Online Synchronous Policy Iteration Method for Optimal Control

2009 ◽  
pp. 357-374 ◽  
Author(s):  
Kyriakos G. Vamvoudakis ◽  
Frank L. Lewis
Keyword(s):  
Optimal Control ◽  
Iteration Method ◽  
Policy Iteration

scholarly journals A policy iteration method for Mean Field Games

2021 ◽  
Author(s):  
Simone Cacace ◽  
Fabio Camilli ◽  
Alessandro Goffi
Keyword(s):  
Optimal Control ◽  
Iteration Method ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Policy Iteration ◽  
Mean Field Games ◽  
Control Problems ◽  
Discrete Problem ◽  
Classical Algorithm ◽  
Dimension One

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of the problem. We also introduce suitable discretizations to numerically solve both stationary and evolutive problems. We show the convergence of the policy iteration method for the discrete problem and we study the performance of the proposed algorithm on some examples in dimension one and two.

Data-based approximate policy iteration for affine nonlinear continuous-time optimal control design

Automatica ◽  
2014 ◽  
Vol 50 (12) ◽  
pp. 3281-3290 ◽  
Author(s):  
Biao Luo ◽  
Huai-Ning Wu ◽  
Tingwen Huang ◽  
Derong Liu
Keyword(s):  
Optimal Control ◽  
Continuous Time ◽  
Control Design ◽  
Policy Iteration ◽  
Time Optimal Control ◽  
Time Optimal ◽  
Approximate Policy Iteration

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

Motion planning of a quadrotor robot game using a simulation-based projected policy iteration method

2019 ◽  
Vol 20 (4) ◽  
pp. 525-537
Author(s):  
Li-dong Zhang ◽  
Ban Wang ◽  
Zhi-xiang Liu ◽  
You-min Zhang ◽  
Jian-liang Ai
Keyword(s):  
Motion Planning ◽  
Iteration Method ◽  
Policy Iteration ◽  
Simulation Based ◽  
Quadrotor Robot

scholarly journals Adaptive Optimal Control for a Class of Nonlinear Systems: The Online Policy Iteration Approach

2020 ◽  
Vol 31 (2) ◽  
pp. 549-558 ◽  
Author(s):  
Shuping He ◽  
Haiyang Fang ◽  
Maoguang Zhang ◽  
Fei Liu ◽  
Zhengtao Ding
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Adaptive Optimal Control
Sign in / Sign up

Export Citation Format

Share Document