scholarly journals Neural-Network-Based Discrete-Time Fuzzy Control of Continuous-Time Nonlinear Systems with Dither

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Zhi-Ren Tsai ◽  
Jiing-Dong Hwang
Keyword(s):  
Neural Network ◽  
Nonlinear System ◽  
Discrete Time ◽  
Continuous Time ◽  
Fuzzy Controller ◽  
Sampling Frequency ◽  
Space Representation ◽  
Linear Matrix ◽  
State Space Representation ◽  
Ct System

This study presents an effective approach to stabilizing a continuous-time (CT) nonlinear system using dithers and a discrete-time (DT) fuzzy controller. A CT nonlinear system is first discretized to a DT nonlinear system. Then, a Neural-Network (NN) system is established to approximate a DT nonlinear system. Next, a Linear Difference Inclusion state-space representation is established for the dynamics of the NN system. Subsequently, a Takagi-Sugeno DT fuzzy controller is designed to stabilize this NN system. If the DT fuzzy controller cannot stabilize the NN system, a dither, as an auxiliary of the controller, is simultaneously introduced to stabilize the closed-loop CT nonlinear system by using the Simplex optimization and the linear matrix inequality method. This dither can be injected into the original CT nonlinear system by the proposed injecting procedure, and this NN system is established to approximate this dithered system. When the discretized frequency or sampling frequency of the CT system is sufficiently high, the DT system can maintain the dynamic of the CT system. We can design the sampling frequency, so the trajectory of the DT system and the relaxed CT system can be made as close as desired.

Robust state derivative feedback LMI-based designs for discretized systems.

2020 ◽  
Author(s):  
Marco A. C. Leandro ◽  
Renan L. Pereira ◽  
Karl H. Kienitz
Keyword(s):  
Discrete Time ◽  
Cartesian Product ◽  
Stable Region ◽  
Space Representation ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Time Model ◽  
State Space Representation ◽  
Augmented System ◽  
Discretized Systems

This work addresses novel Linear Matrix Inequality (LMI)-based conditions for thedesign of discrete-time state derivative feedback controllers. The main contribution of this work consists of an augmented discretized model formulated in terms of the state derivative, such that uncertain sampling periods and parametric uncertainties in polytopic form can be propagated from the original continuous-time state space representation. The resulting discrete-time model is composed of homogeneous polynomial matrices with parameters lying in the Cartesian product of simplexes, plus an additive norm-bounded term representing the residual discretization error. Moreover, the referred condition allows for the closed-loop poles allocation of the augmented system in a D-stable region. Finally, numerical simulations illustrate the effectiveness of the proposed method.

LMI-based Multiobjective Integral Sliding Mode Control for Rotary Inverted Pendulum System Under Load Variations

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Fairus, M. A. ◽  
Mohamed, Z. ◽  
Ahmad, M. N. ◽  
Loi, W. S.
Keyword(s):  
Nonlinear System ◽  
Inverted Pendulum ◽  
Sliding Mode ◽  
Space Representation ◽  
Linear Matrix ◽  
Pendulum System ◽  
Integral Sliding Mode ◽  
State Space Representation ◽  
Inverted Pendulum System ◽  
Rotary Inverted Pendulum

This paper presents a multiobjective integral sliding mode controller (ISMC) for a rotary inverted pendulum system under the influence of varying load. Firstly, the nonlinear system is approximated to facilitate the desired control design via extended linearization and deterministic approach. By using both of these techniques, the nonlinear system is formulated into a nonlinear state-space representation where the uncertainties are retained in the model. Next, the design objectives are formulated into linear matrix inequalities (LMI) which are then solved efficiently through convex optimization algorithms. With proper selection variables, numbers of the decision variables for LMIs are reduced. Hence, it will reduce the numerical burden and believes the calculated values more viable in practice. Finally, simulation works are conducted and comparison is made between the proposed controller, such as normal ISMC and LQR. The simulation results illustrate the effectiveness of the proposed controller and the performance is evaluated through integral of absolute-value error (IAE) performance index. 

