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Maximum Principle and Dynamic Programming Viscosity Solution Approach: From Open-Loop to Closed-Loop
Bing Sun, Bao-Zhu Guo, Zhen-Zhen Tao
Page: 444
Format: pdf, ePub, mobi, fb2
ISBN: 9789819657384
Publisher: Springer Nature Singapore
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This book is concerned with optimal control problems of dynamical systems described by partial differential equations (PDEs). The content covers the theory and numerical algorithms, starting with open-loop control and ending with closed-loop control. It includes Pontryagin’s maximum principle and the Bellman dynamic programming principle based on the notion of viscosity solution. The Bellman dynamic programming method can produce the optimal control in feedback form, making it more appealing for online implementations and robustness. The determination of the optimal feedback control law is of fundamental importance in optimal control and can be argued as the Holy Grail of control theory. The book is organized into five chapters. Chapter 1 presents necessary mathematical knowledge. Chapters 2 and 3 (Part 1) focus on the open-loop control while Chapter 4 and 5 (Part 2) focus on the closed-loop control. In this monograph, we incorporate the notion of viscosity solution of PDE with dynamic programming approach. The dynamic programming viscosity solution (DPVS) approach is then used to investigate optimal control problems. In each problem, the optimal feedback law is synthesized and numerically demonstrated. The last chapter presents multiple algorithms for the DPVS approach, including an upwind finite-difference scheme with the convergence proof. It is worth noting that the dynamic systems considered are primarily of technical or biologic origin, which is a highlight of the book. This book is systematic and self-contained. It can serve the expert as a ready reference for control theory of infinite-dimensional systems. These chapters taken together would also make a one-semester course for graduate with first courses in PDE-constrained optimal control.
Maximum Principle and Dynamic Programming Viscosity Solution .
The content covers the theory and numerical algorithms, starting with open-loop control and ending with closed-loop control. It includes Pontryagin s maximum .
Bing Bing - Mathematics / Science & Math: Books - Amazon.com
Maximum Principle and Dynamic Programming Viscosity Solution Approach: From Open-Loop to Closed-Loop (Systems & Control: Foundations & Applications).
Maximum Principle and Dynamic Programming Viscosity Solution .
Publish Date: July 4th, 2025 ; Publisher: Birkhauser ; ISBN: 9789819657384 ; Pages: 350 ; About the Author. Bing Sun received his Ph.D.
Maximum Principle and Dynamic Programming Viscosity Solution .
E-Book Reader . Maximum Principle and Dynamic Programming Viscosity Solution Approach. From Open-Loop to Closed-Loop, Systems & Control: Foundations & .
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman .
The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of .
Maximum Principle and Dynamic Programming Viscosity . - Leporello
The content covers the theory and numerical algorithms, starting with open-loop control and ending with closed-loop control. It includes Pontryagin s maximum .
State and Control Path-Dependent Stochastic Zero-Sum Differential .
In Section 5, we introduce the lower and upper PHJI equations and prove that the value functionals are viscosity solutions of the corresponding PHJI equations.
Maximum Principle and Dynamic Programming Viscosity Solution .
From Open-Loop to Closed-Loop . This book is concerned with optimal control problems of dynamical systems described by partial differential equations (PDEs).
[PDF] Lecture notes on viscosity solutions - University of Minnesota
Substituting this into the dynamic programming principle (1.3) we deduce max z∈∂B(x,r). {φ(x) − φ(z) − r} ≤ 0, for r > 0 sufficiently small. Since φ is .
Maximum Principle and Dynamic Programming Viscosity Solution .
The content covers the theory and numerical algorithms, starting with open-loop control and ending with closed-loop control. It includes Pontryagin's maximum .