Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems

IEEE Transactions on Neural Networks and Learning Systems
Derong LiuDing Wang

Abstract

In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

References

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Citations

Jun 26, 2015·IEEE Transactions on Neural Networks and Learning Systems·Hamidreza ModaresZhong-Ping Jiang
Sep 12, 2015·IEEE Transactions on Neural Networks and Learning Systems·Quan-Yong Fan, Guang-Hong Yang
Nov 10, 2015·IEEE Transactions on Cybernetics·Qinglai WeiHanquan Lin
Mar 16, 2016·IEEE Transactions on Neural Networks and Learning Systems·Yan-Jun LiuC L Philip Chen
Dec 25, 2015·IEEE Transactions on Neural Networks and Learning Systems·Yufei TangTingwen Huang
Dec 2, 2015·IEEE Transactions on Neural Networks and Learning Systems·Huaguang ZhangTao Feng
Nov 6, 2015·IEEE Transactions on Neural Networks and Learning Systems·Huaguang ZhangYanhong Luo
Nov 10, 2015·IEEE Transactions on Neural Networks and Learning Systems·Zhuo WangHui Peng
Feb 1, 2017·IEEE Transactions on Neural Networks and Learning Systems·Hongliang LiDing Wang
Jul 7, 2017·IEEE Transactions on Cybernetics·Ding WangDerong Liu

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