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Stability Analysis of Optimal Adaptive Control Under Value Iteration Using a Stabilizing Initial Policy.

IEEE Transactions on Neural Networks and Learning Systems

|October 17, 2017

Summary

This study analyzes adaptive optimal control stability during learning. It identifies regions ensuring reliable function approximation by keeping system states within training bounds.

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Area of Science:

Control Theory
Machine Learning
System Stability

Background:

Adaptive optimal control is crucial for dynamic systems.
Value iteration is a common learning method.
Ensuring stability during learning is a key challenge.

Purpose of the Study:

To theoretically analyze the stability of adaptive optimal control using value iteration.
To investigate system stability under fixed and evolving control policies.
To identify conditions for reliable function approximation during learning.

Main Methods:

Theoretical analysis of value iteration for adaptive optimal control.
Stability analysis considering fixed and evolving policies.
Identification of subsets of the region of attraction.

Main Results:

The analysis provides insights into system stability during the learning phase.
Subsets of the region of attraction are identified.
Ensuring initial conditions remain within these subsets guarantees reliable function approximation.

Conclusions:

The proposed method ensures system stability and reliable learning.
Identifying specific initial condition regions prevents extrapolation errors.
This work contributes to robust adaptive optimal control theory.