Almost Automorphy and Riccati Equation

TL;DR

This paper investigates almost automorphic solutions in linear time-invariant systems with almost periodic forcing, introducing a new control problem and analyzing solutions via Riccati equations.

Contribution

It proposes a novel deterministic quadratic control problem and studies the existence and uniqueness of almost automorphic solutions using Riccati equations.

Findings

Established conditions for existence of almost automorphic solutions.

Demonstrated uniqueness of solutions under certain system parameters.

Connected Riccati equations with almost automorphy in control systems.

Abstract

In this paper we first consider a linear time invariant systems with almost periodic forcing term. We propose a new deterministic quadratic control problem, motivated by Da-Prato. With the help of associated degenerate Riccati equation we study the existence and uniqueness of an almost automorphic solutions.