Using neural networks, this paper proposes a new model-following adaptive control design technique for nonlinear systems. The nonlinear system for which the method is applicable is assumed to be of known order. Furthermore, it is assumed that using a nominal model an appropriate nominal controller has been designed for the system. However, it is well-known that because of unmodeled dynamics and/or parameter uncertainties, a nominal controller seldom works the way it is intended to; and sometimes it even leads to instability. Hence there is a need to modify this nominal controller online, in a stable manner, to suppress these unwanted behaviors. An online control adaptation procedure proposed in this paper to achieve this objective. The control design is carried out in two steps: (i) synthesis of a set of neural networks which collectively capture the algebraic function that arises either because of the unmodeled dynamics or uncertainties in parameters and (ii) computation 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 as well as boundedness of the weights of the neural networks. Unlike existing methods, a distinct 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. Moreover, this technique is applicable to non-square and non-affine systems as well. Numerical results for a fairly-challenging problem are presented in this paper, which demonstrate these features and clearly bring out the potential of the proposed approach.
Model Following Robust Neuro-Adaptive Control Design for Non-Square, Non-Affine Systems
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Padhi, R, Unnikrishnan, N, & Balakrishnan, SN. "Model Following Robust Neuro-Adaptive Control Design for Non-Square, Non-Affine Systems." Proceedings of the ASME 2004 International Mechanical Engineering Congress and Exposition. Dynamic Systems and Control, Parts A and B. Anaheim, California, USA. November 13–19, 2004. pp. 653-661. ASME. https://doi.org/10.1115/IMECE2004-59844
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