Constrained controllability of some nonlinear systems

Abstract

We consider the constrained exact local controllability of nonlinear systems and the constrained exact and approximate controllability of semilinear systems. The constraint on the con trol is a time-dependent closed convex cone with possibly empty interior. Some sufficient and necessary conditions are derived by using the controllability of associated linear or nonlinear systems. A result on the solution set of an operator equation with parameter is also given.

Keywords:

• Nonlinear system
• constraint
• exact controllability
• approximate controllability
• local controllability