Local Linear Models for System Control

For function approximation in the context of system control we present a new learning algorithm for a network consisting of local linear models. The algorithm finds a partition of the input space in disjunct regions in which the target function can be “efficiently” approximated by a single linear model: in regions where the function has high curvature more models are positioned, while in regions where the target function is almost linear less models are trained. Due to the composition of linear models the network has a clear interpretation which makes it amenable for stability proofs when used as an adaptive controller. With the proposed algorithm the network is easy to train and tune. Their performance is demonstrated on the well-known Mackey-Glass benchmark test as well as with a robot control task.