Building management system with system identification using multi-step ahead error prediction

A method comprising:

• operating building equipment to heat or cool a building;
• measuring, by one or more sensors, a variable state of the building at each of a plurality of time steps;
• controlling the building equipment by providing a control input to the building equipment for each of the plurality of time steps;
• and
• generating a set of training data for a system model for the building, the training data comprising input training data and output training data for each of the plurality of time steps, the input training data comprising values for one or more input variables of the system model including the control input provided to the building equipment, and the output training data comprising values for one or more output variables of the system model including a variable measured by the one or more sensors;
• and
• performing a system identification process to identify one or more parameters of the system mode, the system identification process comprising:
• predicting, for each time step, a predicted value of one or more of the output variables for each of a plurality of subsequent time steps, wherein each predicted value is generated by applying the input training data for the time step to the system model;
• generating a prediction error function by comparing the output training data to the predicted values of the one or more output variables;
• and
• optimizing the prediction error function to determine values for the one or more parameters of the system model that minimize the prediction error function, the one or more parameters comprising at least one of one or more model parameters or one or more Kalman gain parameters;
• and
• generating additional control inputs for the building equipment by performing a model predictive control process that uses the system model with the one or more parameters identified by the system identification process.

A controller for building equipment, the controller comprising:

• a model identifier configured to identify a model parameter or a Kalman gain parameter by minimizing a prediction error function VN(θ,ZN)=Σk=1N-hmax+1Σh=0hmaxw(h)∥y(k+h)−ŷ(k+h|k−1,θ)∥22;
• wherein:
• y(k+h) is an output of a building system at time step k+h, the output including an indoor air temperature;
• ŷ(k+h|k−1, θ) is a model-predicted output at time step k+h based on input/output data up to time step k−1 and the model parameter or a Kalman gain parameter θ;
• and
• w(h) is a weighting function.