MPC cannot pre-cool buildings with large RC

[YangyangFu]

The MPC test on RC models shew a few issues:

1. when RC values are large (from identification), the MPC cannot produce sufficient pre-cooling even when the prediction horizon (PH) is 1 day.

When RCs were identified as [10384.31640625, 499089.09375, 1321535.125, 1.5348844528198242, 0.5000327825546265, 1.000040054321289, 20.119935989379883], which led to a MSE cost of 0.078, the MPC couldn't pre-cool the buildings when PH=1 day

When RCs were identified as [6.9789902e+03, 2.1591113e+04, 1.8807944e+05, 3.4490612e+00, 4.9556872e-01, 9.8289281e-02, 4.6257420e+00], which lead to a MSE cost of 0.75, the MPC pre-cool the building in a very reasonable way.

2. when RC values are large, the larger the PH is, the large cost is from the MPC.
   This seems very strange.

The reasons might be

• gradient descent optimizers might not converge for large RC, and thus needs to be fine-tuned
• the larger thermal mass the building has, the longer PH should be used, does this hold ??

TODO

• construct the same MPC using optimization modeling framework such as cvxpy so that second-order derivative can be used. This can provide a benchmark to see if the problems are in gradient-based optimizers.
• if the problem is in gradient-descent optimizers, need retune the optimizer
• if the problem is not in gradient-descent optimizers, then need to think why MPC cannot work well with large RCs.