Research Initiation Award: Adaptive Quantification of Model Uncertainties

合理的不确定性界是鲁棒控制和自适应控制的关键。不充分的不确定性边界描述将导致分析要么过于保守，要么过于乐观。尽管这一事实得到广泛认可，但不确定性的量化问题却很少受到重视。本研究旨在发展一种新的方法来获得真实植物的估计，以及不确定度的频率上限。一个出发点是用合理逼近法对不确定性进行自适应量化，该方法将辨识、插值和逼近很好地结合起来。初步结果表明，所提出的方法为不确定性提供了现实的边界。这使我们相信有进一步探索的巨大潜力。概述了进行这项研究的预期策略。预期结果的潜在好处和影响被认为是广泛的，包括对不确定性影响的理解和处理的新见解。鲁棒控制与自适应控制的结合，故障检测的新方法等。

A key element needed in robust control and adaptive control is a reasonable uncertainty bound. An inadequate uncertainty bound description will cause analysis to be either overly conservative or dangerously optimistic. Despite this widely appreciated fact, the problem of the quantification of uncertainty has received scant attention. The research intends to develop a new methodology for obtaining an estimate of the true plant as well as a frequency upper bound on the uncertainty. A starting point is the adaptive quantification of uncertainties by rational approximation which combines identification, interpolation and approximation nicely. Preliminary results show that the methods proposed provide realistic bounds for the uncertainty. This encourages us to believe that there is considerable potential for further exploration. The expected strategies for conducting this research are outlined. The potential benefits and the implications of the expected results are believed to be wide-ranging and include new insights into the understanding and treatment of the effects of the uncertainty, integration of robust control and adaptive control, new method for fault detection and so on.