Learning from neural control

One of the amazing successes of biological systems is their ability to "learn by doing" and so adapt to their environment. In this paper, first, a deterministic learning mechanism is presented, by which an appropriately designed adaptive neural controller is capable of learning closed-loop system dynamics during tracking control to a periodic reference orbit. Among various neural network (NN) architectures, the localized radial basis function (RBF) network is employed. A property of persistence of excitation (PE) for RBF networks is established, and a partial PE condition of closed-loop signals, i.e., the PE condition of a regression subvector constructed out of the RBFs along a periodic state trajectory, is proven to be satisfied. Accurate NN approximation for closed-loop system dynamics is achieved in a local region along the periodic state trajectory, and a learning ability is implemented during a closed-loop feedback control process. Second, based on the deterministic learning mechanism, a neural learning control scheme is proposed which can effectively recall and reuse the learned knowledge to achieve closed-loop stability and improved control performance. The significance of this paper is that the presented deterministic learning mechanism and the neural learning control scheme provide elementary components toward the development of a biologically-plausible learning and control methodology. Simulation studies are included to demonstrate the effectiveness of the approach.