Closed-form nonlinear MPC for multivariable nonlinear systems with different relative degree

For a class of multivariable nonlinear systems with different relative degree, a closed-form nonlinear model predictive controller is derived using Taylor approximation methods, where the nonlinear system is approximated by its Taylor series expansion to any chosen order. The stability of the developed nonlinear model predictive control is established. It is shown that design of the nonlinear MPC for nonlinear systems is as easy as design of the well known linear quadratic regulator (LQR) in many aspects.