Decentralized Control Design with Limited Plant Model Information
2012 (English)Licentiate thesis, monograph (Other academic)
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 thesis. 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. An explicit minimizer of the competitive ratio is sought. As this minimizer might not be unique, we further search for the ones that are undominated, that is, there is no other control design strategy in the set of limited model information design strategies with a better closed-loop performance for all possible plants while maintaining the same worst-case ratio. 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. Surprisingly, the optimal control design strategy with limited model information is still a static one. This is the case even though the optimal decentralized state-feedback controller with full model information is dynamic. Finally, we discuss the design of dynamic controllers for disturbance accommodation under limited model information. This problem is of special interest because the best limited model information control design in this case is a dynamic control design strategy. The optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For constant disturbances, it is shown that this structure corresponds to proportional-integral control.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. , x, 137 p.
Trita-EE, ISSN 1653-5146 ; 2012:003
IdentifiersURN: urn:nbn:se:kth:diva-63858ISBN: 978-91-7501-238-4OAI: oai:DiVA.org:kth-63858DiVA: diva2:482894
2012-02-24, Q2, Osquldas vag 10, Stockholm, 10:15 (English)
Shamma, Jeff S., Professor
Johansson, Karl Henrik, ProfessorGattami, Ather
C 201202012012-02-012012-01-242012-02-01Bibliographically approved