Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systems

We consider the problem of designing distributed controllers to ensure passivity of a large-scale interconnection of linear subsystems connected in a cascade topology. The control design process needs to be carried out at the subsystem-level with no direct knowledge of the dynamics of other subsystems in the interconnection. We present a distributed approach to solve this problem, where subsystem-level controllers are locally designed in a sequence starting at one end of the cascade using only the dynamics of the particular subsystem, coupling with the immediately preceding subsystem and limited information from the preceding subsystem in the cascade to ensure passivity of the interconnected system up to that point. We demonstrate that this design framework also allows for new subsystems to be compositionally added to the interconnection without requiring redesign of the pre-existing controllers.

[1]  Murat Arcak,et al.  Networks of Dissipative Systems: Compositional Certification of Stability, Performance, and Safety , 2016 .

[2]  Cédric Langbort,et al.  Distributed control design for systems interconnected over an arbitrary graph , 2004, IEEE Transactions on Automatic Control.

[3]  Suresh P. Sethi,et al.  Near Optimization of Dynamic Systems by Decomposition and Aggregation , 1998 .

[4]  Farhad Farokhi,et al.  Decentralized Control of Networked Systems : Information Asymmetries and Limitations , 2014 .

[5]  Hemanshu R. Pota,et al.  Stability of locally dissipative interconnected systems , 1993, IEEE Trans. Autom. Control..

[6]  G. Antonelli,et al.  Interconnected dynamic systems: An overview on distributed control , 2013, IEEE Control Systems.

[7]  Melanie Nicole Zeilinger,et al.  Plug and play distributed model predictive control based on distributed invariance and optimization , 2013, 52nd IEEE Conference on Decision and Control.

[8]  Panos J. Antsaklis,et al.  A passivity measure of systems in cascade based on passivity indices , 2010, 49th IEEE Conference on Decision and Control (CDC).

[9]  Richard Bellman,et al.  Large systems , 1974 .

[10]  Dragoslav D. Siljak,et al.  Nested ε-decompositions and clustering of complex systems , 1986, Autom..

[11]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[12]  Romeo Ortega,et al.  On passive systems: from linearity to nonlinearity , 1992 .

[13]  M. Aoki Some control problems associated with decentralized dynamic systems , 1971 .

[14]  Marcello Farina,et al.  Plug-and-play model predictive control based on robust control invariant sets , 2012, Autom..

[15]  P. Moylan,et al.  Tests for stability and instability of interconnected systems , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[16]  E. Davison,et al.  Decentralized stabilization and pole assignment for general proper systems , 1990 .

[17]  Jan Lunze,et al.  Decentralized design of feedback control for large-scale systems , 1988, Kybernetika.

[18]  Pravin Varaiya,et al.  Smart cars on smart roads: problems of control , 1991, IEEE Trans. Autom. Control..

[19]  Giancarlo Ferrari-Trecate,et al.  Plug-and-play control of AC islanded microgrids with general topology , 2016, 2016 European Control Conference (ECC).

[20]  M. Vidyasagar Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability , 1980 .

[21]  Panos J. Antsaklis,et al.  Passivity indices for symmetrically interconnected distributed systems , 2011, 2011 19th Mediterranean Conference on Control & Automation (MED).

[22]  Pravin Varaiya,et al.  Decentralized information and control: A network flow example , 1972 .

[23]  Panos J. Antsaklis,et al.  Large-Scale Dissipative and Passive Control Systems and the Role of Star and Cyclic Symmetries , 2016, IEEE Transactions on Automatic Control.

[24]  R. Braatz,et al.  A tutorial on linear and bilinear matrix inequalities , 2000 .

[25]  Mathukumalli Vidyasagar,et al.  New passivity-type criteria for large-scale interconnected systems , 1979 .

[26]  Mohammad Aldeen,et al.  Stabilization of decentralized control systems , 1997 .

[27]  Calin Belta,et al.  Provably Safe Cruise Control of Vehicular Platoons , 2017, IEEE Control Systems Letters.