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

该项目的目标是研究与设计鲁棒和多变量自适应控制系统有关的问题。稳健性被定义为算法在存在扰动和未建模动态的情况下保持稳定性的能力。我们计划应用平均方法来研究稳健性与用于自适应的误差方程之间的关系。将调查调谐值的存在和位置。这些值确定在存在未建模动态的情况下控制器参数收敛的位置。这一分析有望使人们更好地理解自适应控制中的鲁棒性，并为设计提供新的方法。我们还将关注多变量自适应控制系统的设计。我们计划研究能保证参数收敛到唯一点，且所需参数最少的参数化方法。这些属性是收敛、健壮性和实施考虑因素所必需的。还将研究设计多变量自适应控制系统所需的先验信息，以及从输入/输出测量中获得这些信息的方法。将进行实验以验证理论的结果，并引发新的问题。我们期望这项研究将有助于改进自适应控制系统的设计方法，并使这些方法得到更广泛的应用。

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.