Neural Control of Redundant (Abundant) Systems as Algorithms Stabilizing Subspaces

We address the problem of stability of motor actions implemented by the central nervous system based on simple algorithms potentially reflecting physical (including physiological) processes within the body. A number of conceptually simple algorithms that solve motor tasks with a high probability of success may be based on feedback schemes that ensure stability of subspaces of neural variables associated with accomplishing those tasks. The task is formulated in terms of linear constrains imposed either on the human body mechanical variables or on neural variables; we discuss three reference frames relevant to these processes. We discuss underlying basic principles of such algorithms, their architecture, and efficiency, and compare the outcomes of implementation of such algorithms with the results of experiments performed on the human hand.