  Optimal control models have been successful in describing many aspects of
human movement. The interpretation of such models regarding neuronal
implementation of the human motor system is not clear. An important aspects of
optimal control policies is the notion of cost. Optimal control seeks to
minimize a notion of cost, while meeting certain goals. We offer a method to
transform current methods in the literature from their traditional form by
changing the norm by which cost is assessed. We show how sparsity can be
introduced into current optimal approaches that use continuous control signals.
We assess cost using the infinity norm. This results in optimal signals which
can be represented by a small amount of Dirac delta functions. Sparsity has
played an important role in theoretical neuroscience for information processing
(such as vision). In this work, to obtain sparse control signals, the infinity
norm is used as a penalty on the control signal, which is then encoded with
Dirac delta functions. We show, for a basic physical system, a point mass can
be moved between two points in a way that resembles human fast reaching
movements. Despite the sparse nature of the control signal, the movements that
result are continuous and smooth. These control signals are simpler than their
non-sparse counterparts, yet yield comparable results when applied towards
modeling reaching movements. In addition, such sparse control signals resemble
a sequence of spikes, giving this approach a biological interpretation. Actual
neuronal implementations are more complex. However, this work shows, in
principle, that sparsely encoded control signals are a plausible implementation
for the control of reaching movements. Leading techniques for modeling human
movements can easily be adjusted in order to introduce sparsity, with a
biological interpretation and the simplified information content of the control
signal.
