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E-raamat: Discrete-Time Inverse Optimal Control for Nonlinear Systems

(Unidad Guadalajara, Mexico.),
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"This book presents a novel inverse optimal control approach for stabilization and trajectory tracking of discrete-time nonlinear systems, avoiding the need to solve the associated Hamilton-Jacobi-Bellman equation, and minimizing a cost functional, resulting in efficient controllers. Additionally, the book proposes the use of recurrent neural networks as a tool to model discrete-time nonlinear systems; such models combined with the inverse optimal control constitute a powerful tool to deal with uncertainties such as unmodeled dynamics and disturbances. Different simulations illustrate the effectiveness of the synthesized controllers for stabilization and trajectory tracking of discrete-time nonlinear systems"--



Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller.

Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems

The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). The synthesized discrete-time optimal controller can be directly implemented in real-time systems. The book also proposes the use of recurrent neural networks to model discrete-time nonlinear systems. Combined with the inverse optimal control approach, such models constitute a powerful tool to deal with uncertainties such as unmodeled dynamics and disturbances.

Learn from Simulations and an In-Depth Case Study

The authors include a variety of simulations to illustrate the effectiveness of the synthesized controllers for stabilization and trajectory tracking of discrete-time nonlinear systems. An in-depth case study applies the control schemes to glycemic control in patients with type 1 diabetes mellitus, to calculate the adequate insulin delivery rate required to prevent hyperglycemia and hypoglycemia levels.

The discrete-time optimal and robust control techniques proposed can be used in a range of industrial applications, from aerospace and energy to biomedical and electromechanical systems. Highlighting optimal and efficient control algorithms, this is a valuable resource for researchers, engineers, and students working in nonlinear system control.

