Estimation and Control with Bounded Data Uncertainties

该项目研究了具有有界数据不确定性的输入-输出和状态空间模型的估计和控制策略的发展。为简明起见，新方法将称为BDU估计方法和BDU控制方法。它们基于新的受约束的博弈型公式，允许设计者在问题陈述中明确地将关于模型中不确定性大小的界限的先验信息合并到问题陈述中。这样，不确定因素的影响将不会被不必要地过度强调超出先验界，从而避免过于保守的设计以及过于敏感的设计。BDU公式的一个关键特征是可以在这个新的框架中追求几何洞察力(如正交性条件和投影)和递归(自适应或在线)技术，这些技术对于经典的二次成本设计是广为人知和欣赏的。此外，计算最优解的算法与标准最小二乘解的计算量相同，从而使新的公式具有实际应用的吸引力。这项工作的一个主要主题将是强调几何结构、状态空间公式以及具有参数不确定性的模型的设计。应用将跨越几个学科，包括图像处理、通信、自适应系统、估计和控制。尽管取得了令人感兴趣的初步结果，但仍有几个问题有待解决，并预示着未来的潜在发展。

This project deals with the development of estimation and control strategies for input-output and state-space models with bounded data uncertainties. The new methods will be referred to as BDU estimation and BDU control methods for brevity. They are based on new constrained game-type formulations that allow the designer to explicitly incorporate into the problem statement a-priori information about bounds on the sizes of the uncertainties in the models. In this way, the effect of uncertainties will not be unnecessarily over-emphasized beyound what is implied by the a-priori bounds; consequently, overly conservative designs, as well as overly sensitive designs, will be avoided.A Key feature of the BDU formulations is that geometric insights (such as orthogonality conditions and projections) and recursive (adaptive or online) techniques, which are widely known and appreciated for classical quadratic-cost designs, can be pursued in this new framework. Also, algorithms for computing optimal solutions with the same computational effort as standard least-squares solutions exist, thus making the new formulations attractive for practical use.A major theme in this work will be the emphasis on geometric constructions, on state-space formulations, and on design for models with parametric uncertainties. Applications accross several disciplines, including image processing, communications, adaptive systems, estimation, and control, will be pursued. Despite the interesting preliminary results, several issues remain open and indicate potential future developments.