On Robust Control of Partially Observed Uncertain Systems with Additive Costs

TL;DR

This paper develops a dynamic programming approach for robust control of partially observed systems with uncertain disturbances, introducing new information state concepts to enhance computational efficiency and provide bounded performance guarantees.

Contribution

It introduces a general framework for information states in robust control, including approximate states for tractability, advancing the computational methods for partially observed uncertain systems.

Findings

New information state framework generalizes previous methods

Approximate dynamic programming reduces computational complexity

Numerical example demonstrates effectiveness of the approach

Abstract

In this paper, we consider the problem of optimizing the worst-case behavior of a partially observed system. All uncontrolled disturbances are modeled as finite-valued uncertain variables. Using the theory of cost distributions, we present a dynamic programming (DP) approach to compute a control strategy that minimizes the maximum possible total cost over a given time horizon. To improve the computational efficiency of the optimal DP, we introduce a general definition for information states and show that many information states constructed in previous research efforts are special cases of ours. Additionally, we define approximate information states and an approximate DP that can further improve computational tractability by conceding a bounded performance loss. We illustrate the utility of these results using a numerical example.