List of Figures xiii
List of Tables xvii
Preface xix
Acknowledgments xxiii
Authors xxv
Notations and Acronyms xxvii
Chapter 1 Introduction 1(8)
1.1 Inverse Optimal Control via Passivity
3(1)
1.2 Inverse Optimal Control via CLF
4(2)
1.3 Neural Inverse Optimal Control
6(1)
1.4 Motivation
7(2)
Chapter 2 Mathematical Preliminaries 9(26)
2.1 Optimal Control
9(3)
2.2 Lyapunov Stability
12(3)
2.3 Robust Stability Analysis
15(6)
2.3.1 Optimal Control for Disturbed Systems
20(1)
2.4 Passivity
21(2)
2.5 Neural Identification
23(12)
2.5.1 Nonlinear Systems
24(1)
2.5.2 Discrete-Time Recurrent High Order Neural Network
24(5)
2.5.2.1 RHONN Models
27(1)
2.5.2.2 On-line Learning Law
28(1)
2.5.3 Discrete-Time Recurrent Multilayer Perceptron
29(6)
Chapter 3 Inverse Optimal Control: A Passivity Approach 35(32)
3.1 Inverse Optimal Control via Passivity
35(11)
3.1.1 Stabilization of a Nonlinear System
41(5)
3.2 Trajectory Tracking
46(12)
3.2.1 Example: Trajectory Tracking of a Nonlinear System
49(1)
3.2.2 Application to a Planar Robot
50(17)
3.2.2.1 Robot Model
51(3)
3.2.2.2 Robot as an Affine System
54(1)
3.2.2.3 Control Synthesis
55(1)
3.2.2.4 Simulation Results
56(2)
3.3 Passivity-Based Inverse Optimal Control for a Class of Nonlinear Positive Systems
58(7)
3.4 Conclusions
65(2)
Chapter 4 Inverse Optimal Control: A CLF Approach, Part I 67(42)
4.1 Inverse Optimal Control via CLF
67(14)
4.1.1 Example
75(4)
4.1.2 Inverse Optimal Control for Linear Systems
79(2)
4.2 Robust Inverse Optimal Control
81(11)
4.3 Trajectory Tracking Inverse Optimal Control
92(8)
4.3.1 Application to the Boost Converter
96(13)
4.3.1.1 Boost Converter Model
96(2)
4.3.1.2 Control Synthesis
98(1)
4.3.1.3 Simulation Results
99(1)
4.4 CLF-Based Inverse Optimal Control for a Class of Nonlinear Positive Systems
100(7)
4.5 Conclusions
107(2)
Chapter 5 Inverse Optimal Control: A CLF Approach, Part II 109(34)
5.1 Speed-Gradient Algorithm for the Inverse Optimal Control
109(19)
5.1.1 Speed-Gradient Algorithm
110(5)
5.1.2 Summary of the Proposed SG Algorithm to Calculate Parameter pk
115(2)
5.1.3 SG Inverse Optimal Control
117(5)
5.1.3.1 Example
121(1)
5.1.4 Application to the Inverted Pendulum on a Cart
122(6)
5.1.4.1 Simulation Results
126(2)
5.2 Speed-Gradient Algorithm for Trajectory Tracking
128(7)
5.2.1 Example
133(2)
5.3 Trajectory Tracking for Systems in Block-Control Form
135(7)
5.3.1 Example
140(2)
5.4 Conclusions
142(1)
Chapter 6 Neural Inverse Optimal Control 143(30)
6.1 Neural Inverse Optimal Control Scheme
144(16)
6.1.1 Stabilization
144(1)
6.1.2 Example
145(2)
6.1.2.1 Neural Network Identifier
146(1)
6.1.2.2 Control Synthesis
146(1)
6.1.3 Trajectory Tracking
147(3)
6.1.3.1 Example
149(1)
6.1.4 Application to a Synchronous Generator
150(8)
6.1.4.1 Synchronous Generator Model
152(2)
6.1.4.2 Neural Identification for the Synchronous Generator
154(2)
6.1.4.3 Control Synthesis
156(1)
6.1.4.4 Simulation Results
156(2)
6.1.5 Comparison
158(2)
6.2 Block-Control Form: A Nonlinear Systems Particular Class
160(10)
6.2.1 Block Transformation
161(3)
6.2.2 Block Inverse Optimal Control
164(1)
6.2.3 Application to a Planar Robot
164(13)
6.2.3.1 Robot Model Description
164(1)
6.2.3.2 Neural Network Identifier
165(1)
6.2.3.3 Control Synthesis
166(1)
6.2.3.4 Simulation Results
167(3)
6.3 Conclusions
170(3)
Chapter 7 Glycemic Control of Type 1 Diabetes Mellitus Patients 173(26)
7.1 Introduction
173(4)
7.2 Passivity Approach
177(13)
7.2.1 Virtual Patient
178(6)
7.2.2 State Space Representation
184(5)
7.2.3 Control Law Implementation
189(1)
7.3 CLF Approach
190(7)
7.3.1 Simulation Results via CLF
193(1)
7.3.2 Passivity versus CLF
194(3)
7.4 Conclusions
197(2)
Chapter 8 Conclusions 199(4)
References 203(18)
Index 221
Edgar N. Sanchez is a researcher at CINVESTAV-IPN, Guadalajara Campus, Mexico. He was granted a U.S. National Research Council Award as a research associate at NASA Langley Research Center (January 1985-March 1987). He is also a member of the Mexican National Research System (promoted to the highest rank, III, in 2005), the Mexican Academy of Science, and the Mexican Academy of Engineering. He has published more than 100 technical papers in international journals and conferences, and has served as reviewer for various international journals and conferences. His research interest centers on neural networks and fuzzy logic as applied to automatic control systems.

Fernando Ornelas-Tellez is currently a professor of electrical engineering at Michoacan University of Saint Nicholas of Hidalgo, Mexico. His research interests center on neural control, direct and inverse optimal control, passivity and their applications to biomedical systems, electrical machines, power electronics, and robotics.
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