A system for non-intrusive load monitoring, comprising: an output device; a data storage device including program instructions stored therein; a sensing device operably connected to a common source for a plurality of electrical devices; and an estimator operably connected to the output device, the data storage device, and the sensing device, the estimator configured to execute the program instructions to: obtain data associated with a sensed state of the common source from the sensing device, obtain a mixed integer non-linear programming MINLP model corresponding to a non-linear electrical device from a data storage device, the MINLP model corresponding to a plurality of inputs for the plurality of electrical devices, a plurality of estimated outputs for the plurality of electrical devices and the sensed state of the common source from the sensing device; modify the MINLP model to be a mixed integer linear programming MILP model, the MILP model including an output equation corresponding to the sensed state of the common source from the sensing device and a state equation corresponding to a plurality of constraints for the plurality of inputs for the plurality of electrical devices; solve the MILP model for the non-linear electrical device over a fixed time horizon using the obtained data, and store operational data based on the solved MILP model in the memory for use in identifying subsequent operations of the non-linear electrical device from the data associated with the sensed state of the common source. an output device; a data storage device including program instructions stored therein; a sensing device operably connected to a common source for a plurality of electrical devices; and an estimator operably connected to the output device, the data storage device, and the sensing device, the estimator configured to execute the program instructions to: obtain data associated with a sensed state of the common source from the sensing device, obtain a mixed integer non-linear programming MINLP model corresponding to a non-linear electrical device from a data storage device, the MINLP model corresponding to a plurality of inputs for the plurality of electrical devices, a plurality of estimated outputs for the plurality of electrical devices and the sensed state of the common source from the sensing device; modify the MINLP model to be a mixed integer linear programming MILP model, the MILP model including an output equation corresponding to the sensed state of the common source from the sensing device and a state equation corresponding to a plurality of constraints for the plurality of inputs for the plurality of electrical devices; solve the MILP model for the non-linear electrical device over a fixed time horizon using the obtained data, and store operational data based on the solved MILP model in the memory for use in identifying subsequent operations of the non-linear electrical device from the data associated with the sensed state of the common source. obtain data associated with a sensed state of the common source from the sensing device, obtain a mixed integer non-linear programming MINLP model corresponding to a non-linear electrical device from a data storage device, the MINLP model corresponding to a plurality of inputs for the plurality of electrical devices, a plurality of estimated outputs for the plurality of electrical devices and the sensed state of the common source from the sensing device; modify the MINLP model to be a mixed integer linear programming MILP model, the MILP model including an output equation corresponding to the sensed state of the common source from the sensing device and a state equation corresponding to a plurality of constraints for the plurality of inputs for the plurality of electrical devices; solve the MILP model for the non-linear electrical device over a fixed time horizon using the obtained data, and store operational data based on the solved MILP model in the memory for use in identifying subsequent operations of the non-linear electrical device from the data associated with the sensed state of the common source.