








Singularly perturbed control systems using noncommutative computer algebra






Organization:  University of California, San Diego 
Department:  Department of Mathematics 
Organization:  Cal. Poly. San Luis Obispo 






International Journal of Robust & Nonlinear Control 






Most algebraic calculations which one sees in linear systems theory, for example in IEEE TAC, involve block matrices and so are highly noncommutative. Thus conventional commutative computer algebra packages, as in Mathematica and Maple, do not address them. Here we investigate the usefulness of noncommutative computer algebra in a particular area of control theorysingularly perturbed dynamical systemswhere working with the noncommutative polynomials involved is especially tedious. Our conclusion is that they have considerable potential for helping practitioners with such computations. Commutative Gröbner basis algorithms are powerful and make up the engines in symbolic algebra packages' Solve commands. Noncommutative Gröbner basis algorithms are more recent, but we shall see that they, together with an algorithmfor removing "redundant equations," are useful in manipulating the messy sets of noncommutative polynomial equations which arise in singular perturbation calculations. We use the noncommutative algebra package NCAlgebra and the noncommutative Gröbner basis package NCGB which runs under it on two different 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.












noncommutative algebra, computer algebra, dynamic control, singular perturbation, control systems













   
 
