Stability and Incremental Improvement of Suboptimal MPC Without Terminal Constraints

The stability of suboptimal model predictive control (MPC) without terminal constraints is investigated for continuous-time nonlinear systems under input constraints. Exponential stability and decay of the optimization error are guaranteed if the number of optimization steps in each sampling instant satisfies a lower bound that depends on the convergence ratio of the underlying optimization algorithm. The decay of the optimization error shows the incremental improvement of the suboptimal MPC scheme.