Symplectic Pseudospectral Methods for Optimal Control

1. Front Matter

   Pages i-xi

   PDF

2. Overview of This Book

   • Xinwei Wang, Jie Liu, Haijun Peng

   Pages 1-4

3. Computational Techniques for Nonlinear Optimal Control

   • Xinwei Wang, Jie Liu, Haijun Peng

   Pages 5-14

4. Mathematical Foundation

   • Xinwei Wang, Jie Liu, Haijun Peng

   Pages 15-32

5. SPM for Unconstrained Nonlinear Optimal Control Problems

   • Xinwei Wang, Jie Liu, Haijun Peng

   Pages 33-51

6. SPM for Nonlinear Optimal Control Problems with Inequality Constraints

   • Xinwei Wang, Jie Liu, Haijun Peng

   Pages 53-83

7. SPM for Time-Delayed Nonlinear Optimal Control Problems

   • Xinwei Wang, Jie Liu, Haijun Peng

   Pages 85-113

8. Model Predictive Control: From Open-Loop to Closed-Loop

   • Xinwei Wang, Jie Liu, Haijun Peng

   Pages 115-119

9. Optimal Maneuver for Spacecraft

   • Xinwei Wang, Jie Liu, Haijun Peng

   Pages 121-130

10. Optimal Path Planning of UGS

    • Xinwei Wang, Jie Liu, Haijun Peng

    Pages 131-144

11. Motion Planning and Control for Overhead Cranes

    • Xinwei Wang, Jie Liu, Haijun Peng

    Pages 145-164

12. Path Planning for Tractor-Trailer System

    • Xinwei Wang, Jie Liu, Haijun Peng

    Pages 165-178

The book focuses on symplectic pseudospectral methods for nonlinear optimal control problems and their applications. Both the fundamental principles and engineering practice are addressed. Symplectic pseudospectral methods for nonlinear optimal control problems with complicated factors (i.e., inequality constraints, state-delay, unspecific terminal time, etc.) are solved under the framework of indirect methods. The methods developed here offer a high degree of computational efficiency and accuracy when compared with popular direct pseudospectral methods. The methods are applied to solve optimal control problems arising in various engineering fields, particularly in path planning problems for autonomous vehicles. Given its scope, the book will benefit researchers, engineers and graduate students in the fields of automatic control, path planning, ordinary differential equations, etc. 

• Nonlinear Optimal Control Problem
• Symplectic Pseudospectral Method
• Computational Optimal Control
• Symplectic Conserved
• Pseudospectral Method
• Optimal Path Planning

“The book presents – original, efficient, with good accuracy and convergence – robust numerical methods for solving different nonlinear optimal control problems with dynamics described by ODEs. … The book is well-written.” (Wiesław Kotarski, zbMATH 1491.49001, 2022)

• Department of Engineering Mechanics, Dalian University of Technology, Dalian, China

  Xinwei Wang, Haijun Peng

• War Research Institute, Academy of Military Sciences, Beijing, China

  Jie Liu

Xinwei Wang was born in Dalian, China. He received the Ph.D. degree in computational mechanics from Dalian University of Technology, Dalian, China, in 2019. He is currently a Postdoc with the Department of Engineering Mechanics and Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China. His research interests cover computational optimal control and path planning for autonomous vehicles. He has authored or co-authored over 10 publications in journals. 


Jie Liu was born in Huanggang, China. He received the Ph.D. degree in aerospace science and technology from Naval Aeronautical University, Yantai, China, in 2019. He is currently working in Academy of Military Sciences, Beijing, China. His research interests cover the control of Unmanned Ground Systems, path planning for robots, and optimal control, as well as related fields such as the process industry control and automation. He has authored or co-authoredover 10 publications in journals.



Haijun Peng was born in Handan, China. He received the Ph.D. degree in dynamics and control from Dalian University of Technology, Dalian, China, in 2012. He is currently a Professor with the Department of Engineering Mechanics, and fixed personnel in State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China. His research interests cover the optimal control, multibody dynamics, and robot system. He has authored or co-authored over 50 publications in journals, and received one best paper award.

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