Engineering topics

Sidhu, G. S.

Publications and source records attributed to Sidhu, G. S..

3 records

NASA NTRS1977

Integration-free interval doubling for Riccati equation solutions

Starting with certain identities obtained by Reid (1972) and Redheffer (1962) for general matrix Riccati equations (RE's), we give various algorithms for the case of constant coefficients. The algorithms are based on two ideas - first, relate the RE solution with general initial conditions to anchored RE solutions; and second, when the coefficients are constant, the anchored solutions have a basic shift-invariance property. These ideas are used to construct an integration-free, superlinearly convergent iterative solution to the algebraic RE. Preliminary numerical experiments show that our algorithms, arranged in square-root form, provide a method that is numerically stable and appears to be competitive with other methods of solving the algebraic RE.

Sidhu, G. S.↗

NASA NTRS1976

Integration-free interval doubling for Riccati equation solutions

Various algorithms are given for the case of constant coefficients. The algorithms are based on two ideas: first, relate the Re solution with general initial conditions to anchored RE solutions; and second, when the coefficients are constant the anchored solutions have a basic shift-invariance property. These ideas are used to construct an integration free superlinearly convergent iterative solution to the algebraic RE. The algorithm, arranged in square-root form, is thought to be numerically stable and competitive with other methods of solving the algebraic RE.

Bierman, G. J.↗

NASA NTRS1975

Some estimation formulae for continuous time-invariant linear systems

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Bierman, G. J.↗