Differential Neural Networks for Robust Nonlinear Control : Identification, State Estimation and Trajectory Tracking

by Poznyak, Alexander S.; Sanchez, Edgar N.; Yu, Wen

• ISBN13: 9789810246242
• ISBN10: 9810246242
• Format: Hardcover
• Copyright: 2001-10-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Deals with continuous time dynamic neural networks theory applied to the solution of basic problems in robust control theory, including identification, state space estimation and trajectory tracking.

Table of Contents

Abstract	vi
Preface	vii
Acknowledgments	ix
Introduction	xxiii
Guide for the Readers	xxiv
Notations	xxix
I Theoretical Study	1	(254)
Neural Networks Structures	3	(56)
Introduction	3	(1)
Biological Neural Networks	4	(6)
Neuron Model	10	(2)
Neural Networks Structures	12	(25)
Single-Layer Feedforward Networks	13	(4)
Multilayer Feedforward Neural Networks	17	(4)
Radial Basis Function Neural Networks	21	(7)
Recurrent Neural Networks	28	(3)
Differential Neural Networks	31	(6)
Neural Networks in Control	37	(12)
Identification	38	(5)
Control	43	(6)
Conclusions	49	(1)
References	50	(9)
Nonlinear System Identification: Differential Learning	59	(46)
Introduction	59	(3)
Identification Error Stability Analysis for Simplest Differential Neural Networks without Hidden Layers	62	(14)
Nonlinear System and Differential Neural Network Model	62	(2)
Exact Neural Network Matching with Known Linear Part	64	(5)
Non-exact Neural Networks Modelling: Bounded Unmodelled Dynamics Case	69	(4)
Estimation of Maximum Value of Identification Error for Nonlinear Systems with Bounded Unmodelled Dynamics	73	(3)
Multilayer Differential Neural Networks for Nonlinear System On-line Identification	76	(14)
Multilayer Structure of Differential Neural Networks	76	(2)
Complete Model Matching Case	78	(5)
Unmodelled Dynamics Presence	83	(7)
Illustrating Examples	90	(8)
Conclusion	98	(2)
References	100	(5)
Sliding Mode Identification: Algebraic Learning	105	(22)
Introduction	105	(2)
Sliding Mode Technique: Basic Principles	107	(6)
Sliding Model Learning	113	(4)
Simulations	117	(6)
Conclusion	123	(1)
References	123	(4)
Neural State Estimation	127	(62)
Nonlinear Systems and Nonlinear Observers	127	(7)
The Nonlinear State Observation Problem	127	(2)
Observers for Autonomous Nonlinear System with Complete Information	129	(3)
Observers for Controlled Nonlinear Systems	132	(2)
Robust Nonlinear Observer	134	(14)
System Description	134	(3)
Nonlinear Observers and The Problem Setting	137	(2)
The Main Result on The Robust Observer	139	(9)
The Neuro-Observer for Unknown Nonlinear Systems	148	(23)
The Observer Structure and Uncertainties	148	(3)
The Signal Layer Neuro Observer without A Delay Term	151	(8)
Multilayer Neuro Observer with Time-Delay Term	159	(12)
Application	171	(12)
Concluding Remarks	183	(2)
References	185	(4)
Passivation via Neuro Control	189	(26)
Introduction	189	(3)
Partially Known Systems and Applied DNN	192	(4)
Passivation of Partially Known Nonlinear System via DNN	196	(9)
Structure of Storage Function	200	(1)
Thresholds Properties	200	(1)
Stabilizing Robust Linear Feedback Control	201	(1)
Situation with Complete Information	201	(1)
Two Coupled Subsystems Interpretation	201	(1)
Some Other Uncertainty Descriptions	202	(3)
Numerical Experiments	205	(5)
Single link manipulator	205	(1)
Benchmark problem of passivation	206	(4)
