Approximate Information States for Worst-case Control of Uncertain Systems

TL;DR

This paper introduces a framework for worst-case control of uncertain systems with partial observations, using approximate information states to reduce computational complexity while bounding optimality loss.

Contribution

It generalizes the concept of information states to approximate versions, enabling more efficient dynamic programming in worst-case control scenarios.

Findings

Conditional range is an example of an information state.

Approximate DPs can be used with bounded optimality loss.

Numerical example demonstrates the effectiveness of the approach.

Abstract

In this paper, we investigate a worst-case-scenario control problem with a partially observed state. We consider a non-stochastic formulation, where noises and disturbances in our dynamics are uncertain variables which take values in finite sets. In such problems, the optimal control strategy can be derived using a dynamic program (DP) with respect to the memory. The computational complexity of this DP can be improved using a conditional range of the state instead of the memory. We present a more general definition of an information state which is sufficient to construct a DP without loss of optimality, and show that the conditional range is an example of an information state. Next, we extend this notion to define an approximate information state and an approximate DP. We also bound the maximum loss of optimality when using an approximate DP to derive the control strategy. Finally, we illustrate our results in a numerical example.