Estimation and Control with Bounded Data Uncertainties

该项目涉及具有有限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。为简便起见，将新方法分别称为BDU估计方法和BDU控制方法。它们基于新的约束游戏类型公式，允许设计师明确地将关于模型中不确定性大小界限的先验信息整合到问题陈述中。这样，不确定性的影响就不会被不必要地过分强调，超出了先验界限所隐含的范围；因此，过度保守的设计和过度敏感的设计将被避免。BDU公式的一个关键特征是几何洞察力（如正交性条件和投影）和递归（自适应或在线）技术，这些在经典的二次成本设计中广为人知并受到赞赏，可以在这个新的框架中追求。此外，存在与标准最小二乘解相同的计算工作量计算最优解的算法，从而使新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、状态空间公式和具有参数不确定性的模型的设计。应用跨越几个学科，包括图像处理，通信，自适应系统，估计和控制，将继续进行。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，并表明了潜在的未来发展。

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.