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。对这类混合动态过程的研究是现代工程系统分析和设计的核心。这项工作的目的是开发新的方法和计算机算法来解决混杂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的挑战性问题，例如安装在空间或水下平台上的多机器人系统、自主车辆的eET以及化工和制造工厂。所提出的工作使用了基于离散抽象的调节反馈控制的混合系统框架，它对于成功地解决一些开放的控制设计问题具有重要的意义。该方法利用连续动力学的离散近似或近似，并用拟决定论的概念加以适当的约束，以提供足够的信息，从而设计出满足控制要求的控制器。建议将分段线性化模型的初始控制综合结果推广到更一般的系统，并发展基于Lyapunov函数和基于PETRI网监督控制方法的附加设计方法。这项研究包括从制造和自动驾驶汽车领域探索实际应用，这项工作的影响将在理论和应用两个方面。特别是，它将为混杂系统的调节反馈控制提供一个理论设计框架，并将在可达性分析、混杂自动机和验证算法等领域得到应用。此外，它还将提供自治系统的控制算法，这些算法将在我们的复杂系统仿真设备上进行测试。

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.