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2016•Unpublished venueRequires access

On the structure of the solutions of the constrained generalized discrete-time algebraic Riccati equation

Lorenzo Ntogramatzidis, Augusto Ferrante

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Abstract

This paper introduces a new decomposition of the constrained generalized discrete-time algebraic Riccati equation arising in linear quadratic optimal control problems into two parts: the first part is an explicit expression which is common to all solutions. The second part can be either a reduced-order discrete-time algebraic Riccati equation with non-singular associated closed-loop matrix, or a symmetric Stein equation.

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What this paper is about

This paper introduces a new decomposition of the constrained generalized discrete-time algebraic Riccati equation arising in linear quadratic optimal control problems into two parts: the first part is an explicit expression which is common to all solutions. The second part can be either a reduced-order discrete-time algebraic Riccati equation with non-singular associated closed-loop matrix, or a symmetric Stein equation.

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Available abstract

This paper introduces a new decomposition of the constrained generalized discrete-time algebraic Riccati equation arising in linear quadratic optimal control problems into two parts: the first part is an explicit expression which is common to all solutions. The second part can be either a reduced-order discrete-time algebraic Riccati equation with non-singular associated closed-loop matrix, or a symmetric Stein equation.

Key concepts: Algebraic Riccati equation, Riccati equation, Linear-quadratic regulator, Mathematics, Algebraic solution, Matrix difference equation, Discrete time and continuous time, Algebraic number

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