Nonlinear H2/H-Infinity Constrained Feedback Control: A Practical Design Approach Using Neural Networks (Google eBook)

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Springer Science & Business Media, Aug 2, 2006 - Technology & Engineering - 224 pages
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The authors present algorithms for H2 and H-infinity design for nonlinear systems which provide solution techniques which can be implemented in real systems; neural networks are used to solve the nonlinear control design equations. Constraints on the control actuator inputs are dealt with. Results are proven to give confidence and performance guarantees. The algorithms can be used to obtain practical controllers. Nearly optimal applications to constrained-state and mimimum-time problems are discussed as is discrete-time design for digital controllers. 'Nonlinear H2/H-infinity Constrained Feedback Control' is of importance to control designers working in a variety of industrial systems. Case studies are given and the design of nonlinear control systems of the same caliber as those obtained in recent years using linear optimal and bounded-norm designs is explained. The book will also be of interest to academics and graduate students in control systems as a complete foundation for H2 and H-infinity design.
  

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Contents

Preliminaries and Introduction
1
112 Discretetime Nonlinear Systems
2
12 Stability of Nonlinear Systems
3
121 Lyapunov Stabiltity of Continuoustime Nonlinear Systems
4
13 Dissipativity of Nonlinear Systems
8
131 Dissipativity of Continuoustime Nonlinear Systems
9
132 Dissipativity of Discretetime Nonlinear Systems
12
14 Optimal Control of Nonlinear Systems
14
36 Policy Iterations Without Solving the LEVu
75
37 Bibliographical Notes
76
Policy Iterations and Nonlinear H Constrained State Feedback Control
77
42 Policy Iterations and the Nonlinear Bounded Real Lemma
78
43 L2gain of Nonlinear Control Systems with Input Saturation
83
44 The HJI Equation and the Saddle Point
86
45 Solving the HJI Equation Using Policy Iterations
90
Nearly H Optimal Neural Network Control for ConstrainedInput Systems
95

142 Discretetime HJB Equation
17
15 Policy Iterations and Optimal Control
18
151 Policy Iterations and H2 Optimal Control
19
152 Policy Iterations and the Bounded Real Lemma
21
16 Zerosum Games of Nonlinear Systems
23
162 Linear Quadratic Zerosum Games and H0 Optimal Control
25
163 Discretetime HJI Equation
26
17 Neural Networks and Function Approximation
28
172 Function Approximation Theorems
30
18 Bibliographical Notes
31
Policy Iterations and Nonlinear H2 Constrained State Feedback Control
32
22 Optimal Regulation of Systems with Actuator Saturation
34
23 Policy Iterations for ConstrainedInput Systems
37
24 Nonquadratic Performance Functionals for Minimumtime and Constrained States Control
41
25 Bibliographical Notes
42
Nearly H2 Optimal Neural Network Control for ConstrainedInput Systems
43
32 Convergence of the Method of Least Squares to the Solution of the LEVu
45
33 Convergence of the Method of Least Squares to the Solution of the HJB Equation
52
Introducing a Mesh in Rn
54
35 Numerical Examples
56
352 Nonlinear Oscillator with Constrained Input
62
353 Constrained State Linear System
65
354 Minimumtime Control
68
355 Parabolic Tracker
71
51 Neural Network Representation of Policies
96
52 Stability and Convergence of Least Squares Neural Network Policy Iterations
100
The Nonlinear Benchmark Problem
104
54 Bibliographical Notes
113
Taylor Series Approach to Solving HJI Equation
115
62 Power Series Solution of HJI Equation
118
63 Explicit Expression for Hk
126
64 The Disturbance Attenuation of RTAC System
135
65 Bibliographical Notes
146
An Algorithm to Solve Discrete HJI Equations Arising from Discrete Nonlinear H Control Problems
147
72 Taylor Series Solution of Discrete HamiltonJacobiIsaacs Equation
151
73 Disturbance Attenuation of Discretized RTAC System
164
74 Computer Simulation
172
H Static Output Feedback
176
82 Intermediate Mathematical Analysis
178
83 Coupled HJ Equations for H Static Output Feedback Control
182
84 Existence of Static Output Feedback Game Theoretic Solution
185
85 Iterative Solution Algorithm
187
86 H Static Output Feedback Design for F16 Normal Acceleration Regulator
188
87 Bibliographical Notes
192
References
193
Index
201
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