Abstract: A model learning apparatus is configured to learn a model that shows a relationship between an input variable u input into a system and an output variable y output from the system. The model learning apparatus includes a storage that stores store a model used to learn a nonlinear equation of state for predicting the output variable y by using the input variable u; and a processor programmed to learn the equation of state by using the model and an input-output data set including a set of data of a steady-state value of the output variable y and data of the input variable u corresponding to the data of the steady-state value. The model is an equation of state including a bijective mapping ? that uses the output variable y as an input thereof.

Abstract: A method includes obtaining sensor data from a plurality of sensors disposed at a plurality of routing control locations of an environment, where the sensor data is indicative of a number of a plurality of pallets at the plurality of routing control locations. The method includes calculating a plurality of difference values based on the sensor data, calculating a transient production value based on the sensor data and a transient objective function, and calculating a steady state production value based on the sensor data and a steady state objective function. The method includes generating a state vector based on the plurality of difference values, the transient production value, and the steady state production value, and defining a set of routes for a set of pallets from among the plurality of pallets based on the state vector and a digital twin of the environment.