The geometry of the generalized algebraic Riccati equation and of the singular Hamiltonian system

DOI10.1080/03081087.2017.1415292zbMath1440.93052arXiv1706.05828OpenAlexW2962900756MaRDI QIDQ5205773

Lorenzo Ntogramatzidis, Augusto Ferrante

Publication date: 16 December 2019

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.05828

zbMATH Keywords

Hamiltonian systemLQ optimal controlgeneralised Riccati equation

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Matrix equations and identities (15A24) Linear-quadratic optimal control problems (49N10) Algebraic methods (93B25)

Related Items (1)

On the reduction of the continuous-time generalized algebraic Riccati equation: an effective procedure for solving the singular LQ problem with smooth solutions

Uses Software

• Matlab

Cites Work

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• Continuous-time singular linear-quadratic control: necessary and sufficient conditions for the existence of regular solutions
• The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control
• System structure and singular control
• The singular \(H_ 2\) control problem
• The discrete algebraic Riccati equation and linear matrix inequality
• Matrix Riccati equations in control and systems theory
• Rational matrix equations in stochastic control.
• On a class of rational matrix differential equations arising in stochastic control.
• Properties of the solutions of rational matrix difference equations
• Discrete-time indefinite LQ control with state and control dependent noises
• Generalized continuous-time Riccati theory
• The generalised discrete algebraic Riccati equation in linear-quadratic optimal control
• The discrete-time generalized algebraic Riccati equation: order reduction and solutions' structure
• A new approach to the cheap LQ regulator exploiting the geometric properties of the Hamiltonian system
• A Contraction Analysis of the Convergence of Risk-Sensitive Filters
• Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems
• Singular Optimal Control: A Geometric Approach
• Cheap and singular controls for linear quadratic regulators
• On the Structure of the Solutions of Discrete-Time Algebraic Riccati Equation With Singular Closed-Loop Matrix
• Singular LQ Control, Optimal PD Controller and Inadmissible Initial Conditions
• Convergence Analysis of a Family of Robust Kalman Filters Based on the Contraction Principle
• Control theory for linear systems
• Newton's method for a rational matrix equation occurring in stochastic control

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