Discrete-time model reference adaptive control of nonlinear dynamical systems using neural networks

A multilayer discrete-time neural net (NN) controller is presented for the direct model reference adaptive control of a class of multi-input multi-output (MIMO) nonlinear dynamical systems. The nonlinear dynamical system is assumed to be controllable and its state vector is available for measurement. The NN controller exhibits learning-while-functioning features instead of learning-then-control so that control is immediate with no explicit learning phase needed. The tracking error between the output of a nonlinear plant and an ideal linear model converges within a very short time. Persistence of excitation (PE) is not needed, linearity in the parameters is not required, and certainty equivalence is not used. This overcomes several limitations of standard adaptive control. The novel weight tuning paradigm for the NN controller is based on the well-known delta rule but includes a modification to the learning rate parameter plus a correction term. It guarantees tracking as well as bounded NN weights in non-ideal situations so that a persistency of excitation conditions on the internal signals is not needed. It is found that the constant learning rate parameter at a given layer should decrease with the number of hidden-layer neurons present in that particular layer; this is a major drawback often documented in the NN control literature. This drawback is easily overcome by employing a projection algorithm at each layer. Theoretical analysis is justified through extensive simulation studies.