不精确模型预测控制中系统-优化器组合动态的李雅普诺夫函数
A Lyapunov Function for the Combined System-Optimizer Dynamics in Inexact Model Predictive Control
摘要：
本文对一类不精确非线性模型预测控制方法给出了渐近稳定性证明。一般的Q-线性收敛的在线最优化方法被认为是一个渐近稳定性的结果是来自设置在有限数量的迭代优化器进行每个采样时间。在解的Lipschitz连续性的假设下，我们构造了一个李雅普诺夫函数，证明了在采样时间足够短的情况下，系统的渐近稳定性是可以实现的.结果构成了现有的吸引力的结果，在简化的设置，其中不等式约束是不存在或不活跃的吸引力考虑的区域中持有的扩展。此外，相对于已建立的结果鲁棒渐近稳定性的次优模型预测控制，我们开发了一个框架，考虑到优化器的动态，不需要减少的目标函数跨越迭代。通过推广这些结果，弥合了标准实时迭代策略的理论与实践之间的差距，并保证了更广泛的一类方法的渐近稳定性。
英文摘要：
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.
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