scholarly journals USE OF NEURAL NETWORKS TO MAKE COMPLEX DECISIONS TO OPERATE ELECTRIC TRANSPORT UNDER UNCERTAINTY

2020 ◽  
Vol 6 (159) ◽  
pp. 173-175
Author(s):  
D. Zubenko ◽  
S. Zakurdai ◽  
O. Donets
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Discrete Time ◽  
Continuous Time ◽  
Fuzzy Controller ◽  
Dynamic Error ◽  
Dead Zone ◽  
Stability And Convergence ◽  
Electric Transport ◽  
State Variables

The use of neural networks to solve the problems of insolubility and the solution of complex computational equations becomes a common practice in academic circles and industry. It has been shown that, despite the complexity, these problems can be formulated as a set of equations, and the key is to find zeros from them. Zero Neural Networks (ZNNs), as a class of neural networks specially designed to find zeros of equations, have played an indispensable role in online decision-changing problems over time in recent years, and many fruitful research results have been documented in literature. The purpose of this article is to provide a comprehensive overview of ZNN studies, including ZNN continuous time and discrete time models for solving various problems, and their application in motion planning and superfluous manipulator management, chaotic system tracking, or even population control in mathematical biological sciences. Considering the fact that real-time performance is in demand for time-varying problems in practice, analysis of the stability and convergence of various ZNN models with continuous time is considered in a unified form in detail. In the case of solving the problems of discrete time, procedures are summarized for how to discriminate a continuous ZNN model and methods for obtaining an accuracy decision. Approaches based on the neural network to address various nodal tasks have attracted considerable attention in many areas. For example, an adaptive fuzzy controller based on a neural network is constructed for a class of nonlinear systems with discrete time with a dead zone with discrete time in. An applied decentralized circuit, based on a neural network, is presented for multiple nonlinear input and multiple output systems (MIMO) using the methods of the reverse step in. Such a scheme guarantees a uniform limiting limit of all signals in a closed system relative to the average square. In order to overcome the structural complexity of the nonlinear feedback structure, uses the method of dividing variables for the decomposition of unknown functions of all state variables into the sum of smooth functions of each dynamic error.

scholarly journals Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Feng-Hsiag Hsiao
Keyword(s):  
Neural Network ◽  
State Space ◽  
Direct Method ◽  
Exponential Synchronization ◽  
Disturbance Attenuation ◽  
Space Representation ◽  
Linear Matrix ◽  
Multiple Time ◽  
State Space Representation ◽  
Delay Dependent

A novel approach is presented to realize the optimal exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems via fuzzy control scheme. A neural-network (NN) model is first constructed for the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov's direct method is proposed to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). According to the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal performance by minimizing the disturbance attenuation level at the same time. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

scholarly journals Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

2009 ◽  
Vol 43 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Sannay Mohamad ◽  
Haydar Akça ◽  
Valéry Covachev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Continuous Time ◽  
Global Exponential Stability ◽  
Exponential Convergence ◽  
Unique Equilibrium ◽  
Transmission Delays

Abstract A discrete-time analogue is formulated for an impulsive Cohen- -Grossberg neural network with transmission delay in a manner in which the global exponential stability characterisitics of a unique equilibrium point of the network are preserved. The formulation is based on extending the existing semidiscretization method that has been implemented for computer simulations of neural networks with linear stabilizing feedback terms. The exponential convergence in the p-norm of the analogue towards the unique equilibrium point is analysed by exploiting an appropriate Lyapunov sequence and properties of an M-matrix. The main result yields a Lyapunov exponent that involves the magnitude and frequency of the impulses. One can use the result for deriving the exponential stability of non-impulsive discrete-time neural networks, and also for simulating the exponential stability of impulsive and non-impulsive continuous-time networks.

scholarly journals Design of a Discrete Tracking Controller for a Magnetic Levitation System: A Nonlinear Rational Model Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Fernando Gómez-Salas ◽  
Yongji Wang ◽  
Quanmin Zhu
Keyword(s):  
Discrete Time ◽  
Magnetic Levitation ◽  
Approximate Model ◽  
Space Representation ◽  
State Space Representation ◽  
Classical State ◽  
System A ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Model Approach

This work proposes a discrete-time nonlinear rational approximate model for the unstable magnetic levitation system. Based on this model and as an application of the input-output linearization technique, a discrete-time tracking control design will be derived using the corresponding classical state space representation of the model. A simulation example illustrates the efficiency of the proposed methodology.

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