Hybrid MPC: An Application to Semiactive Control of Structures

  • Wael M. ElhaddadEmail author
  • Erik A. Johnson
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


In clipped LQR, a common strategy for semiactive structural control, a primary feedback controller is designed using LQR and a secondary controller clips forces that the semiactive control device cannot realize. However, when the primary controller commands highly non-dissipative forces, the frequent clipping may render a controller far from being optimal. A hybrid system model is better suited for semiactive control as it accurately models the passivity constraints by introducing auxiliary variables into the system model. In this paper, a hybrid model predictive control (MPC) scheme, which uses a system model with both continuous and discrete variables, is used for semiactive control of structures. Optimizing this control results in a mixed integer quadratic programming problem, which can be solved numerically to find the optimal control input. It is shown that hybrid MPC produces nonlinear state feedback control laws that achieve significantly better performance for some control objectives (e.g., the reduction of absolute acceleration). Responses of a typical structure to historical earthquakes, and response statistics from a Monte Carlo simulation with stochastic excitation, are computed. Compared to clipped LQR, hybrid MPC is found to be more consistent in the reduction of the objective functions, although it is more computationally expensive.


Structural control Semiactive dampers Hybrid systems Model predictive control Clipped LQR 



The authors gratefully acknowledge the partial support of this work by the National Science Foundation, through awards CMMI 08-26634 and 11-00528, and by a USC Viterbi Doctoral Fellowship. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or of the University of Southern California.


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Copyright information

© The Society for Experimental Mechanics, Inc. 2013

Authors and Affiliations

  1. 1.Sonny Astani Department of Civil and Environmental EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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