Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach

Area of Science:

• Control Theory
• Optimization
• Stochastic Systems

Background:

• Decentralized stochastic control (DSC) involves multiple controllers with limited system and inter-controller observation capabilities.
• Traditional DSC faces challenges with controllers needing infinite memory and the impossibility of reducing complex estimations to finite-dimensional filters, even in LQG problems.

Purpose of the Study:

• To introduce a novel theoretical framework, memory-limited DSC (ML-DSC), addressing practical limitations of conventional DSC.
• To enable controllers to jointly optimize observation history compression and control determination within finite memory constraints.

Main Methods:

• Formulating ML-DSC with explicit finite-dimensional memory for controllers.
• Developing an optimization approach where controllers compress infinite-dimensional observation histories into finite-dimensional memories.
• Applying ML-DSC to linear-quadratic-Gaussian (LQG) problems to demonstrate its efficacy.

Main Results:

• ML-DSC provides a practical formulation for memory-constrained controllers.
• The proposed framework successfully solves LQG problems with more general controller interactions than conventional DSC.
• Unlike traditional DSC, ML-DSC is not restricted to scenarios with independent or partially nested controller information.

Conclusions:

• ML-DSC represents a significant advancement in decentralized stochastic control, making it applicable to real-world systems with memory limitations.
• The framework expands the scope of solvable LQG problems by accommodating complex inter-controller dependencies.
• ML-DSC offers a viable and more general approach to decentralized control optimization.