On Decentralized Minimax Control with Nested Subsystems

TL;DR

This paper addresses a decentralized control problem with nested subsystems and finite set uncertainties, proposing a structural form for optimal strategies that simplifies long-term control design.

Contribution

It introduces a prescription-based approach to derive a structural form for optimal control strategies in nested decentralized systems with finite set uncertainties.

Findings

Structural form simplifies control strategy design.

Dynamic programming approach for optimal control.

Validation through numerical example.

Abstract

In this paper, we investigate a decentralized control problem with nested subsystems, which is a general model for one-directional communication amongst many subsystems. The noises in our dynamics are modelled as uncertain variables which take values in finite sets. The objective is to minimize a worst-case shared cost. We demonstrate how the prescription approach can simplify the information structure and derive a structural form for optimal control strategies. The structural form allows us to restrict attention to control strategies whose domains do not grow in size with time, and thus, this form can be utilized in systems with long time horizons. Finally, we present a dynamic program to derive the optimal control strategies and validate our results with a numerical example.