Inherent Stochastic Robustness of Model Predictive Control to Large and Infrequent Disturbances
Inherent Stochastic Robustness of Model Predictive Control to Large and Infrequent Disturbances
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DOI：
10.1109/tac.2021.3122365
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发表时间：
2022-10
影响因子：
6.8
通讯作者：
Robert D. McAllister;J. Rawlings
中科院分区：
文献类型：
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作者：
Robert D. McAllister;J. Rawlings
我们介绍了一类新的大型，不经常的干扰，以补充稳健性分析中通常考虑的小型持续干扰。这类新的干扰包括离散的干扰，这些干扰在考虑控制问题中的离散执行器和生产计划时会变得相关。为了适当说明这些干扰的不经常性质，我们定义了一种稳健性的随机形式。在适当的假设下，我们证明某些闭环系统受到较大的，不经常的干扰承认了siss- lyapunov的功能，并且在这种随机背景下很健壮。我们将这些结果应用于经济模型预测控制（MPC），并具有严格的耗散性名义系统和舞台成本，其中包括将MPC作为特殊情况，并证明经济MPC对大型，罕见的骚乱是可靠的。在没有耗散性假设的情况下，我们为经济MPC定义并建立了强大的渐近性能。我们提出了一个简单的跟踪问题，以说明这项工作的结果以及生产计划（经济MPC）问题，以证明该分析与实际应用的相关性。
We introduce a new class of large, infrequent disturbances to complement the small, persistent disturbances typically considered in robustness analysis. This new class of disturbances includes discrete disturbances that become pertinent when considering discrete actuators and production scheduling in control problems. To properly account for the infrequent nature of these disturbances, we define a stochastic form of robustness. Under suitable assumptions, we prove that certain closed-loop systems subject to large, infrequent disturbances admit an SISS-Lyapunov function and are robust in this stochastic context. We apply these results to economic model predictive control (MPC) with a strictly dissipative nominal system and stage cost, which includes tracking MPC as a special case, and prove that economic MPC is robust to large, infrequent disturbances. Without dissipativity assumptions, we define and establish robust asymptotic performance for economic MPC. We present a simple tracking problem to illustrate the results of this work, and a production scheduling (economic MPC) problem, to demonstrate the relevance of this analysis to practical applications.