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A reduction technique for generalised Riccati difference equations arising in linear-quadratic optimal control

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Authors
Ferrante, A.
Ntogramatzidis, Lorenzo
Date
2012
Type
Conference Paper

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Ferrante, Augusto and Ntogramatzidis, Lorenzo. 2012. A reduction technique for generalised Riccati difference equations arising in linear-quadratic optimal control, in Proceedings of the 2012 IEEE 51st Annual Conference on Decision and Control, Dec 10-13 2012, pp. 7043-7048. Maui, Hawaii: IEEE.
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Proceedings of the 51st Conference on Decision and Control (CDC 12)
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51st IEEE Conference on Decision and Control
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Abstract

In this paper we develop a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a decomposition method for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of iteration steps equal to the nilpotency index of the closed-loop, from another part that can be computed by iterating a reduced-order Riccati difference equation.