Structured exploration in the finite horizon linear quadratic dual control problem

TL;DR

This paper introduces a structured approach to dual control in finite horizon LQ problems, balancing system identification and cost optimization for unknown LTI systems.

Contribution

It formulates a novel synthesis problem that captures exploration and control trade-offs in a finite horizon setting, exploiting problem structure for efficiency.

Findings

Efficient exploration strategies are developed.

The approach balances system identification and control performance.

Structured problem formulation improves synthesis efficiency.

Abstract

This paper presents a novel approach to synthesize dual controllers for unknown linear time-invariant systems with the tasks of optimizing a quadratic cost while reducing the uncertainty. To this end, a synthesis problem is defined where the feedback law has to simultaneously gain knowledge of the system and robustly optimize the cost. By framing the problem in a finite horizon setting, the trade-offs arising when the tasks include both identification and control are formally captured in the optimization problem. Results show that efficient exploration strategies are achieved when the structure of the problem is exploited.