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、切换或非切换的动态输出反馈补偿器并满足一组特定设计约束的对象或对象族进行分类。灵敏度最小化、镇定、极点配置、干扰解耦、跟踪等。并不是所有的对象和补偿器都满足一组特定的设计约束，因此对那些满足特定设计约束的对象和补偿器进行参数化是很有意义的。此外，为了将辨识和自适应控制问题作为递推算法在对象-补偿器对的参数化空间上提出和分析，了解这种参数化的几何性质是很有意义的。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了系统的参数化问题。随后，将参数辨识问题作为参数空间上的递推算法进行研究，并将进行局部和全局收敛分析。最后研究了被控对象和补偿器参数实时变化的自适应控制问题。该研究的目的是将允许鲁棒输出反馈补偿并满足一定设计约束的某些系统类进行参数化。预计这种参数化将允许为所考虑的一类系统开发新的镇定、辨识和自适应控制算法。

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.