Revisiting the derivation of stage costs in infinite horizon discrete-time optimal control

TL;DR

This paper revisits and generalizes a technique for designing stage costs in infinite horizon discrete-time optimal control, making it more flexible and expanding its applicability to methods like model predictive control.

Contribution

It generalizes a previous stage cost design method, weakens assumptions, and demonstrates the fundamental limits of these assumptions, enhancing optimization-based control strategies.

Findings

Improved stage cost design options for infinite horizon control.

Weakened assumptions for stage cost construction.

Enhanced applicability to model predictive control.

Abstract

In many applications of optimal control, the stage cost is not fixed, but rather a design choice with considerable impact on the control performance. In infinite horizon optimal control, the choice of stage cost is often restricted by the requirement of uniform cost controllability, which is nontrivial to satisfy. Here we revisit a previously proposed constructive technique for stage cost design. We generalize its setting, weaken the required assumptions and add additional flexibility. Furthermore, we show that the required assumptions essentially cannot be weakened anymore. By providing improved design options for stage costs, this work contributes to expanding the applicability of optimization-based control methodologies, in particular, model predictive control.