Research Papers: Design Automation

On Decentralized Optimization for a Class of Multisubsystem Codesign Problems

[+] Author and Article Information
Tianchen Liu

Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: tianchen@umd.edu

Shapour Azarm

ASME Fellow
Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: azarm@umd.edu

Nikhil Chopra

Associate Professor
Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: nchopra@umd.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 1, 2016; final manuscript received September 1, 2017; published online October 26, 2017. Assoc. Editor: Gary Wang.

J. Mech. Des 139(12), 121404 (Oct 26, 2017) (11 pages) Paper No: MD-16-1405; doi: 10.1115/1.4037893 History: Received June 01, 2016; Revised September 01, 2017

Codesign refers to the process of integrating the optimization of the physical plant design and control of a system. In this paper, a new class of codesign problems with a multisubsystem architecture in both design and control is formulated and solved. Our work here extends earlier research on models and solution approaches from single system to multisubsystem codesign. In this class, the optimization model for the physical design part in each subsystem is assumed to have a convex objective function with convex inequality and linear equality constraints. The optimization model for the control part of each subsystem belongs to a class of finite time-horizon linear quadratic regulator (LQR) feedback control. A new multilevel decentralized method is proposed that can obtain optimal or near-optimal solutions for this class of codesign problems. Details of the model and approach are presented and demonstrated by a numerical as well as a more complex spring–mass–damper system example. The proposed decentralized approach has been compared with a centralized approach. Using a scalable test problem, it is shown that as the size of the problem is increased, the computation effort for the decentralized approach increases linearly while that of the centralized approach increases nonlinearly.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Fathy, H. K. , Reyer, J. A. , Papalambros, P. Y. , and Ulsoy, A. G. , 2001, “ On the Coupling Between the Plant and Controller Optimization Problems,” American Control Conference (ACC), Arlington, VA, June 25–27, pp. 1864–1869.
Allison, J. T. , and Herber, D. R. , 2014, “ Multidisciplinary Design Optimization of Dynamic Engineering Systems,” AIAA J., 52(4), pp. 691–710. [CrossRef]
Allison, J. T. , and Nazari, S. , 2010, “ Combined Plant and Controller Design Using Decomposition-Based Design Optimization and the Minimum Principle,” ASME Paper No. DETC2010-28887.
Allison, J. T. , and Han, Z. , 2011, “ Co-Design of an Active Suspension Using Simultaneous Dynamic Optimization,” ASME Paper No. DETC2011-48521.
Allison, J. T. , Guo, T. , and Han, Z. , 2015, “ Co-Design of an Active Suspension Using Simultaneous Dynamic Optimization,” ASME J. Mech. Des., 136(8), p. 081003. [CrossRef]
Allison, J. T. , Herber, D. R. , and Deshmukh, A. P. , 2015, “ Integrated Design of Dynamic Sustainable Energy Systems,” 20th International Conference on Engineering Design (ICED) Milan, Italy, July 27–30, pp. 299–308.
Peters, D. L. , Papalambros, P. , and Ulsoy, A. , 2011, “ Control Proxy Functions for Sequential Design and Control Optimization,” ASME J. Mech. Des., 133(9), p. 091007. [CrossRef]
Peters, D. L. , Papalambros, P. Y. , and Ulsoy, A. G. , 2013, “ Sequential Co-Design of an Artifact and Its Controller Via Control Proxy Functions,” Mechatronics, 23(4), pp. 409–418. [CrossRef]
Jiang, Y. , Wang, Y. , Bortoff, S. A. , and Jiang, Z.-P. , 2015, “ Optimal Codesign of Nonlinear Control Systems Based on a Modified Policy Iteration Method,” IEEE Trans. Neural Networks Learn. Syst., 26(2), pp. 409–414. [CrossRef]
Ravichandran, T. , Wang, D. , and Heppler, G. , 2006, “ Simultaneous Plant-Controller Design Optimization of a Two-Link Planar Manipulator,” Mechatronics, 16(3), pp. 233–242. [CrossRef]
Sandoval, L. R. , Budman, H. M. , and Douglas, P. L. , 2008, “ Simultaneous Design and Control of Processes Under Uncertainty: A Robust Modelling Approach,” J. Process Control, 18(7), pp. 735–752. [CrossRef]
Alyaqout, S. F. , Papalambros, P. Y. , and Ulsoy, A. G. , 2011, “ Combined Robust Design and Robust Control of an Electric DC Motor,” IEEE/ASME Trans. Mechatronics, 16(3), pp. 574–582. [CrossRef]
Reyer, J. A. , and Papalambros, P. Y. , 2002, “Combined Optimal Design and Control With Application to an Electric DC Motor,” ASME. J. Mech. Des., 124(2), pp. 183–191.
Deshmukh, A. P. , and Allison, J. T. , 2013, “ Design of Nonlinear Dynamic Systems Using Surrogate Models of Derivative Functions,” ASME Paper No. DETC2013-12262.
