Robust model predictive control of constrained non-linear systems: adopting the non-squared integrand objective function

This study presents a novel robust model predictive control (MPC) method for constrained non-linear systems with control constraints and external disturbances. The control signal is obtained by optimising an objective function consisting of two terms: an integral non-squared stage cost and a non-squared terminal cost. The terminal weighting matrix is designed appropriately such that: (i) the terminal cost serves as a control Lyapunov function; and (ii) the resultant finite horizon cost can be treated as a quasi-infinite horizon cost. Provided that the Jacobian linearisation of the system to be controlled is stabilisable and the optimisation is initially feasible, sufficient conditions ensuring the recursive feasibility of the optimisation and the robust stability of the closed-loop system are established. It is shown that the conditions rely on an appropriate design of the sampling interval with respect to a certain given disturbance level. The effectiveness of the proposed method is illustrated through a numerical example.