Discrete-time approximated linearization of SISO systems under output feedback

1729 For the third term on the RHS of (39), by 2) of Lemmas 1 and 4 we have (41) where is given in Theorem 1. In this paper, we have studied the adaptive control of a class of discrete-time stochastic nonlinear systems whose nonlinearities satisfy the linear growth condition. (This condition cannot be essentially relaxed in general as recently shown in [13].) The prediction/WLS-based adaptive control is shown to be globally stable in the presence of random noise. Of course, there are many problems which still remain open. For example, 1) it would be of considerable interest to find a simple recursive procedure for calculating the optimal prediction-based adaptive predictors (14) and 2) it is not clear if the WLS algorithm used in the controller design can be replaced by the standard LS. These belong to a further investigation. REFERENCES [1] B. Bercu, " Weighted estimation and tracking for ARMAX models, " SIAM J. [2] L. Guo, " Self-convergence of weighted least-squares with applications to stochastic adaptive control, " IEEE Trans. , " On critical stability of discrete-time adaptive nonlinear control, " IEEE Trans. Adaptive control of a class of nonlinear discrete-time systems, " Int. Adaptive controller design for tracking and disturbance attenuation in parameter-strict-feedback nonlinear systems, " IEEE Trans. Abstract— This paper deals with higher order approximation for discrete-time systems. It is shown that approximated feedback lineariza-tion at the second order can always be achieved under feedback compensation based on an approximated observer. An example is given in order to illustrate the control design and the efficiency of the proposed method.