Model-following neuro-adaptive control design for non-square, non-affine nonlinear systems

A new model-following adaptive control design technique for a class of non-affine and non-square nonlinear systems using neural networks is proposed. An appropriate stabilising controller is assumed available for a nominal system model. This nominal controller may not be able to guarantee stability/satisfactory performance in the presence of unmodelled dynamics (neglected algebraic terms in the mathematical model) and/or parameter uncertainties present in the system model. In order to ensure stable behaviour, an online control adaptation procedure is proposed. The controller design is carried out in two steps: (i) synthesis of a set of neural networks which capture matched unmodelled (neglected) dynamics or model uncertainties because of parametric variations and (ii) synthesis of a controller that drives the state of the actual plant to that of a desired nominal model. The neural network weight update rule is derived using Lyapunov theory, which guarantees both stability of the error dynamics (in a practical stability sense) and boundedness of the weights of the neural networks. The proposed adaptation procedure is independent of the technique used to design the nominal controller, and hence can be used in conjunction with any known control design technique. Numerical results for two challenging illustrative problems are presented, which demonstrate these features and clearly bring out the potential of the proposed approach.