Zhang, W. , Li, Q. , and Guo, L. , 1999, “ Integrated Design of Mechanical Structure and Control Algorithm for a Programmable Four-Bar Linkage,” IEEE/ASME Trans. Mechatronics, 4(4), pp. 354–362. [CrossRef]
Yan, H.-S. , and Yan, G.-J. , 2009, “ Integrated Control and Mechanism Design for the Variable Input-Speed Servo Four-Bar Linkages,” Mechatronics, 19(2), pp. 274–285. [CrossRef]
Sridharan, S. , Echols, J. A. , Rodriguez, A. A. , and Mondal, K. , 2014, “ Integrated Design and Control of Hypersonic Vehicles,” American Control Conference, (ACC) Portland, OR, June 4–6, pp. 1371–1376.
Kim, M.-J. , and Peng, H. , 2006, “ Combined Control/Plant Optimization of Fuel Cell Hybrid Vehicles,” American Control Conference (ACC), Minneapolis, MN, June 14–16, pp. 1–6.
Geoffrion, A. M. , 1972, “ Generalized Benders Decomposition,” J. Optim. Theory Appl., 10(4), pp. 237–260. [CrossRef]
Tosserams, S. , Etman, L. F. P. , and Rooda, J. E. , 2007, “ An Augmented Lagrangian Decomposition Method for Quasi-Separable Problems in MDO,” Struct. Multidiscip. Optim., 34(3), pp. 211–227. [CrossRef]
Tosserams, S. , Etman, L. F. P. , and Rooda, J. E. , 2008, “ Augmented Lagrangian Coordination for Distributed Optimal Design in MDO,” Int. J. Numer. Methods Eng., 73(13), pp. 1885–1910. [CrossRef]
Geromel, J. C. , and Bernussou, J. , 1982, “ Optimal Decentralized Control of Dynamic Systems,” Automatica, 18(5), pp. 545–557. [CrossRef]
Nedic, A. , and Ozdaglar, A. , 2009, “ Distributed Subgradient Methods for Multi-Agent Optimization,” IEEE Trans. Autom. Control, 54(1), pp. 48–61. [CrossRef]
Nedic, A. , Ozdaglar, A. , and Parrilo, P. A. , 2010, “ Constrained Consensus and Optimization in Multi-Agent Networks,” IEEE Trans. Autom. Control, 55(4), pp. 922–938. [CrossRef]
Maasoumy, M. , Pinto, A. , and Sangiovanni-Vincentelli, A. , 2011, “ Model-Based Hierarchical Optimal Control Design for HVAC Systems,” ASME Paper No. DSCC2011-6078.
Jamshidi, M. , 1996, “ A Multi-Level Structure for a Class of Dynamical Optimization Problems,” Master's thesis, Case Western Reserve University, Cleveland, OH.
Jamshidi, M., 1997, Large-Scale Systems: Modeling, Control, and Fuzzy Logic, Prentice Hall, Upper Saddle River, NJ.
Cohen, G. , and Joalland, G. , 1976, “ Coordination Methods by the Prediction Principle in Large Dynamic Constrained Optimization Problems,” IFAC Proc. Vol., 9(3), pp. 539–547. [CrossRef]
Smith, N. J. , and Sage, A. P. , 1973, “ An Introduction to Hierarchical Systems Theory,” Comput. Electr. Eng., 1(1), pp. 55–71. [CrossRef]
Sadati, N. , and Babazadeh, A. , 2006, “ Optimal Control of Robot Manipulators With a New Two-Level Gradient-Based Approach,” Electr. Eng., 88(5), pp. 383–393. [CrossRef]
Osiadacz, A. J. , and Bell, D. J. , 1986, “ A Simplified Algorithm for Optimization of Large-Scale Gas Networks,” Optim. Control Appl. Methods, 7(1), pp. 95–104. [CrossRef]
Joalland, G. , and Cohen, G. , 1980, “ Optimal Control of a Water Distribution Network by Two Multilevel Methods,” Automatica, 16(1), pp. 83–88. [CrossRef]
Boyd, S. , Xiao, L. , Mutapcic, A. , and Mattingley, J. , 2007, “ Notes on Decomposition Methods Notes for EE364B,” Stanford University, Stanford, CA, accessed Sept. 26, 2017, hthttps://stanford.edu/class/ee364b/lectures/decomposition_notes.pdf
Peters, D. L. , Papalambros, P. Y. , and Ulsoy, A. G. , 2009, “ On Measures of Coupling Between the Artifact and Controller Optimal Design Problems,” ASME Paper No. DETC2009-86868.
Rutquist, P. E. , and Edvall, M. M. , 2010, “ Propt-MATLAB Optimal Control Software,” TOMLAB Optimization, Pullman, WA.
Azarm, S. , and Papalambros, P. , 1982, “ An Interactive Design Procedure for Optimization of Helical Compression Springs,” University of Michigan, Ann Arbor, MI, Technical Report No. UM-MEAM-82-7.


Grahic Jump Location
Fig. 1

Problem structure—three coupled subsystems

Grahic Jump Location
Fig. 2

Scheme of multilevel decentralized approach

Grahic Jump Location
Fig. 5

Engineering example: series of three spring–mass–damper subsystems

Grahic Jump Location
Fig. 4

Illustrative numerical example: SS2 optimal controller

Grahic Jump Location
Fig. 8

Example: series of multiple spring–mass–damper subsystems

Grahic Jump Location
Fig. 9

Comparison of computational time between centralized and proposed decentralized approaches

Grahic Jump Location
Fig. 3

Flowchart of the approach

Grahic Jump Location
Fig. 6

Engineering example: optimal control variables (ui(t), i = 1, 2, 3): (a) decentralized and (b) centralized

Grahic Jump Location
Fig. 7

Engineering example: optimal state variables—velocity (xi2(t), i = 1, 2, 3): (a) decentralized and (b) centralized



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In