Model Following Neuro-Adaptive Control Design for Non-square, Non-affine Nonlinear Systems

Radhakant Padhi , Nishant Unnikrishnan , S. N. Balakrishnan 3 Department of Aerospace Engineering, Indian Institute of Science – Bangalore, India Department of Mechanical and Aerospace Engineering, University of Missouri – Rolla, USA Abstract This paper proposes a new model-following adaptive control design technique for a class of non-affine and nonsquare nonlinear systems using neural networks. An appropriate stabilizing 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 unmodeled dynamics (neglected algebraic terms in the mathematical model) and/or parameter uncertainties present in the system model. In order to ensure stable behavior, an online control adaptation procedure is proposed in this paper. The controller design is carried out in two steps: (i) synthesis of a set of neural networks which capture matched unmodeled (neglected) dynamics or model uncertainties due to 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. A desirable characteristic of the adaptation procedure presented in this paper is that it 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 in this paper which demonstrate these features and clearly bring out the potential of the proposed approach.