Seminar Details
2012-08-28 (14.00) : On the Value of Model Information in Decentralized Control Design
At Euler building
Organized by Mathematical Engineering
Speaker :
Fahrad FAROKHI (KTH (Stockholm))
Abstract :
Large-scale control systems are often composed of several smaller interconnected units. For these systems, it is common to employ local controllers, which observe and act locally. At the heart of common control design procedures for distributed systems lies the often implicit assumption that the designer has access to the global plant model information when designing a local controller. However, there are several reasons why such plant model information would not be globally known. One reason could be that the designer wants the parameters of each local controller to only depend on local model information, so that the controllers are not modified if the model parameters of a particular subsystem change. It might also be the case that the design of each local controller is done by individual designers with no access to the global plant model, for instance, due to the fact that the designers refuse to share their model information since they consider it private. This class of problems, which we refer to as limited model information control design, is the topic of the presentation. In this presentation, first, we investigate the achievable closed-loop performance of discrete-time linear time-invariant plants under a separable quadratic cost performance with structured static state-feedback controllers. To do so, we introduce control design strategies as mappings, which construct controllers by accessing the plant model information in a constrained way according to a given design graph. We compare control design strategies using the competitive ratio as a performance metric, that is, we compare the worst case control performance for a given design strategy normalized with the optimal control performance based on full model information. We study the trade-off between the amount of model information exploited by a control design strategy and the best possible closed-loop performance. We generalize this setup to structured dynamic state-feedback controllers for H_2 performance. Finally, we discuss a very recent extension in which we generalize the set of applicable controllers to nonlinear and adaptive discrete-time systems to achieve a competitive ratio equal to one.