Input-to-state stabilizing MPC for neutrally stable linear systems subject to input constraints

MPC (model predictive control) is representative of control methods which are able to handle physical constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global asymptotic stability can be obtained. A globally stabilizing finite-horizon MPC has lately been suggested for the neutrally stable systems using a nonquadratic terminal cost which consists of cubic as well as quadratic functions of the state. In this paper, an input-to-state-stabilizing MPC is proposed for the discrete-time input-constrained neutrally stable system using a non-quadratic terminal cost which is similar to that used in the global stabilizing MPC, provided that the external disturbance is sufficiently small. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.