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。本论文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，其动机是解决现代复杂工程应用中具有挑战性的控制和协调问题，如安装在空间或水下平台上的多机器人系统，自动驾驶车辆的eets，提出的工作使用一个混合系统框架的调节反馈控制是基于离散的抽象和它oers重大的承诺，成功地解决了一些开放的控制设计问题。所提出的方法利用离散近似或连续动态的抽象，适当地使用拟定的概念，以提供足够的信息，以便控制器可以设计，以满足控制规格。建议将初始控制合成结果，使用分段线性模型更一般的系统，并开发其他设计方法的基础上Lyapunovfunctions和Petri网监督控制方法。该研究计划包括对制造业和自动驾驶汽车领域的实际应用进行探索，其影响将体现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，并将对可达性分析、混杂自动机和验证算法等领域产生影响。此外，它将提供算法控制的自治系统，将测试我们的复杂系统仿真设施。

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.