Exact controllability of non-Lipschitz semilinear systems

TL;DR

This paper establishes conditions under which certain infinite-dimensional semilinear systems can be exactly controlled, even when the nonlinear disturbance lacks Lipschitz continuity, using fixed point methods.

Contribution

It introduces new sufficient conditions for exact controllability of non-Lipschitz semilinear systems via a fixed point approach, applicable to systems with noncompact semigroups.

Findings

Established controllability conditions for non-Lipschitz systems

Applied the theory to a nonlinear transport PDE

Demonstrated the effectiveness of fixed point methods

Abstract

We present sufficient conditions for exact controllability of a semilinear infinite dimensional dynamical system. The system mild solution is formed by a noncompact semigroup and a nonlinear disturbance that does not need to be Lipschitz continuous. Our main result is based on a fixed point type application of the Schmidt existence theorem and illustrated by a nonlinear transport partial differential equation.