Sampled-Data and Discrete-Time Control of Infinite Dimensional Systems

两种类型的控制问题被认为是控制器设计的信息是有限的。 在一类问题中，输出数据仅在离散时间可用，因此使用采样数据控制代替连续时间控制。 项目包括如何设计偏微分方程的采样数据控制器;分析哪些系统可以通过简单的采样数据控制器来稳定;如何修改连续时间反馈控制器，使其成为有效的采样数据控制器;分析采样数据控制器的性能如何与相关的连续时间控制器进行比较;以及采样数据控制器的设计，该控制器跟踪外部参考信号，即使在关于被控对象的信息非常少的情况下也是如此。 在这些项目中，感兴趣的不仅是采样数据控制设计可以做什么，而且它的局限性。 由于离散时间控制器只能在有限的频率响应下工作，而无穷维系统往往具有不可忽略的高频效应，因此无穷维系统的采样数据和离散时间控制非常微妙。 此外，考虑了由无穷维离散时间系统（如积分差分方程）建模的种群动力学问题。 种群生态学中的大多数此类问题具有高度不确定性的数据，我们将分析增长或衰减如何受到数据不确定性的影响。采样数据控制的发展部分是由数字电子学的进步推动的，这导致了越来越多的采样数据设计和控制算法的实现。 此外，在许多实际应用中，来自系统的输出数据通常仅在离散时间而不是在连续时间可用，因此知道如何处理此类数据具有实用价值。 拟议中的研究将解决有关无限维系统的采样数据控制设计的能力的基本问题。 种群生态学中的保护问题通常具有非常不确定的数据，这种不确定性会极大地影响濒危或入侵物种的生长或衰退。 无限维模型用于模拟种群的空间分布或生长阶段连续分布的情况。 这项研究将开发新的技术，并使用鲁棒控制理论的技术，来分析不确定数据对长期人口增长的影响。 这些技术将可用于解决类似的人口问题。 本科生和研究生研究人员将被纳入本研究计划。

Two types of control problems are considered where the information available for controller design is limited. In one type of problem, output data is available only at discrete times, so sampled-data control is used instead of continuous-time control. Projects include how to design sampled-data controllers for partial differential equations; an analysis of which systems can be stabilized by a simple sampled-data controller; how to modify continuous-time feedback controllers so that they are effective sampled-data controllers; an analysis of how the performance of a sampled-data controller compares to that of related continuous time controllers; and the design of sampled-data controllers which track an external reference signals, even when very little information about the plant is available. In these projects, the interest lies not only in what can be done with sampled-data control design, but also its limitations. Since a discrete time controller can operate with only limited frequency response, and infinite-dimensional systems often have high frequency effects which cannot be ignored, sampled-data and discrete-time control of infinite-dimensional systems is very delicate. In addition, population dynamics problems modeled by infinite-dimensional discrete-time systems, such as integro-difference equations, are considered. Most such problems in population ecology have highly uncertain data, and we will analyze how growth or decay is affected by the data uncertainties.The development of sampled-data control is motivated in part by advances in digital electronics, which has led increasingly to sampled-data design and implementation of control algorithms. Furthermore, in many practical applications output data from a system is often only available at discrete times rather than in continuous time, so it is of practical value to know how to deal with such data. The proposed research will address basic questions about the capabilities of sampled-data control design for infinite-dimensional systems. Conservation problems in population ecology typically have very uncertain data, and the growth or decay of an endangered or invasive species can be dramatically affected by this uncertainty. Infinite-dimensional models are used to model spatial spread of a population or in cases where the growth stages are continuously distributed. This research will develop new techniques, and use techniques from robust control theory, to analyze the effect of uncertain data on long-term population growth. These techniques will be available and accessible for use on similar population problems. Undergraduate and graduate researchers will be incorporated into this research program.