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We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid)…

Optimization and Control · Mathematics 2009-03-09 Francesca Bucci , Irena Lasiecka

The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the…

Dynamical Systems · Mathematics 2013-05-24 Augusto Ferrante , Lorenzo Ntogramatzidis

Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution…

Numerical Analysis · Mathematics 2026-01-30 Stefano Massei , Luca Saluzzi

Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati…

Numerical Analysis · Mathematics 2017-06-09 Matthew M. Lin , Chun-Yueh Chiang

As it is popular known, Riccati equation is the key basic tool for optimal control in the modern control theory. The solvability conditions of optimal control, stabilization conditions and controller design are all based on the Riccati…

Optimization and Control · Mathematics 2017-12-27 Huanshui Zhang , Juanjuan Xu

This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the solution of the classic infinite-horizon linear quadratic control problem. In particular, a geometric analysis…

Optimization and Control · Mathematics 2012-01-19 Augusto Ferrante , Lorenzo Ntogramatzidis

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…

Optimization and Control · Mathematics 2016-11-25 Indira Mishra

We generalize the classical theory on algebraic Riccati equations and optimization to infinite-dimensional well-posed linear systems, thus completing the work of George Weiss, Olof Staffans and others. We show that the optimal control is…

Optimization and Control · Mathematics 2016-03-01 Kalle M. Mikkola

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…

Optimization and Control · Mathematics 2022-12-06 Chun-Yueh Chiang , Hung-Yuan Fan

A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general…

Mathematical Finance · Quantitative Finance 2021-10-13 Hongyan Cai , Danhong Chen , Yunfei Peng , Wei Wei

This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is…

Optimization and Control · Mathematics 2013-12-30 Kai Du

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 some mild assumptions and the framework of the…

Numerical Analysis · Mathematics 2022-05-31 Hung-Yuan Fan , Chun-Yueh Chiang

This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…

Optimization and Control · Mathematics 2024-12-31 Lander Vanroye , Joris De Schutter , Wilm Decré

We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $M\times \mathbb R_+$, where $M$ is a complete noncompact Riemannian manifold. Under specific assumptions, we establish…

Analysis of PDEs · Mathematics 2015-12-01 Paolo Mastrolia , Dario D. Monticelli , Fabio Punzo

This paper analyzes the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to…

Optimization and Control · Mathematics 2017-06-20 Lorenzo Ntogramatzidis , Augusto Ferrante

This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike…

Optimization and Control · Mathematics 2025-06-12 Hongwei Mei , Rui Wang , Jiongmin Yong

This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…

Optimization and Control · Mathematics 2019-11-12 Jingrui Sun , Jie Xiong , Jiongmin Yong

We study the Linear-Quadratic optimal control problem for a general class of infinite-dimensional passive systems, allowing for unbounded input and output operators. We show that under mild assumptions, the finite cost condition is always…

Optimization and Control · Mathematics 2025-06-05 Anthony Hastir , Birgit Jacob

A discrete-time stochastic LQ problem with multiplicative noises and state transmission delay is studied in this paper, which does not require any definiteness constraint on the cost weighting matrices. From some abstract representations of…

Optimization and Control · Mathematics 2017-05-30 Yuan-Hua Ni , Cedric Ka-Fai Yiu , Huanshui Zhang , Ji-Feng Zhang

This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and…

Optimization and Control · Mathematics 2021-04-13 Jingrui Sun , Zhen Wu , Jie Xiong