Drift Instabilities in Underexcited Adaptive Systems

目前在理论文献中占主导地位的自适应控制算法最近被证明当用于证明其理想化行为的假设被违反时表现不佳。尽管这种违规行为在实践中无疑会发生，但自适应控制器在各种应用中一再被证明是成功的。这项研究将集中于消除由于当前不切实际的理论限制而造成的理论与实践之间的差距，即控制器结构足以任意修改对象行为的所有模式。因此，这项研究的目的是开发一个理论框架来描述并随后改进受限复杂性自适应控制器的鲁棒性。主要的研究方向是描述受限复杂性自适应控制中不期望的参数估计漂移，以及在对现有算法中的稳定/不稳定机制有更好的理解的情况下生成和评估算法修正。

Adaptive control algorithms presently dominating the theoretical literature have recently been demonstrated to behave poorly when assumptions used to prove their idealized behavior are violated. Though such violations undoubtedly occur in practice, adaptive controllers have been repeatedly documented as successful in a variety of applications. This research will focus on eliminating the theory-practice gap due to the impractical, current theoretical limitation that the controller structure be sufficient to arbitrarily modify all modes of the plant behavior. Thus, the aim of this research is the development of a theoretical framework for describing, and subsequently improving, the robustness of restricted complexity adaptive controllers. The major directions to be pursued are the characterization of undesirable parameter estimate drift in restricted complexity adaptive control as well as generation and evaluation of algorithm fixes given improved understanding of stability/instability mechanisms in existing algorithms.