Control Mathematics deals with the mathematical methods and procedures that arise in control tasks in automation. Fundamental to this are ordinary differential equations and dynamic systems, the Laplace transformation and associated modeling methods, input-output systems and related mathematics, as well as machine learning (ML) and artificial intelligence (AI) methods, which also play a role in control engineering.

The basic structure of a control task can be characterized by the block diagram in the following figure, which is referred to as the control loop.

The plant is a model of a real system to which a certain (predefined) behavior is to be imposed. This is achieved by the controller, which is responsible for fulfilling the control task.

The mathematical problems that arise in these scenarios range from optimization tasks to simulation-based studies, as well as ML/AI tasks. The field is particularly characterized by mathematical multidisciplinarity, encompassing everything from differential equations and optimization problems to statistics, machine learning, and artificial intelligence.