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ODE indoor-climate model with Fourier heat loss and window air exchange; device effects via sparse M1, M2 on binary Y; quadratic discomfort with SPD S_i; derived c_opt = (Σ S_i)^(-1) Σ S_i c_{pi} and S_eff = Σ S_i. Time-weighted least squares (daily/weekly/annual kernels) to estimate c_opt(t) and the exchange-rate matrix σ; S_eff configured (SPD). Implemented a thresholded control rule for device switching.
Overview
- ODE indoor-climate model with Fourier heat loss and window air exchange.
- Device effects via sparse matrices $M_1$, $M_2$ acting on binary state $Y$.
- Quadratic discomfort with SPD $S_i$; derived:
- $c_{\mathrm{opt}}=(\sum_i S_i)^{-1}\sum_i S_i c_{pi}$
- $S_{\mathrm{eff}}=\sum_i S_i$
- Time-weighted least squares (daily/weekly/annual kernels) to estimate $c_{\mathrm{opt}}(t)$ and the exchange-rate matrix $\sigma$; $S_{\mathrm{eff}}$ configured (SPD). Implemented a thresholded control rule for device switching.