Lie Derivative Inclusion for a Class of Polynomial State Feedback Controls

Abstract

In this paper, we deal with two problems of input-affine polynomial dynamical systems. One aims to obtain a state feedback controller such that a prescribed algebraic set is invariant for the resulting closed-loop system. The other aims to obtain a state feedback controller such that the resulting closed-loop system has a prescribed vector field on a given algebraic set. It is shown that the two problems can be represented by a particular inclusion of polynomials, and the inclusion can be solved. As a result, all the state feedback controllers required in the problems can be exactly represented by using free polynomial parameters.

Attracting and Natural Invariant Varieties for Polynomial Vector Fields and Control Systems

“…The theory has been generalized to nonlinear systems by Isidori [10] and several other authors. Recently, some progress has been made in the area of nonlinear polynomial systems; see [15][16][17]21], and Yuno and Ohtsuka [19,20], where it is shown that methods from symbolic computation can be used to test the conditions for controlled invariance of varieties constructively. The purpose of the present work, which is in part based on the doctoral dissertations [11,17] by two authors of the present manuscript, is twofold.…”