Quantified multivariate polynomial inequalities: the mathematics of (almost) all practical control design problems

摘要

In this plenary talk we show how a large number of practical feedback design problems, for both linear and nonlinear systems, can be reduced to the study of quantified multivariate (multivariable) polynomial inequalities. Three approaches for the study of this class of mathematical problems will be reviewed, symbolic quantifier elimination methods, Bernstein-branch-and-bound methods, and Monte Carlo (probabilistic) methods.