Research Initiation Award: Adaptive Control System Redesignfor Improving Transient Performance

由于观察到大多数现有的关于自适应控制的结果本质上是定性的，并且仅涉及渐近性能(例如稳定性和鲁棒性)，该项目的主要重点是为自适应系统开发建设性的设计方法，该方法同时考虑了暂态响应和稳态响应。通过在控制系统中加入辨识方案，并用未知参数的估计值代替未知参数，设计了一个标准的自适应控制系统。这种设计方法在适应性文献中被称为“确定性等价原则”(CEP)。这并不能保证所得到的系统具有良好的暂态性能，因为它会将辨识误差传递到设计阶段。在这个项目中，我们将重新设计自适应控制系统，以克服CEP设计的内在约束，从而提高性能。为了实现这一目标，提出了一种新的设计方法--建模误差补偿(MEC)。为了适应错误识别和CEP设计造成的错误，我们将使用有关识别质量的信息在CEP设计之上引入额外的控制信号。该策略提供了一种通过CEP设计无法获得的补偿机制--它补偿了误识别的影响。我们建议从理论和设计两个方面研究所提出的自适应方案。我们还将研究MEC在一类非自适应设计中的应用，以寻找自适应系统是否以及何时会优于非自适应系统的问题的答案。

Motivated by the observation that most existing results on adaptive control are qualitative in nature and address only asymptotic performance (such as stability and robustness), the main focus of the proposed project is to develop constructive design approaches for adaptive systems which take into account both the transient response and the steady-state response. A standard adaptive control system is designed by incorporating an identification scheme into the control system and replacing the unknown parameters with their estimates. Such design methodology is referred to as the "certainty equivalence principle"(CEP) in adaptive literature. It does not guarantee good transient performance of the resulting system since it passes on the error of identification to the design stage. In this project, we will redesign adaptive control systems to overcome the inherent constraint due to CEP design, and thus improve performance. A new design technique -- modeling error compensation (MEC) -- is proposed to achieve this goal. To accommodate the error due to misidentification and CEP design, we will use the information about the quality of the identification to introduce an additional control signal on top of the CEP design. This strategy provides a compensation mechanism that cannot be obtained via CEP design -- it compensates the effects of misidentification. We propose to study both theoretical and design aspects of the proposed adaptive scheme. We will also study the application of MEC to a class of nonadaptive designs, to find answers for the question whether and when an adaptive system will outperform a nonadaptive system.