Efficient control of disturbed industrial systems requires methods to handle complex and nondifferentiable performance criteria given by customers directly in the control design process. In the design of control laws, our works evaluates nonlinear performance criterion for nonlinear systems subject to additive disturbances. Model Predictive Control using barrier functions is proposed. First of all, the stability of the method is proven in the linear case using Lyapunov function and invariant set theories. The presented law is also improved by considering robust tube-based Model Predictive Control for systems subject to additive disturbances. The method is then extended to nonlinear systems that neural networks can model when the knowledge-based model is unknown. The stability in the nonlinear case is not proven, but the method has shown its efficiency for different applications.