Regulatory Control of Hybrid Systems Based on Discrete Abstractions: Theory & Applications

复杂系统的动力学行为通常涉及连续动力学和离散动力学的相互作用。这种混合动态过程的研究是现代工程系统分析和设计的核心。提出的工作的目的是开发新的方法和计算机算法来解决混合系统中重要的反馈控制问题。这项工作的动机是需要解决现代复杂工程应用中控制和协调方面的挑战性问题，例如安装在太空或水下平台上的多个机器人系统，自动驾驶车辆的设备，以及化学和制造工厂。所提出的工作使用基于离散抽象的混合系统框架进行调节反馈控制，并且它在成功解决许多开放控制设计问题方面具有重要意义。所提出的方法利用连续动力学的离散近似或抽象，适当地使用准量纲概念重新定义，以提供足够的信息，以便可以设计控制器以满足控制规范。建议将使用分段线性模型的初始控制综合结果扩展到更一般的系统，并开发基于李雅普诺夫函数和Petri网监督控制方法的附加设计方法。拟议的研究包括探索制造业和自动驾驶汽车领域的实际应用。这项工作的影响将在理论和应用两个方面。特别是，它将为混合系统的调节反馈控制提供理论设计框架，并且还将影响可达性分析，混合自动机和验证算法领域。此外，它将为自主系统的控制提供算法，这些算法将在我们的复杂系统仿真设施中进行测试。

The dynamic behavior of complex systems typically involves the interaction of continuous anddiscrete dynamics. The study of such hybrid dynamic processes is central in the analysis anddesign of modern engineering systems. The aim of the proposed work is to develop new method-ologies and computer algorithms to solve important feedback control problems in hybrid systems.This work is motivated by the need to address challenging problems in the control and coordi-nation of modern complex engineering applications such as multiple robotic systems mounted onspace or underwater platforms, eets of autonomous vehicles, and chemical and manufacturingplants.The proposed work uses a hybrid system framework for regulatory feedback control that is basedon discrete abstractions and it o_ers signi_cant promise in addressing successfully a number ofopen control design issues. The proposed approach utilizes discrete approximations or abstrac-tions of the continuous dynamics, which are re_ned appropriately using the concept of quasideter-minism, to provide adequate information so that a controller can be designed to meet the controlspeci_cations. It is proposed to extend initial control synthesis results that use piecewise-linearmodels to more general systems, and also develop additional design methods based on Lyapunovfunctions and on Petri net supervisory control methodologies. The proposed research includes theexploration of realistic applications from the areas of manufacturing and autonomous vehicles.The impact of this work will be in both theory and applications. In particular, it will providea theoretical design framework for regulatory feedback control of hybrid systems and will alsoin uence the areas of reachability analysis, hybrid automata, and veri_cation algorithms. Fur-thermore, it will provide algorithms for the control of autonomous systems which will be testedon our Complex Systems Simulation Facility.