Controlled Invariant Sets for Polynomial Systems Defined by Non-polynomial Equations

This study proposes a method for designing a feedback controller that makes a prescribed set invariant for a given polynomial system. Although the system is restricted to polynomial systems, the class of invariant sets is not limited to algebraic sets; it is the zero sets of nonlinear functions satisfying a specific type of partial differential equations (PDE) with coefficients in polynomials. Based on the algebraic relations between a nonlinear function and its derivatives derived from the PDE, a constructive sufficient condition for the existence of the desired controllers is provided. Using symbolic computation, the controllers can be computed exactly. Numerical examples are provided to illustrate the effectiveness of the proposed method.