Inheritance properties of the conjugate discrete-time algebraic Riccati equation

TL;DR

This paper studies inheritance properties of conjugate discrete-time Riccati equations from linear quadratic regulation problems, proposing an accelerated fixed-point iteration method for computing maximal solutions with numerical validation.

Contribution

It establishes inheritance properties of solutions from conjugate to transformed Riccati equations and introduces a new efficient iterative algorithm for maximal solutions.

Findings

Inheritance of maximal solutions under mild assumptions.

Proposed accelerated fixed-point iteration converges effectively.

Numerical examples confirm theoretical and algorithmic validity.

Abstract

In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of the maximal solution to the conjugate discrete-time Riccati equation, in which the control weighting matrix is nonsingular and its constant term is Hermitian, will be inherited to a transformed discrete-time algebraic Riccati equation. Based on this inheritance property, an accelerated fixed-point iteration is proposed for finding the maximal solution via the transformed Riccati equation. Numerical examples are shown to illustrate the correctness of our theoretical results and the feasibility of the proposed algorithm.