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Various types and techniques of on-line approximation have been used in feedback control of uncertain non-linear systems. In many practical applications, saturation of the control input influences significantly the performance of adaptive and learning control systems. This article addresses the issue of control input saturation in on-line approximation based control of non-linear systems. A modified control design framework is presented for preventing the presence of input saturation from destroying the learning capabilities and memory of an on-line approximator in feedback control systems. The stability properties of the proposed feedback control law are obtained via Lyapunov analysis. Particular emphasis is given to aircraft longitudinal control, which extends the results to the backstepping feedback control procedure.
Polycarpou et al. (2004) studied this question.