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Approximate dynamic programming for optimal stationary control with control-dependent noise.

Yu Jiang¹, Zhong-Ping Jiang

¹Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY 11201, USA. yu.jiang@nyu.edu

IEEE Transactions on Neural Networks

|September 29, 2011

Summary

This summary is machine-generated.

This study introduces a reinforcement learning approach for stochastic optimal control using adaptive dynamic programming (ADP). The method ensures convergence to optimal control solutions even with complex noise, validated by a numerical example.

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Area of Science:

Control Theory
Machine Learning
Stochastic Systems

Background:

Stochastic optimal control problems are challenging due to uncertainties.
Reinforcement learning and adaptive dynamic programming (ADP) offer potential solutions.
Existing methods may struggle with complex noise structures.

Purpose of the Study:

To develop a reinforcement learning-based policy iteration algorithm for stochastic optimal control.
To address problems with both additive and multiplicative noise.
To demonstrate the convergence and efficiency of the proposed ADP methodology.

Main Methods:

Utilizing Itô calculus for deriving a policy iteration algorithm.
Applying approximate/adaptive dynamic programming (ADP) principles.
Analyzing the convergence properties of the approximated cost matrix.

Main Results:

The expectation of the approximated cost matrix converges to the solution of an algebraic Riccati equation.
The covariance of the approximated cost matrix can be reduced by adjusting iteration intervals.
A numerical example confirms the effectiveness of the ADP approach.

Conclusions:

The proposed ADP methodology provides an efficient way to solve stochastic optimal control problems.
The algorithm is robust in the presence of both additive and multiplicative noise.
Further improvements in covariance reduction are possible through iterative refinement.