Neuro – Fuzzy Control Schemes Based on High Order Neural Network Function Approximators

2010 ◽  
pp. 450-483 ◽  
Author(s):  
Dimitris C. Theodoridis ◽  
M. A. Christodoulou ◽  
Yiannis S. Boutalis
Keyword(s):  
Nonlinear Dynamical Systems ◽  
High Order ◽  
Nonlinear Dynamical ◽  
Network Function ◽  
Neuro Fuzzy ◽  
Control Scheme ◽  
Fuzzy Dynamical System ◽  
Novel Method ◽  
Square Systems ◽  
System States

The indirect or direct adaptive regulation of unknown nonlinear dynamical systems is considered in this chapter. Since the plant is considered unknown, we first propose its approximation by a special form of a fuzzy dynamical system (FDS) and in the sequel the fuzzy rules are approximated by appropriate high order neural networks (HONN’s). The system is regulated to zero adaptively by providing weight updating laws for the involved HONN’s, which guarantee that both the identification error and the system states reach zero exponentially fast. At the same time, all signals in the closed loop are kept bounded. The existence of the control signal is always assured by introducing a novel method of parameter hopping, which is incorporated in the weight updating laws. The indirect control scheme is developed for square systems (number of inputs equal to the number of states) as well as for systems in Brunovsky canonical form. The direct control scheme is developed for systems in square form. Simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given.

INDIRECT ADAPTIVE CONTROL OF UNKNOWN MULTI VARIABLE NONLINEAR SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTIES USING A NEW NEURO-FUZZY SYSTEM DESCRIPTION

2010 ◽  
Vol 20 (02) ◽  
pp. 129-148 ◽  
Author(s):  
DIMITRIOS THEODORIDIS ◽  
YIANNIS BOUTALIS ◽  
MANOLIS CHRISTODOULOU
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
High Order ◽  
Control Signal ◽  
Parameter Uncertainties ◽  
Fuzzy Partitioning ◽  
Neuro Fuzzy ◽  
Square Systems ◽  
System States ◽  
Dynamic Uncertainties

The indirect adaptive regulation of unknown nonlinear dynamical systems with multiple inputs and states (MIMS) under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new neuro-fuzzy dynamical systems description, which uses the fuzzy partitioning of an underlying fuzzy systems outputs and high order neural networks (HONN's) associated with the centers of these partitions. Every high order neural network approximates a group of fuzzy rules associated with each center. The indirect regulation is achieved by first identifying the system around the current operation point, and then using its parameters to device the control law. Weight updating laws for the involved HONN's are provided, which guarantee that, under the presence of both parameter and dynamic uncertainties, both the identification error and the system states reach zero, while keeping all signals in the closed loop bounded. The control signal is constructed to be valid for both square and non square systems by using a pseudoinverse, in Moore-Penrose sense. The existence of the control signal is always assured by employing a novel method of parameter hopping instead of the conventional projection method. The applicability is tested on well known benchmarks.

A NEW DIRECT ADAPTIVE REGULATOR WITH ROBUSTNESS ANALYSIS OF SYSTEMS IN BRUNOVSKY FORM

2010 ◽  
Vol 20 (04) ◽  
pp. 319-339 ◽  
Author(s):  
DIMITRIOS THEODORIDIS ◽  
YIANNIS BOUTALIS ◽  
MANOLIS CHRISTODOULOU
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Robustness Analysis ◽  
Modeling Error ◽  
Nonlinear Dynamical ◽  
Neuro Fuzzy ◽  
Fuzzy Dynamical System ◽  
Error Terms ◽  
System States ◽  
The Stability ◽  
Adaptive Regulator

The direct adaptive regulation of unknown nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. Since the plant is considered unknown, we propose its approximation by a special form of a Brunovsky type neuro–fuzzy dynamical system (NFDS) assuming also the existence of disturbance expressed as modeling error terms depending on both input and system states plus a not-necessarily-known constant value. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. The existence and boundness of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating laws. Simulations illustrate the potency of the method and its applicability is tested on well known benchmarks, as well as in a bioreactor application. It is shown that the proposed approach is superior to the case of simple recurrent high order neural networks (HONN's).

