Verified calculation of the solution of algebraic Riccati equation

Wolfram Luther () and Werner Otten ()
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Wolfram Luther: Gerhard-Mercator-Universität — GH Duisburg, Informatik II
Werner Otten: Gerhard-Mercator-Universität — GH Duisburg, Informatik II

A chapter in Developments in Reliable Computing, 1999, pp 105-118 from Springer

Abstract: Abstract In this note we describe a new method to calculate verified solutions of the matrix Riccati equation (ARE) with interval coefficients. Such an equation has to be solved when we want to find the steady state solutions of matrix Riccati differential equation with constant coefficients which arises in the theory of automatic control and linear filtering. Given the Riccati polynomial P(X) we use the Fréchet-derivative at X to derive a linear equation of type CX + XD = P. Applying Brouwer’s fixed point theorem, we find an interval matrix [X] that includes a positive definite solution of the equation P(X) = Ω. First we want to give an outline of linear-quadratic control theory. Then we present results concerning the geometric structures of all solutions and enumerate linearly and quadratically convergent algorithms to find a solution used to construct the optimal feedback control for linear-quadratic optimal control problems.

Keywords: Algebraic matrix Riccati equation; interval arithmetic; verified solution (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-1247-7_8

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DOI: 10.1007/978-94-017-1247-7_8

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