A control theory for complex specifications

控制理论是一门连接数学和工程的学科，其功能是为分析和控制综合问题提供理论，框架，原理和算法，这些问题出现在一系列应用学科中。其客户包括能源系统，生物医学工程，机电一体化，机器人，航空航天系统，纳米技术，运输系统，过程控制，制造业，生物学，生态学，经济学和其他领域。 在过去的200年里，控制理论一直专注于调节和跟踪问题。调节的常见示例是保持建筑物中的恒定温度或保持车辆巡航控制中的期望速度。通过旋转太阳能电池的表面以在白天持续面对太阳来优化太阳能电池的性能是跟踪的一个示例。跟踪和调节是简单的控制系统规范。 随着控制系统在高端工程系统和消费产品中的集成度越来越高，它们有望实现更丰富的规范，这些规范将调节和跟踪与安全要求、启动程序、逻辑规则等相结合。复杂规范的好例子是化学或核反应堆的启动，自动停车系统的要求，或双足机器人不同步态之间的转换。由于历史上强调调节和跟踪，即使是最简单的非传统规范的控制问题也没有已知的解决方法。 我们的研究计划涉及复杂规格的控制理论的发展。这是一个多步骤的奋进，涉及到控制系统内的基本数学结构的发现，确定它是否可以实现复杂的规范，以及具体的设计方法，可用于不同的应用领域的从业者的发展。

Control theory is a discipline bridging mathematics and engineering and its function is to supply the theories, frameworks, principles, and algorithms for analysis and control synthesis problems arising in a spectrum of application disciplines. Its clients include energy systems, biomedical engineering, mechatronics, robotics, aerospace systems, nanotechnology, transportation systems, process control, manufacturing, biology, ecology, economics, and other areas. Control theory has focused over the last 200 years on problems of regulation and tracking. Common examples of regulation are maintaining a constant temperature in a building or maintaining a desired speed in a vehicle cruise control. Optimizing a solar cell performance by rotating its surface to continually face the sun during daylight hours is an example of tracking. Tracking and regulation are simple control system specifications. As control systems become more integrated within high-end engineering systems as well as consumer products, they are expected to achieve richer specifications that intertwine regulation and tracking with safety requirements, startup procedures, logic rules, and so forth. Good examples of complex specifications are the startup of a chemical or nuclear reactor, requirements for an automated parking system, or transition between different gaits in a bipedal robot. Because of the historical emphasis on regulation and tracking, even the simplest control problems with non-traditional specifications have no known solution method. Our research program concerns the development of a control theory for complex specifications. This is a multistep endeavor involving both the discovery of fundamental mathematical structures within a control system that determine if it can achieve a complex specification, as well as the development of concrete design methods that can be used by practitioners in diverse application fields.