H-Infinity Loop-Shaped Model Predictive Control with HVAC Application

    •  Bortoff, S.A., Schwerdtner, P., Danielson, C., Di Cairano, S., Burns, D.J., "H-Infinity Loop-Shaped Model Predictive Control with HVAC Application", IEEE Transactions on Control Systems Technology, DOI: 10.1109/​TCST.2022.3141937, Vol. 30, No. 5, pp. 2188-2203, March 2022.
      BibTeX TR2022-028 PDF
      • @article{Bortoff2022mar,
      • author = {Bortoff, Scott A. and Schwerdtner, Paul and Danielson, Claus and Di Cairano, Stefano and Burns, Daniel J.},
      • title = {H-Infinity Loop-Shaped Model Predictive Control with HVAC Application},
      • journal = {IEEE Transactions on Control Systems Technology},
      • year = 2022,
      • volume = 30,
      • number = 5,
      • pages = {2188--2203},
      • month = mar,
      • doi = {10.1109/TCST.2022.3141937},
      • issn = {1063-6536},
      • url = {}
      • }
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  • Research Areas:

    Control, Multi-Physical Modeling, Optimization


We formulate a Model Predictive Control (MPC) for linear time-invariant systems based on H-infinity loop-shaping.
The design results in a closed-loop system that includes a state estimator and attains an optimized stability margin. Input and output weights are designed in the frequency domain to satisfy steady-state and transient performance requirements, in lieu of standard MPC plant model augmentations. The H-infinity loopshaping synthesis results in an observer-based state feedback structure. An inverse optimal control problem is solved to construct the MPC cost function, so that the control input computed by MPC is equal to the H-infinity control input when the constraints are inactive. The MPC inherits the closed-loop performance and stability margin of the loop-shaped design when constraints are inactive. We apply the methodology to a multizone heat pump, and validate the results in simulations and laboratory experiments. The design rejects constant unmeasured disturbances, tracks constant references with zero steady-state error, meets transient performance requirements, provides an excellent stability margin, and enforces input and output constraints.