Research Initiation Award: Parameter Estimation in Adaptive Control

该研究的目的是分析和量化在自适应控制系统中具有预期应用的估值器的设计。人们的兴趣主要集中在在存在不确定性的情况下闭环系统性能的某些方面，特别是防止闭环系统信号在短时间内达到过大的幅度，即通常所说的“突发”现象。这种不良现象具有很大的实际意义，特别是在自适应控制器的真正非线性性质非常明显的弱激励系统的情况下。我们的计划是调查估计器的性质，估计器的设计是通过信号能量和幅度标准来进行的。虽然最小化估计误差的最大幅度通常会导致增加维度的线性规划问题，但为了缓解这一问题，将考虑递归次优解。初步调查表明，这些技术允许在设计自适应系统时考虑幅度，并更有效地利用现有的测量。将特别强调将这一方法扩展到时变系统，并评估相关的性能权衡。期望研究结果对实际可接受的自适应控制器的设计有重要的贡献。

The objective of the research is to analyze and quantify the design of estimators with intended application in adaptive control systems. Interest is mainly focused on certain aspects of closed-loop performance in the presence of uncertainty and, particularly, on preventing the closed loop signals from reaching excessively large magnitude for short time periods, commonly known as "burst" phenomena. Such undesirable phenomena are of great practical significance, especially in cases of poorly excited systems where the true nonlinear nature of adaptive controllers is highly pronounced. The plan is to investigate the properties of estimators whose design is performed via signal energy as well as amplitude criteria. Although the minimization of the maximum amplitude of the estimation error typically leads to a linear programming problem of increasing dimensionality, recursive suboptimal solutions will be considered in order to alleviate this problem. The preliminary investigations indicate that these techniques allow for amplitude considerations in the design of adaptive systems and for a more efficient use of the available measurements. Particular emphasis will be given to the extension of this approach to time-varying systems and the assessment of the associated performance trade-offs. It is expected that the results of the research will make a significant contribution in the design of practically acceptable adaptive controllers.