Abstract
SUMMARY Most algebraic calculations which one sees in linear systems theory, for example in IEEE TAC, involve block matrices and so are highly non-commutative. Thus conventional commutative computer algebra packages, as in Mathematica and Maple, do not address them. Here we investigate the usefulness of non-commutative computer algebra in a particular area of control theory*singularly perturbed dynamic systems*where working with the non-commutative polynomials involved is especially tedious. Our conclusion is that they have considerable potential for helping practitioners with such computations. Commutative GroK bner basis algorithms are powerful and make up the engines in symbolic algebra packages’ Solve commands. Non-commutative GroK bner basis algorithms are more recent, but we shall see that they, together with an algorithm for removing &&redundant equations’’, are useful in manipulating the messy sets of non-commutative polynomial equations which arise in singular perturbation calculations. We use the non-commutative algebra package NCAlgebra and the non-commutative GroK bner basis package NCGB which runs under it on two di!erent problems. We illustrate the method on the classical state feedback optimal control problem, see [1], where we obtain one more (very long) term than was done previously. Then we use it to derive singular perturbation expansions for the relatively new (linear) information state equation. Copyright ( 2000 John Wiley & Sons, Ltd.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: International Journal of Robust and Nonlinear Control
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.