Control of Plastic Processes

Abstract

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.