Before we can even think about controlling anything, we need to understand what a system is. In control theory, a system is anything that takes inputs, processes them, has an internal state, and produces outputs. This applies to mechanical systems, electrical circuits, biological organisms, economic markets, and yes, even you, scrolling through endless feeds.
For you, the system:
Control theory seeks to understand how to influence a system's state or output by manipulating its inputs. To do this, we first need a clear picture of the system itself.
The visualization below conceptually illustrates a simple system with its inputs, outputs, and state.
Inputs are external factors that influence the system. We can represent inputs as variables that change over time, e.g., $u(t)$.
Example: For your "notification addiction" system, an input could be the rate of incoming notifications.
Outputs are the measurable results or behaviors of the system. We can represent outputs as variables, e.g., $y(t)$.
Example: An output could be your total daily screen time or the speed at which you respond to messages.
The state of a system is the set of variables that completely describe the system's internal condition at any given time. The state changes over time based on the current state and the inputs. We can represent the state as a vector of variables, e.g., $\mathbf{x}(t)$.
Example: Your state could include your current focus level, energy level, and anxiety level.
The relationship between inputs, state, and outputs is often described by differential equations (as we saw in Lesson 4!) or difference equations.