For deterministic discrete time systems, the system's update operator is applied iteratively to get the state at the next time points (see Discrete Time Update Operator).
Often, especially in Machine Learning applications, the system receives sequential inputs which affect the behaviour of the following states in the trajectory. This is taken into account by making the update equation also dependent on the input.
| \( T \) | This is the symbol for a dynamical system's update operator. |
| \( \mathbf{x} \) | This symbol represents a state of the dynamical system at some time point. |
| \( \mathbf{u} \) | This symbol represents the input of a dynamical system. |
| \( n \) | This symbol represents any given whole number, \( n \in \htmlClass{sdt-0000000014}{\mathbb{W}}\). |