Research Initiation: Design of Robust and Multivariable Adaptive Control Systems - (REU SUPPLEMENT)

该项目的目标是研究与 鲁棒和多变量自适应控制系统的设计。 鲁棒性被定义为算法保持 存在扰动和未建模动态时的稳定性。 我们 计划采用平均法研究 鲁棒性和用于自适应的误差方程。 存在 并且将研究调谐值的位置。 这些值 确定控制器参数在存在以下情况下收敛于何处： 未建模的动态 分析预计将导致更好的 了解自适应控制中的鲁棒性，并提出新的 设计的方法。 我们还将关注 多变量自适应控制系统 我们计划学习 参数化，保证参数收敛到一个唯一 点，并且需要最少数量的参数。 这些属性 对于收敛性、鲁棒性和实现来说是理想的 注意事项。 多变量设计所需的先验信息 自适应控制系统也将研究，以及方法 以从输入/输出测量获得该信息。 将进行实验来验证理论的结果， 并激发新的问题。 我们预计这项研究将 有助于改进自适应控制的设计方法 系统，以及这些方法的更广泛应用。

The objective of the project is to study problems related to the design of robust and multivariable adaptive control systems. Robustness is defined as the ability of an algorithm to maintain stability in the presence of disturbances and unmoldeled dynamics. We plan to apply averaging methods to study the relationship between robustness and the error equation used for adaptation. The existence and location of the tuned values will be investigated. These values determine where the controller parameters converge in the presence of unmodeled dynamics. The analysis is expected to lead to a better understanding of robustness in adaptive control, and to suggest new approaches for design. We will also be concerned with the design of multivariable adaptive control systems. We plan to study parameterizations which guarantee parameter convergence to a unique point, and require a minimal number of parameters. These properties are desirable for convergence, robustness, and implementation considerations. The prior information needed to design multivariable adaptive control systems will also be investigated, together with ways to obtain this information from input/output measurements. Experiments will be carried out to validate the results of the theory, and motivate new problems. We expect that the research will contribute to improve design methodologies for adaptive control systems, and to a wider application of these methods.