The Generalised Discrete Algebraic Riccati Equation in LQ optimal control

2012/01/18 by Augusto Ferrante, Ferrante, Augusto, Lorenzo Ntogramatzidis +1
Engineering · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations #math.DS #math.OC

paper · pdf · doi:10.48550/arxiv.1201.3704

arxiv created 2012/01/18 · openalex publication_date 2012/01/18 · arxiv updated 2012/01/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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 is used to study the relationship existing between the solutions of the generalised Riccati equation and the output-nulling subspaces of the underlying system and the corresponding reachability subspaces. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem, which is reflected in the generalised eigenstructure of the corresponding extended symplectic pencil. In establishing themain results of this paper, several ancillay problems on the discrete Lyapunov equation and spectral factorisation are also addressed and solved.

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