Benes P., Bukovsky I. (2016) On the Intrinsic Relation of Linear Dynamical Systems and Higher Order Neural Units. In: Silhavy R., Senkerik R., Oplatkova Z., Silhavy P., Prokopova Z. (eds) Automation Control Theory Perspectives in Intelligent Systems. Advances in Intelligent Systems and Computing, vol 466. Springer, Cham
This paper summarizes the fundamental construction of higher-order-neural-units (HONU) as a class of polynomial function based neural units, which are though non-linear discrete time models, are linear in their parameters. From this a relation will be developed, ultimately leading to a new definition for analysing the global stability of a HONU, not only as a model itself, but further as a means of justifying the global dynamic stability of the whole control loop under HONU feedback control. This paper is organised to develop the fundamentals behind this intrinsic relation of linear dynamic systems and HONUs accompanied by a theoretical example to illustrate the functionality and principles of the concept.
Adaptive control Higher-order neural units (HONUs) Gradient descent (GD) Levenberg-Marquardt (LM) Batch propagation through time (BPTT)