Estimation and Control with Bounded Data Uncertainties

本计画主要研究输入输出与状态空间模型之估计与控制策略。 为简洁起见，新方法将被称为BDU估计和BDU控制方法。 它们是基于新的约束博弈型配方，使设计师明确纳入到问题的陈述先验信息的边界上的模型中的不确定性的大小。 这样，不确定性的影响就不会被不必要地过分强调，超出先验界限所暗示的范围;因此，可以避免过于保守的设计，也可以避免过于敏感的设计。BDU公式的一个关键特点是，（如正交条件和投影）和递归（自适应或在线）技术，这是广为人知的和经典的二次成本设计的赞赏，可以在这个新的框架中进行。 此外，算法计算的最优解与标准的最小二乘解决方案存在相同的计算工作量，从而使新的配方有吸引力的实际用途。在这项工作中的一个主要主题将是强调几何结构，状态空间配方，和设计的模型参数的不确定性。 跨几个学科的应用，包括图像处理，通信，自适应系统，估计和控制，将追求。 尽管取得了令人感兴趣的初步结果，但仍有若干问题有待解决，这些问题表明了未来的潜在发展。

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.