Parameterization for Robustness in Linear Systems

多输入多输出系统设计中的一个经典问题是对具有鲁棒、开关或非开关动态输出反馈补偿器的对象或对象族进行分类，并满足一组特定的设计约束，即灵敏度最小化、镇定、极点配置、干扰解耦、跟踪等。并非所有的植物和补偿器都满足一组特定的设计约束，因此对那些满足的植物和补偿器进行参数化是有意义的。此外，为了提出和分析作为一种递归算法在植物补偿器对参数化空间上的辨识和自适应控制问题，了解这种参数化的几何性质是有意义的。本研究计划分为三个部分。首先从参数辨识和自适应控制的角度研究参数化问题。随后将参数辨识问题作为参数空间上的递归算法进行研究，并进行局部收敛性和全局收敛性分析。最后研究了对象参数和补偿器参数实时变化的自适应控制问题。研究的目的是参数化某些类型的系统，使其具有鲁棒输出反馈补偿，并满足一定的设计约束。预计这种参数化将允许为所考虑的系统开发新的稳定、识别和自适应控制算法。

A classical problem in multi input multi output system design is to classify plants or families of plants that admit a robust, switching or nonswitching, dynamic output feedback compensator and satisfy a specific set of design constraints viz. sensitivity minimization, stabilization, pole assignment, disturbance decoupling, tracking, etc. Not all plants and compensators satisfy a specific set of design constraints and it is therefore of interest to parameterize those plants and compensators that do. Furthermore, in order to pose and analyze identification and adaptive control problems as a recursive algorithm on the parameterized space of plant-compensator pair, it is of interest to understand the geometric properties of such a parameterization. This research programme is divided in three parts. First the parameterization problem will be studied with a view towards parameter- identification and adaptive control. Subsequently the parameter- identification problem will be studied as a recursive algorithm on the parameter space and the analysis of both local and global convergence will be carried out. Finally the adaptive control problem wherein the parameters of the plant and the compensator vary in real time will be studied. The aim of the research is to parameterize certain classes of systems which admit robust output feedback compensation and satisfy certain design constraints. It is expected that such parameterizations will allow the development of new classes of stabilization, identification and adaptive control algorithms for the classes of systems being considered.