Conclusions	210	(1)
References	211	(4)
Neuro Trajectory Tracking	215	(40)
Tracking Using Dynamic Neural Networks	215	(9)
Trajectory Tracking Based Neuro Observer	224	(21)
Dynamic Neuro Observer	227	(1)
Basic Properties of DNN-Observer	228	(3)
Learning Algorithm and Neuro Observer Analysis	231	(3)
Error Stability Proof	234	(8)
Tracking Error Analysis	242	(3)
Simulation Results	245	(6)
Conclusions	251	(1)
References	251	(4)
II Neurocontrol Applications	255	(164)
Neural Control for Chaos	257	(22)
Introduction	257	(2)
Lorenz System	259	(10)
Duffing Equation	269	(3)
Chua's Circuit	272	(3)
Conclusion	275	(1)
References	276	(3)
Neuro Control for Robot Manipulators	279	(50)
Introduction	279	(3)
Manipulator Dynamics	282	(5)
Robot Joint Velocity Observer and RBF Compensator	287	(5)
PD Control with Velocity Estimation and Neuro Compensator	292	(13)
Simulation Results	305	(19)
Robot's Dynamic Identification based on Neural Network	306	(6)
Neuro Control for Robot	312	(5)
PD Control for robot	317	(7)
Conclusion	324	(1)
References	324	(5)
Identification of Chemical Processes	329	(22)
Nomenclature	329	(1)
Introduction	330	(4)
Process Modeling and Problem Formulation	334	(2)
Reactor Model and Measurable Variables	334	(2)
Organic Compounds Reactions with Ozone	336	(1)
Problem Setting	336	(1)
Observability Condition	336	(2)
Neuro Observer	338	(4)
Neuro Observer Structure	338	(1)
Basic Assumptions	339	(1)
Learning Law	339	(1)
Upper Bound for Estimation Error	340	(2)
Estimation of the Reaction Rate Constants	342	(1)
Simulation Results	343	(2)
Experiment 1 (standard reaction rates)	344	(1)
Experiment 2 (more quick reaction)	345	(1)
Conclusions	345	(2)
References	347	(4)
Neuro-Control for Distillation Column	351	(26)
Introduction	351	(4)
Modeling of A Multicomponent Distillation Column	355	(5)
A Local Optimal Controller for Distillation Column	360	(6)
Application to Multicomponent Nonideal Distillation Column	366	(7)
Conclusion	373	(1)
References	374	(3)
General Conclusions and future work	377	(4)
Appendix A: Some Useful Mathematical Facts	381	(10)
Basic Matrix Inequality	381	(1)
Barbalat's Lemma	381	(1)
Frequency Condition for Existence of Positive Solution to Matrix Algebraic Riccati Equation	382	(4)
Conditions for Existence of Positive Solution to Matrix Differential Riccati Equation	386	(2)
Lemmas on Finite Argument Variations	388	(2)
References	390	(1)
Appendix B: Elements of Qualitative Theory of ODE	391	(18)
Ordinary Differential Equations: Fundamental Properties	391	(3)
Autonomous and Controlled Systems	391	(1)
Existence of Solution for ODE with Continuous RHS	392	(1)
Existence of Solution for ODE with Discontinuous RHS	393	(1)
Boundness of Solutions	394	(3)
Boundness of Solutions ``On Average''	397	(1)
Stability ``in Small'', Globally, ``in Asymptotic'' and Exponential	398	(2)
Stability of a particular process	398	(1)
Different Types of Stability	399	(1)
Stability Domain	400	(1)
Sufficient Conditions	400	(4)
Basic Criteria of Stability	404	(3)
References	407	(2)
Appendix C: Locally Optimal Control and Optimization	409	(10)
Idea of Locally Optimal Control Arising in Discrete Time Controlled Systems	409	(2)
Analogue of Locally Optimal Control for Continuous Time Controlled Systems	411	(2)
Damping Strategies	413	(3)
Optimal control	414	(2)
Gradient Descent Technique	416	(2)
References	418	(1)
Index	419