Distributed control design with local model information and guaranteed stability

作者: Frederik Deroo , Martin Meinel , Michael Ulbrich , Sandra Hirche

DOI: 10.3182/20140824-6-ZA-1003.00917

关键词: Stability (learning theory)Matrix (mathematics)Gradient descentControl theoryOptimal controlTerm (time)Mathematical optimizationComputer scienceDistributed algorithmModel predictive control

摘要: Abstract Most results on distributed control design of large-scale interconnected systems assume a central designer with global model knowledge. The wish for privacy subsystem data raises the desire to find methods determine an optimal law without centralized knowledge, i.e. in fashion. In this paper we present method guaranteed stability minimize infinite horizon LQ cost functional. introduction adjoint states allows iteratively optimize feedback matrix using gradient descent way, based finite formulation. Inspired by ideas stabilizing predictive control, terminal term is used, which gives bound functional and ensures stability. A presented that are validated numerical experiments.

参考文章(18)
Michael Gerers, Robert P. Bithmead, Vincent Wertz, Adaptive Optimal Control: The Thinking Man's G.P.C. Prentice Hall Professional Technical Reference. ,(1991)
Farhad Farokhi, Cédric Langbort, Karl H. Johansson, Optimal structured static state-feedback control design with limited model information for fully-actuated systems Automatica. ,vol. 49, pp. 326- 337 ,(2013) , 10.1016/J.AUTOMATICA.2012.10.004
Martin Meinel, Michael Ulbrich, Sebastian Albrecht, A class of distributed optimization methods with event-triggered communication Computational Optimization and Applications. ,vol. 57, pp. 517- 553 ,(2014) , 10.1007/S10589-013-9609-9
Frederik Deroo, Michael Ulbrich, Brian D. O. Anderson, Sandra Hirche, Accelerated iterative distributed controller synthesis with a Barzilai-Borwein step size 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). pp. 4864- 4870 ,(2012) , 10.1109/CDC.2012.6426735
Assad Al Alam, Ather Gattami, Karl H. Johansson, Suboptimal decentralized controller design for chain structures: Applications to vehicle formations conference on decision and control. pp. 6894- 6900 ,(2011) , 10.1109/CDC.2011.6160938
Sunyoung Kim, Masakazu Kojima, Martin Mevissen, Makoto Yamashita, Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion Mathematical Programming. ,vol. 129, pp. 33- 68 ,(2011) , 10.1007/S10107-010-0402-6
K. Martensson, A. Rantzer, A scalable method for continuous-time distributed control synthesis advances in computing and communications. pp. 6308- 6313 ,(2012) , 10.1109/ACC.2012.6314762
Frederik Deroo, Michael Ulbrich, Sandra Hirche, Brian D.O. Anderson, Distributed controller design for a class of sparse singular systems with privacy constraints IFAC Proceedings Volumes. ,vol. 46, pp. 190- 197 ,(2013) , 10.3182/20130925-2-DE-4044.00007