Comments on the Bellman functional for linear time-delay systems

TL;DR

This paper investigates the properties of the Bellman functional in infinite horizon optimal control for linear time-delay systems, showing that the optimal control law does not include concentrated delay terms.

Contribution

It provides formal proofs of properties of matrices in the Bellman functional and demonstrates the absence of concentrated delay terms in the optimal control law.

Findings

Matrices in the Bellman functional have specific properties.

Optimal control law lacks concentrated delay terms.

Theoretical insights into time-delay system control.

Abstract

In this note, we present some complementary results on the infinite horizon optimal control for linear time-delay systems. We formally establish some properties of the matrices arising in the Bellman functional, and we prove that no concentrated delay term is present in the optimal control law.