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In this paper we study the explicit model predictive control (MPC) design for approximately symmetric systems. The approximately symmetric system is modeled as a symmetric system plus an additive disturbance residing in a symmetric set. The explicit MPC controller is computed using symmetry to minimize the number of critical regions stored in memory while being robust to model mismatch and disturbances. We show through numerical examples that approximating an approximately symmetric systems using a full symmetric system can drastically reduce memory usage and computation time for explicit controllers while still guaranteeing feasibility and input-to-state stability.

Radiant slab systems have the potential to significantly reduce energy consumption in buildings. However, control of radiant slab systems is challenging. Classical feedback control is inadequate due to the large thermal inertia of the systems and heuristic feed-forward control often leads to unacceptable indoor comfort and may not achieve the full energy savings potential. Model predictive control (MPC) is now attracting increasing interest in the building industry and holds promise for radiant systems. However, an often-cited barrier to its implementation in the building industry is the high computational cost and complexity relative to the feedback controls used in conventional systems. The objectives of this study were to (i) verify the correct operation of an open source MPC toolchain developed for radiant slab systems, and (ii) demonstrate its efficacy in a test facility. A matched pair of cells in the FLEXLAB building test facility at the Lawrence Berkeley National Laboratory was used in the study. The proposed MPC toolchain was implemented in one cell and the performance compared to that of the other cell, which used a conventional heuristic control strategy. The results showed that the simplified MPC approach applied in the toolchain worked as expected and realized energy savings over the conventional control strategy. The MPC yielded 42% chilled water pump power reduction and 16% cooling thermal energy savings, while maintaining equal or better indoor comfort.

Abstract-In this paper we study the optimality of the certainty equivalence approximation in robust finite-horizon optimization problems with expected cost. We provide an algorithm for determining the subset of the state-space for which the certainty equivalence technique is optimal. In the second part of the paper we show how patterns in the problem structure called symmetries can be used to reduce the computational complexity of the previous algorithm. Finally we demonstrate our technique through numerical examples. In particular we examine networked battery systems and radiant slab building control, for which we show the certainty equivalence controller is optimal over the entire operating range.

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