How to perform eQuest Matlab co-simulation

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You can't. Unlike EnergyPlus or Modelica, there isn't any built in capabilities to enable co-simulation. By co-simulation, I mean exchange of data between two programs at each time step. But this isn't even what you are trying to achieve here anyways. What you want to do is to launch subsequent simulations, in which each finished simulation informs the modification of your input parameters for the next one.

eQuest has a text-based input format, and has some text-based output files too, and it can be run in command line via DOE2. So it's up to you to connect the dots: you need a parser for the output results, and you need functions to modify the input files, you need some "logic" (an algorithm) to tweak the input parameters based on output results, and one to launch the simulation.

But instead, please do note that there are tools which do just that and will make your life much easier instead of reinventing the wheel, in particular I can personally recommend ExcalibBEM from SIMEB (available in english and in french), which allows you to relatively simply use GenOpt (an optimization framework) with simulation files such as DOE (therefore eQuest), but also Energyplus. I've successfully used it in the past to calibrate energy consumption of eQuest models.