论文标题
在不精确模型预测控制中，用于组合系统反射器动力学的Lyapunov函数
A Lyapunov Function for the Combined System-Optimizer Dynamics in Inexact Model Predictive Control
论文作者
论文摘要
在本文中，提出了一类无需非线性模型预测控制方法的渐近稳定性证明。考虑了一般Q线性收敛的在线优化方法，并在每个采样时间进行优化器的迭代次数有限的设置中得出了渐近稳定性结果。在溶液的Lipschitz连续性的假设下，我们明确地为组合的系统反射器动力学构建了Lyapunov函数，该功能表明，如果采样时间足够短，则可以获得渐近稳定性。该结果构成了现有的吸引力结果的扩展，该结果在简化的设置中存在，其中不等式约束在所考虑的吸引力区域中不存在或不活动。此外，就次优模型预测控制的鲁棒渐近稳定性而建立的结果，我们开发了一个框架，该框架考虑了优化器的动力学，并且不需要降低跨迭代元素的目标函数。通过扩展这些结果，可以保证标准实时迭代策略的理论与实践之间的差距，并保证更广泛的方法的渐近稳定性。
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.
