Adaptive System

cognition adaptive-systems cybernetics

Definition

Adaptive System

An adaptive system is a system whose internal parameters change in response to experience or feedback, thereby changing its future behaviour.

Let $u_t$ be an input, $y_t$ the resulting output, ${\theta }_t$ the system’s internal parameters, and ${\rho }_t$ an optional feedback signal. Its behaviour and adaptation may be written as

$$y_t=G_{{\theta }_t}(u_t),{\theta }_{t+1}=A({\theta }_t,u_t,y_t,{\rho }_t).$$

The change is adaptive only when it can alter the input–output relation:

$$\exists t,u:G_{{\theta }_{t+1}}(u)\ne G_{{\theta }_t}(u).$$

Thus adaptation changes how the system will respond, rather than merely changing its transient state.