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Discrete-Time Inverse Optimal Control for Nonlinear Systems





ISBN 9781138073814
Published March 29, 2017 by CRC Press
268 Pages 10 Color & 70 B/W Illustrations

 
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Book Description

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.

Table of Contents

Introduction
Inverse Optimal Control via Passivity
Inverse Optimal Control via CLF
Neural Inverse Optimal Control
Motivation

Mathematical Preliminaries
Optimal Control
Lyapunov Stability
Robust Stability Analysis
Passivity
Neural Identification

Inverse Optimal Control: A Passivity Approach
Inverse Optimal Control via Passivity
Trajectory Tracking
Passivity-based Inverse Optimal Control for a Class of Nonlinear Positive Systems
Conclusions

Inverse Optimal Control: A CLF Approach, Part I
Inverse Optimal Control via CLF

Robust Inverse Optimal Control
Trajectory Tracking Inverse Optimal Control
CLF-based Inverse Optimal Control for a Class of Nonlinear Positive Systems
Conclusions

Inverse Optimal Control: A CLF Approach, Part II
Speed-Gradient Algorithm for the Inverse Optimal Control
Speed-Gradient Algorithm for Trajectory Tracking
Trajectory Tracking for Systems in Block-Control Form
Conclusions

Neural Inverse Optimal Control
Neural Inverse Optimal Control Scheme
Block-Control Form: A Nonlinear Systems Particular Class

Conclusions

Glycemic Control of Type 1 Diabetes Mellitus Patients
Introduction
Passivity Approach
CLF Approach
Conclusions

Conclusions

References

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Author(s)

Biography

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.