Nonlinear self-triggered MPC without terminal conditions for trajectory tracking

In this article, a trajectory tracking problem for a class of nonlinear discrete-time systems is investigated by a model predictive control (MPC) strategy. Compared with the standard MPC strategy, the proposed MPC strategy removes terminal conditions, including terminal penalty terms and terminal state constraints. This novel design requires fewer parameters to be determined, which leads to high practicability. Moreover, to reduce the computational burden, a self-triggered mechanism is presented by using the discrepancy in the cost function between adjacent time instants. Then, an additional compensation variable is designed for the redundancy from the self-triggered mechanism. Finally, we present a mathematical proof for the recursive feasibility of the optimization problem. The effectiveness and practicality of the proposed self-triggered MPC strategy are verified through simulation examples and experimental results on a mobile vehicle experimental platform.