In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is derived for the setting where a limited number of iterations of the optimizer are carried out per sampling time. Under the assumption of Lipschitz continuity of the solution, we explicitly construct a Lyapunov function for the combined system-optimizer dynamics, which shows that asymptotic stability can be obtained if the sampling time is sufficiently short. The results constitute an extension to existing attractivity results which hold in the simplified setting where inequality constraints are either not present or inactive in the region of attraction considered. Moreover, with respect to the established results on robust asymptotic stability of suboptimal model predictive control, we develop a framework that takes into account the optimizer’s dynamics and does not require decrease of the objective function across iterates. By extending these results, the gap between theory and practice of the standard real-time iteration strategy is bridged and asymptotic stability for a broader class of methods is guaranteed.

在本文中，提出了一类非精确非线性模型预测控制方法的渐近稳定性证明。考虑了一般的 Q 线性收敛在线优化方法，并为每个采样时间执行有限次数的优化器迭代的设置导出了渐近稳定性结果。在解的 Lipschitz 连续性假设下，我们显式构造了一个Lyapunov 函数对于组合系统优化器动力学，这表明如果采样时间足够短，可以获得渐近稳定性。结果构成了现有吸引力结果的扩展，这些结果适用于简化设置，即所考虑的吸引力区域中不存在不平等约束或不活动。此外，关于次优模型预测控制的鲁棒渐近稳定性的既定结果，我们开发了一个框架，该框架考虑了优化器的动力学，并且不需要在迭代中减少目标函数。通过扩展这些结果，弥合了标准实时迭代策略的理论与实践之间的差距，并保证了更广泛的方法类别的渐近稳定性。