-adaptive ANC algorithm thus developed is implemented within a free-field environment and simulation results verifying its performance are presented and discussed.

Multirate Constrained Predictive Control: Algorithm and Experimental Results

2007 ◽  
Vol 2 (3) ◽  
Author(s):  
Qiuping Hu ◽  
Sohrab Rohani
Keyword(s):  
Control System ◽  
Predictive Control ◽  
Control Algorithm ◽  
Design Method ◽  
Pi Control ◽  
State Variables ◽  
Challenging Problem ◽  
State Estimator ◽  
Performance Specifications ◽  
Tank System

Control of multirate systems is a challenging problem due to several reasons such as increased complexity in the design with tighter performance specifications. In this work, an algorithm for multirate constrained predictive control (MCPC) is presented. The multirate predictive control system includes a multirate state estimator, which provides inter-sample estimates of state variables of the process from infrequent and slow measurements. Constraints are addressed rigorously in this framework. The proposed design method is verified via simulation as well as experimentation. The results of the multirate predictive control for temperature control of a stirred tank system are shown and compared with those of a proportional integral (PI) control system.

Parameter Estimation of Nonlinear Biomedical Systems Using Extended Kalman Filter Algorithm

2017 ◽  
pp. 76-99 ◽  
Author(s):  
Kamalanand Krishnamurthy
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Computational Models ◽  
Three Dimensional ◽  
Model Parameters ◽  
State Variables ◽  
Three Dimensional Model ◽  
Biomedical Systems ◽  
Estimation Of Model Parameters

Parameter estimation is a central issue in mathematical modelling of biomedical systems and for the development of patient specific models. The technique of estimating parameters helps in obtaining diagnostic information from computational models of biological systems. However, in most of the biomedical systems, the estimation of model parameters is a challenging task due to the nonlinearity of mathematical models. In this chapter, the method of estimation of nonlinear model parameters from measurements of state variables, using the extended Kalman filter, is extensively explained using an example of the three-dimensional model of the HIV/AIDS system.

scholarly journals Neural Nonlinear Autoregressive Model with Exogenous Input (NARX) for Turboshaft Aeroengine Fuel Control Unit Model

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 206
Author(s):  
Maria Grazia De Giorgi ◽  
Luciano Strafella ◽  
Antonio Ficarella
Keyword(s):  
Neural Networks ◽  
Control System ◽  
Fuel Consumption ◽  
Control Method ◽  
Engine Performance ◽  
Control Unit ◽  
Specific Fuel Consumption ◽  
Engine Fuel ◽  
State Variables ◽  
Nonlinear Autoregressive

One of the most important parts of a turboshaft engine, which has a direct impact on the performance of the engine and, as a result, on the performance of the propulsion system, is the engine fuel control system. The traditional engine control system is a sensor-based control method, which uses measurable parameters to control engine performance. In this context, engine component degradation leads to a change in the relationship between the measurable parameters and the engine performance parameters, and thus an increase of control errors. In this work, a nonlinear model predictive control method for turboshaft direct fuel control is implemented to improve engine response ability also in presence of degraded conditions. The control objective of the proposed model is the prediction of the specific fuel consumption directly instead of the measurable parameters. In this way is possible decentralize controller functions and realize an intelligent engine with the development of a distributed control system. Artificial Neural Networks (ANN) are widely used as data-driven models for modelling of complex systems such as aeroengine performance. In this paper, two Nonlinear Autoregressive Neural Networks have been trained to predict the specific fuel consumption for several transient flight maneuvers. The data used for the ANN predictions have been estimated through the Gas Turbine Simulation Program. In particular the first ANN predicts the state variables based on flight conditions and the second one predicts the performance parameter based on the previous predicted variables. The results show a good approximation of the studied variables also in degraded conditions.

scholarly journals Supervised neural networks learning algorithm for three dimensional hybrid nanofluid flow with radiative heat and mass fluxes

2021 ◽  
Author(s):  
Muhammad Asif Zahoor Raja ◽  
Muhammad Shoaib ◽  
Zeeshan Khan ◽  
Samina Zuhra ◽  
C. Ahamed Saleel ◽  
...  
Keyword(s):  
Neural Networks ◽  
Radiative Heat ◽  
Learning Algorithm ◽  
Three Dimensional ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Mass Fluxes
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