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A boundedness result for the direct heuristic dynamic programming.

Feng Liu1, Jian Sun, Jennie Si

  • 1Department of Electrical Engineering, Tsinghua University, Beijing, 100084, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|March 9, 2012
PubMed
Summary
This summary is machine-generated.

Approximate dynamic programming (ADP) offers scalable solutions for complex control problems. This study proves the direct heuristic dynamic programming (direct HDP) controller

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Area of Science:

  • Control Systems Engineering
  • Machine Learning
  • Optimization Theory

Background:

  • Approximate/adaptive dynamic programming (ADP) is increasingly studied for scalability in large state/control spaces.
  • Adaptive critic designs, a subset of ADP, have proven effective in case studies.
  • Direct heuristic dynamic programming (direct HDP) is an ADP algorithm inspired by adaptive critic designs, applicable to complex industrial problems.

Purpose of the Study:

  • To provide a uniformly ultimately boundedness (UUB) result for the direct HDP learning controller.
  • To establish convergence guarantees for direct HDP.
  • To analyze the boundedness of estimation errors in direct HDP.

Main Methods:

  • Lyapunov stability analysis.
  • Theoretical analysis of learning parameter/weight convergence.
  • Development of conditions for UUB of direct HDP controller.

Main Results:

  • A uniformly ultimately boundedness (UUB) result is established for the direct HDP learning controller.
  • Estimation errors of learning parameters (weights) in action and critic networks are shown to remain UUB.
  • Mild and intuitive conditions for UUB were identified.

Conclusions:

  • This work provides the first controller convergence guarantee for direct HDP designs.
  • The findings support the theoretical foundation and practical applicability of direct HDP.
  • The Lyapunov approach confirms the stability and boundedness of the direct HDP learning process.