Stabilization of linear predictive control systems with softening constraints

Model predictive control(MPC) instabilities caused by a short predictive horizon can be stabilized using a predictive contractive constraint for a linear predictive control system with softening constraints.The state contractive constraint concept is extended to a predictive input/output contractive constraint with convergence factors.With the open-loop optimal performance index based on the Lyapunov function,Lyapunov's second theorem is used to show that the MPC closed-loop system with the designed constraint is nominally stable.Simulations with a cascade integral object indicate that the method can stabilize a closed-loop system and the convergence factors can be used to adjust the convergence speed.Smaller convergence factors lead to the faster closed-loop system convergence.