Unconstrained NCGPC with a guaranteed closed-loop stability: Case of nonlinear SISO systems with the relative degree greater than four

This paper presents a new approach to solve a tracking problem for nonlinear minimum-phase systems with a relative degree greater than four by applying nonlinear continuous-time generalized predictive control (NCGPC). In fact, these systems present the particularity to have an unstable closed-loop behavior even if the derived NCGPC control law is applied to them. Indeed, the Routh-Hurwitz criterion of stability is not verified for the resulted linear closed-loop system. Inspired by the paper of Chen et al., see, our proposition consists in adding a specific (linear) term of correction to the receding horizon performance index such that the derived control law yields a companion form of controllability and observability for the linear closed-loop system. Therefore a pole-placement can be done and hence closed-loop stability achieved. Nevertheless, when the relative degree is less than or equal to four, this specific (linear) term is not necessary to be added to the criterion because closed-loop stability of the resulting linear system is achieved, by construction. Simulation results are presented to highlight the efficiency of the approach.