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 model learning apparatus is configured to learn a model that shows a relationship between an input variable v input into a system and an output variable y output from the system. The model learning apparatus includes a storage that stores a model used to learn a nonlinear equation of state for predicting the output variable y by using the input variable v, and a processor programmed to learn the equation of state by using the model and an input-output data set including multiple sets of input variable data and output variable data with respect to the model. The model is an equation of state including a bijective mapping ? that uses the input variable v as an input thereof and a bijective mapping ? that uses the output variable y as an input thereof.

Abstract: An internal combustion engine is provided, in which a quantity of NOx emission can be reduced without using any special components even when a NOx reduction catalyst has an elevated temperature due to high-load operation. The internal combustion engine includes an engine, a three-way catalyst and a NOx reduction catalyst for purifying exhaust gas emitted from the engine, a temperature sensor for acquiring the temperature of the NOx reduction catalyst, a rotation speed sensor for acquiring an engine rotation speed, an injection controller for controlling a fuel injection quantity in the engine, and a combustion switching controller for switching a combustion mode of the engine between lean and stoichiometric combustion modes based on the NOx reduction catalyst temperature, the engine rotation speed, and the fuel injection quantity acquired from the fuel injection controller.