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Improved value iteration for neural-network-based stochastic optimal control design.

Mingming Liang1, Ding Wang2, Derong Liu3

  • 1State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China.

Neural Networks : the Official Journal of the International Neural Network Society
|February 10, 2020
PubMed
Summary
This summary is machine-generated.

A new adaptive dynamic programming algorithm improves policy stability for discrete stochastic processes. This novel method ensures value functions converge to optimal solutions, validated by simulations.

Keywords:
Adaptive critic designsAdaptive dynamic programmingNeural networksOptimal controlStochastic processesValue iteration

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Area of Science:

  • Control Theory
  • Optimization
  • Machine Learning

Background:

  • Discrete stochastic processes require robust methods for optimal policy determination.
  • Existing adaptive dynamic programming (ADP) algorithms face challenges in policy stability verification.

Purpose of the Study:

  • To introduce an improved value iteration adaptive dynamic programming (ADP) algorithm.
  • To develop a novel criterion for verifying policy stability in stochastic processes.
  • To demonstrate the convergence and effectiveness of the proposed ADP algorithm.

Main Methods:

  • A novel value iteration ADP algorithm is developed.
  • A new stability verification criterion for policies in stochastic processes is proposed.
  • Convergence properties of the algorithm are analyzed theoretically.

Main Results:

  • The improved value iteration ADP algorithm achieves optimal policies for discrete stochastic processes.
  • A new criterion for policy stability in stochastic processes is successfully introduced.
  • The algorithm's value functions are proven to converge to the optimum.
  • The method accommodates arbitrary positive semi-definite initial value functions.

Conclusions:

  • The developed improved value iteration ADP algorithm effectively obtains optimal policies.
  • The novel stability criterion enhances the reliability of ADP for stochastic processes.
  • Simulation examples confirm the algorithm's practical applicability and effectiveness.