Exact Controllability Theorems and Numerical Simulations for Some Nonlinear Differential Equations

We study exact controllability problems for some nonlinear systems with linear controls. Our tools are contraction fixed point theorems and nonlinear semigroup properties. We show that under the assumptions of low order nonlinearity, reversibility and the existence of certain feedback controls, the nonlinear system is exactly controllable. The constructive aspect of the theory allows the application of numerical simulation. An analog-digital realization diagram is discussed. Accurate numerical schemes are developed and error estimates are presented with concrete examples to illustrate the theory.