Identification of Nonlinear Systems Using a New Neuro-Fuzzy Dynamical System Definition Based on High Order Neural Network Function Approximators

2010 ◽  
pp. 423-449 ◽  
Author(s):  
Yiannis S. Boutalis ◽  
M. A. Christodoulou ◽  
Dimitris C. Theodoridis
Keyword(s):  
Neural Network ◽  
Fuzzy Systems ◽  
Nonlinear Dynamical Systems ◽  
High Order ◽  
Nonlinear Dynamical ◽  
Adaptive Fuzzy ◽  
Network Function ◽  
Fuzzy Dynamical System ◽  
Definition Of ◽  
High Order Neural Network

A new definition of adaptive dynamic fuzzy systems (ADFS) is presented in this chapter for the identification of unknown nonlinear dynamical systems. The proposed scheme uses the concept of adaptive fuzzy systems operating in conjunction with high order neural networks (HONN’s). Since the plant is considered unknown, we first propose its approximation by a special form of an adaptive fuzzy system and in the sequel the fuzzy rules are approximated by appropriate HONN’s. Thus the identification scheme leads up to a recurrent high order neural network, which however takes into account the fuzzy output partitions of the initial ADFS. Weight updating laws for the involved HONN’s are provided, which guarantee that the identification error reaches zero exponentially fast. Simulations illustrate the potency of the method and comparisons on well known benchmarks are given.

A New Method for Equilibria and Stability Analysis of Nonlinear Dynamical Systems

2014 ◽  
Vol 534 ◽  
pp. 131-136
Author(s):  
Long Cao ◽  
Yi Hua Cao
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
Vehicle Model ◽  
Nonlinear Dynamical ◽  
Novel Method ◽  
Linearized System ◽  
Continuation Algorithm

A novel method based on numerical continuation algorithm for equilibria and stability analysis of nonlinear dynamical system is introduced and applied to an aircraft vehicle model. Dynamical systems are usually modeled with differential equations, while their equilibria and stability analysis are pure algebraic problems. The newly-proposed method in this paper provides a way to solve the equilibrium equation and the eigenvalues of the locally linearized system simultaneously, which avoids QR iterations and can save much time.

PREDICTIVE CONTROL OF NONLINEAR SYSTEMS BASED ON IDENTIFICATION BY BACKPROPAGATION NETWORKS

1994 ◽  
Vol 05 (04) ◽  
pp. 335-344 ◽  
Author(s):  
JIANBIN HAO ◽  
JOOS VANDEWALLE ◽  
SHAOHUA TAN
Keyword(s):  
Nonlinear Systems ◽  
Predictive Control ◽  
Neural Control ◽  
Nonlinear Dynamical Systems ◽  
Universal Approximation ◽  
Backpropagation Algorithm ◽  
Nonlinear Dynamical ◽  
Control Scheme ◽  
One Step ◽  
Simulation Results

Using the property of universal approximation of multilayer perceptron neural network, a class of discrete nonlinear dynamical systems are modeled by a perceptron with two hidden layers. A backpropagation algorithm is then used to train the model to identify the nonlinear systems to a desired level of accuracy. Based on the identified model, a one-step-ahead predictive control scheme is proposed in which the future control inputs are obtained through some nonlinear optimization process. Making use of the online learning properties of neural networks, the predictive control scheme is further developed into an adaptive one which is robust to the incompleteness of identification. Simulation results show that this neural control scheme works well even for some very complicated nonlinear systems.

Design of GA-Based Control for Electrical Servo Drive

2011 ◽  
Vol 201-203 ◽  
pp. 2375-2378
Author(s):  
Kuo Ho Su ◽  
Feng Hsiang Hsiao
Keyword(s):  
Genetic Algorithm ◽  
Gradient Descent ◽  
Nonlinear Dynamical System ◽  
Servo Drive ◽  
Control Effort ◽  
Nonlinear Dynamical ◽  
Supervisory Controller ◽  
Control Scheme ◽  
Control Schemes ◽  
System States

An alternative control scheme including a directional genetic algorithm controller (DGAC) and a supervisory controller is developed to control the position of an electrical servo drive in this study. In the DGAC design, the spirit of gradient descent training is embedded in genetic algorithm (GA) to construct a main controller to search optimum control effort under possible occurrence of uncertainties. In order to ensure the system states around a defined bound region, a supervisory controller, which is derived in the sense of Lyapunov stability theorem, is added to adjust the control effort. Compared with enunciated GA control methods, the proposed control scheme possesses some salient advantages of simple framework, fewer executing time and good self-organizing properties even for nonlinear dynamical system. The effectiveness is demonstrated by simulation results, and its advantages are indicated in comparison with other GA control schemes for a field-oriented control induction motor drive.

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