Quantified multivariate polynomial inequalities. The mathematics of practical control design problems

Author

Dorato, Peter ; Kun Li ; Kosmatopoulos, Elias B. ; Ioannou, Petros A.

Author_Institution

Dept. of Electr. & Comput. Eng., New Mexico Univ., Albuquerque, NM

Volume

20

Issue

5

fYear

2000

fDate

10/1/2000 12:00:00 AM

Firstpage

48

Lastpage

58

Abstract

This article describes how a large number of practical feedback design problems can be reduced to the study of quantified multivariate polynomial inequalities (MPIs). However, the computation required to solve quantified MPI problems is very intensive. As defined here, most practical control problems do not have analytical solutions. Three approaches for the study of this class of mathematical problems are reviewed: symbolic quantifier elimination methods, Bernstein branch-and-bound methods, and probabilistic (Monte Carlo) methods. The three approaches are listed in order of computational complexity required for a solution, with symbolic computation the most computationally complex and probabilistic methods the least

Keywords

Monte Carlo methods; computational complexity; control system synthesis; feedback; optimisation; probability; symbol manipulation; Bernstein method; Monte Carlo methods; branch-and-bound method; computational complexity; control design; feedback; multivariate polynomial inequality; probabilistic methods; symbolic quantifier elimination; Boolean functions; Control design; Feedback; Logic design; Mathematics; NASA; Optimal control; Polynomials; Robust stability; Transfer functions;

fLanguage

English

Journal_Title

Control Systems, IEEE

Publisher

ieee

ISSN

1066-033X

Type

jour

DOI

10.1109/37.872903

Filename

872903