Design a thermostat for a home that has a furnace with On/Off control. The home is initially unheated in 40°F weather. When the heater is turned on, the temperature in the home reaches 63% of the steady state value in 120 minutes, starting from 40°F. If left on indefinitely, the home eventually reaches 100°F. Optimize the heater response for the first 2 1/2 hours starting from a cold home at 40°F. The target range for the home is between 68 and 70°F.
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The Gekko Optimization Suite is a machine learning and optimization package in Python for mixed-integer and differential algebraic equations. The GEKKO package is available in Python with pip install gekko. There are additional example problems for equation solving, optimization, regression, dynamic simulation, model predictive control, and machine learning.