Discrete-time neural net controller for a class of nonlinear dynamical systems

A family of two-layer discrete-time neural net (NN) controllers is presented for the control of a class of mnth-order MIMO dynamical system. No initial learning phase is needed so that the control action is immediate; in other words, the neural network (NN) controller exhibits a learning-while-functioning-feature instead of a learning-then-control feature. A two-layer NN is used which is linear in the tunable weights. The structure of the neural net controller is derived using a filtered error approach. It is indicated that delta-rule-based tuning, when employed for closed-loop control, can yield unbounded NN weights if: 1) the net cannot exactly reconstruct a certain required function, or 2) there are bounded unknown disturbances acting on the dynamical system. Certainty equivalence is not used, overcoming a major problem in discrete-time adaptive control. In this paper, new online tuning algorithms for discrete-time systems are derived which are similar to ε-modification for the case of continuous-time systems that include a modification to the learning rate parameter and a correction term to the standard delta rule