Memory-Limited Partially Observable Stochastic Control and Its Mean-Field Control Approach

Area of Science:

• Control Theory
• Optimization
• Stochastic Systems

Background:

• Practical control problems often involve incomplete information and memory limitations.
• Partially observable stochastic control (POSC) theoretically addresses incomplete information but lacks memory constraints and is often unsolvable.
• Existing methods struggle with real-world scenarios demanding memory considerations.

Purpose of the Study:

• To propose a novel theoretical framework, memory-limited POSC (ML-POSC), that integrates memory limitations into control problems.
• To develop a practical solution for control problems with both incomplete information and memory constraints.
• To generalize and enhance the linear-quadratic-Gaussian (LQG) problem by incorporating memory.

Main Methods:

• Developed the memory-limited partially observable stochastic control (ML-POSC) framework.
• Employed mean-field control theory to ensure practical solvability of ML-POSC.
• Modified the Riccati equation to a partially observable Riccati equation for improved estimation and control in memory-limited LQG problems.

Main Results:

• ML-POSC effectively addresses control problems with both incomplete information and memory limitations.
• The modified partially observable Riccati equation enhances both estimation and control performance.
• Demonstrated the efficacy of ML-POSC for non-LQG problems through comparison with local LQG approximation.

Conclusions:

• ML-POSC offers a practical and effective solution for complex control problems previously unaddressed by conventional methods.
• The framework provides a generalized approach to the LQG problem, incorporating crucial memory constraints.
• ML-POSC shows significant potential for improving control system performance in real-world applications with information and memory constraints.