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Discrete-Time Inverse Optimal Control for Nonlinear Systems

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

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Table of Contents
  7. List of Figures
  8. List of Tables
  9. Preface
  10. Acknowledgments
  11. Authors
  12. Notations and Acronyms
  13. Chapter 1 Introduction
    1. 1.1 Inverse Optimal Control via Passivity
    2. 1.2 Inverse Optimal Control via CLF
    3. 1.3 Neural Inverse Optimal Control
    4. 1.4 Motivation
  14. Chapter 2 Mathematical Preliminaries
    1. 2.1 Optimal Control
    2. 2.2 Lyapunov Stability
    3. 2.3 Robust Stability Analysis
      1. 2.3.1 Optimal Control for Disturbed Systems
    4. 2.4 Passivity
    5. 2.5 Neural Identification
      1. 2.5.1 Nonlinear Systems
      2. 2.5.2 Discrete-Time Recurrent High Order Neural Network
        1. 2.5.2.1 RHONN Models
        2. 2.5.2.2 On-line Learning Law
      3. 2.5.3 Discrete-Time Recurrent Multilayer Perceptron
  15. Chapter 3 Inverse Optimal Control: A Passivity Approach
    1. 3.1 Inverse Optimal Control via Passivity
      1. 3.1.1 Stabilization of a Nonlinear System
    2. 3.2 Trajectory Tracking
      1. 3.2.1 Example: Trajectory Tracking of a Nonlinear System
      2. 3.2.2 Application to a Planar Robot
        1. 3.2.2.1 Robot Model
        2. 3.2.2.2 Robot as an Affine System
        3. 3.2.2.3 Control Synthesis
        4. 3.2.2.4 Simulation Results
    3. 3.3 Passivity-Based Inverse Optimal Control for a Class of Nonlinear Positive Systems
    4. 3.4 Conclusions
  16. Chapter 4 Inverse Optimal Control: A CLF Approach, Part I
    1. 4.1 Inverse Optimal Control via CLF
      1. 4.1.1 Example
      2. 4.1.2 Inverse Optimal Control for Linear Systems
    2. 4.2 Robust Inverse Optimal Control
    3. 4.3 Trajectory Tracking Inverse Optimal Control
      1. 4.3.1 Application to the Boost Converter
        1. 4.3.1.1 Boost Converter Model
        2. 4.3.1.2 Control Synthesis
        3. 4.3.1.3 Simulation Results
    4. 4.4 CLF-Based Inverse Optimal Control for a Class of Nonlinear Positive Systems
    5. 4.5 Conclusions
  17. Chapter 5 Inverse Optimal Control: A CLF Approach, Part II
    1. 5.1 Speed-Gradient Algorithm for the Inverse Optimal Control
      1. 5.1.1 Speed-Gradient Algorithm
      2. 5.1.2 Summary of the Proposed SG Algorithm to Calculate Parameter pk
      3. 5.1.3 SG Inverse Optimal Control
        1. 5.1.3.1 Example
      4. 5.1.4 Application to the Inverted Pendulum on a Cart
        1. 5.1.4.1 Simulation Results
    2. 5.2 Speed-Gradient Algorithm for Trajectory Tracking
      1. 5.2.1 Example
    3. 5.3 Trajectory Tracking for Systems in Block-Control Form
      1. 5.3.1 Example
    4. 5.4 Conclusions
  18. Chapter 6 Neural Inverse Optimal Control
    1. 6.1 Neural Inverse Optimal Control Scheme
      1. 6.1.1 Stabilization
      2. 6.1.2 Example
        1. 6.1.2.1 Neural Network Identifier
        2. 6.1.2.2 Control Synthesis
      3. 6.1.3 Trajectory Tracking
        1. 6.1.3.1 Example
      4. 6.1.4 Application to a Synchronous Generator
        1. 6.1.4.1 Synchronous Generator Model
        2. 6.1.4.2 Neural Identification for the Synchronous Generator
        3. 6.1.4.3 Control Synthesis
        4. 6.1.4.4 Simulation Results
      5. 6.1.5 Comparison
    2. 6.2 Block-Control Form: A Nonlinear Systems Particular Class
      1. 6.2.1 Block Transformation
      2. 6.2.2 Block Inverse Optimal Control
      3. 6.2.3 Application to a Planar Robot
        1. 6.2.3.1 Robot Model Description
        2. 6.2.3.2 Neural Network Identifier
        3. 6.2.3.3 Control Synthesis
        4. 6.2.3.4 Simulation Results
    3. 6.3 Conclusions
  19. Chapter 7 Glycemic Control of Type 1 Diabetes Mellitus Patients
    1. 7.1 Introduction
    2. 7.2 Passivity Approach
      1. 7.2.1 Virtual Patient
      2. 7.2.2 State Space Representation
      3. 7.2.3 Control Law Implementation
    3. 7.3 CLF Approach
      1. 7.3.1 Simulation Results via CLF
      2. 7.3.2 Passivity versus CLF
    4. 7.4 Conclusions
  20. Chapter 8 Conclusions
  21. References
  22. Index