Control of Plastic Processes

Learning systems interact with an environment by means of input (sensory) and output (motor) interfaces, so that the system’s internal state is a function of the prior behaviour of both the system and the environment. These defining properties can be described by the following set of equations: $$\frac{{dy\left( t \right)}}{{dt}} = f\left( {x\left( t \right),s\left( t \right)} \right)$$ (1) $$\frac{{dx\left( t \right)}}{{dt}} = g\left( {y\left( t \right),t} \right)$$ (2) $$\frac{{ds\left( t \right)}}{{dt}} = h\left( {x\left( t \right),s\left( t \right)} \right)$$ (3) where x = system input vector y = system output vector s = system internal state vector t = time.