Model predictive control under model structure uncertainty for stochastic systems

在基于模型的控制中，由于模型结构和/或参数不足而导致的模型不确定性普遍存在。在各种控制应用中，系统动态的时变特性(由于对象和/或干扰动态的变化，或系统故障和故障的发生)通常增加了与控制器调试期间识别的系统模型相关的不确定性。随着时间的推移，模型不确定性的增加最终会导致闭环系统控制性能的下降，这通常需要对模型进行某种形式的维护以恢复控制性能。本研究的主要目的是开发一种不确定系统的集成随机最优控制与主动学习的框架，以便于在线模型结构自适应。本项目的主要研究目标是研究两类不同的模型结构不确定性问题：I类--系统存在几个相互竞争的模型结构(例如，由于未知的反应动力学或系统故障的发生)，并且未知哪种模型结构提供了对系统动力学的最准确的描述；II类--本质随机系统的动力学由一系列跨越操作区域的模型描述(例如，每个模型代表不同的操作模式)，并且未知何时发生系统模型之间的转换。这项研究将集中于开发具有集成学习能力的随机模型预测控制(SMPC)公式，用于I类和II类的主动模型结构自适应。受对偶控制范式的启发，将开展三项研究工作：1.开发具有集成输入设计的随机最优控制框架，用于主动模型结构识别；2)开发SMPC框架，作为不同模型结构之间的随机系统在不同模式/行为之间的转换；以及3.通过闭环实验验证SMPC方法在大气压等离子射流(APPJ)实时控制中的有效性。正在研究的等离子体喷射应用的典型例子包括热敏(生物)材料的治疗和医学治疗。拟议的教育和外展活动包括指导本科生，为外展目的开发课程，以及在服务不足的学区进行科学课程。

Model uncertainty due to inadequate model structure and/or parameters is prevalent in model-based control. In various control applications, the time-varying nature of system dynamics (due to changes in plant and/or disturbance dynamics, or occurrence of system faults and failures) typically increases the uncertainty associated with a system model identified during controller commissioning. The increased model uncertainty over time can eventually lead to degradation of the closed-loop control performance, which will often necessitate some form of model maintenance to restore the control performance. The overarching goal of this research is to develop a framework for integrated stochastic optimal control and active learning of uncertain systems to facilitate online model structure adaptation. The main research objective of this project is to investigate two different classes of model structure uncertainty problems: Class I-several rival model structures exist for a system (e.g., due to unknown reaction kinetics, or occurrence of system faults) and it is unknown which model structure provides the most accurate description of system dynamics; and Class II-the dynamics of an intrinsically stochastic system are described by a series of models across an operating region (e.g., each model represents a different operating mode) and it is unknown when the transition between the system models occurs. The proposed research will focus on the development of stochastic model predictive control (SMPC) formulations with integrated learning capability for active model structure adaptation for both Classes I and II. Inspired by the dual control paradigm, three research tasks will be pursued: 1. Development of a computationally tractable framework for stochastic optimal control with integrated input design for active model structure discrimination; 2. Development of a SMPC framework that actively switches between different model structures as a stochastic system transitions between different modes/behaviors; and 3. Demonstration of the effectiveness of the SMPC approaches for real-time control of an atmospheric-pressure plasma jet (APPJ) through closed-loop experiments. Prototypical examples of applications of the plasma jet under study include treatment of heat-sensitive (bio)materials and medical therapy. The proposed educational and outreach activities include mentoring undergraduate students, curriculum development for outreach purposes, and conducting science lessons in an underserved school district.