论文标题
基于有限地平线优化的控制的稳定性无终端重量
Stability of Finite Horizon Optimisation based Control without Terminal Weight
论文作者
论文摘要
本文介绍了模型预测控制（MPC）的稳定分析工具，其中通过在有限的地平线上优化成本函数来生成控制动作。 MPC的稳定性分析有限，但没有末端重量是一个众所周知的具有挑战性的问题。我们根据与阶段成本相关的辅助一步优化定义了一个新的值函数，即最佳的一步值函数（OSVF）。结果表明，如果OSVF是（局部）控制Lyapunov函数（CLF），则可以使有限的地平线MPC渐近稳定。更具体地说，通过利用OSFV的CLF属性来构建承包终端集，提出了一种新的稳定MPC算法（CMPC）。我们表明，在OSVF为CLF的情况下，CMPC是可行的，并保证稳定性。讨论了检查此条件和最大终端集的估计。提供了数值示例，以证明所提出的稳定性条件和相应的CMPC算法的有效性。
This paper presents a stability analysis tool for model predictive control (MPC) where control action is generated by optimising a cost function over a finite horizon. Stability analysis of MPC with a limited horizon but without terminal weight is a well known challenging problem. We define a new value function based on an auxiliary one-step optimisation related to stage cost, namely optimal one-step value function (OSVF). It is shown that a finite horizon MPC can be made to be asymptotically stable if OSVF is a (local) control Lyapunov function (CLF). More specifically, by exploiting the CLF property of OSFV to construct a contractive terminal set, a new stabilising MPC algorithm (CMPC) is proposed. We show that CMPC is recursively feasible and guarantees stability under the condition that OSVF is a CLF. Checking this condition and estimation of the maximal terminal set are discussed. Numerical examples are presented to demonstrate the effectiveness of the proposed stability condition and corresponding CMPC algorithm.
