In this paper, the interpolation line search (ILS) algorithm to find the desirable step length in a numerical optimization method is investigated to determine the optimal saturation limits with non-smooth nonlinearities. The simple steepest descent algorithm is used to illustrate that the ILS algorithm can provide adequate reductions in an objective function at minimal cost with fast convergence. The power system stabilizer (PSS) with output limits is used as an example for a nonlinear controller to be tuned. The efficient computation to implement the ILS algorithm in the steepest descent method is available by using the hybrid system model with the differential-algebraic-impulsive-switched (DAIS) structure. The simulation results are given to show the performance improved by the ILS algorithm.

This letter describes the first derivatives estimation of nonlinear parameters through an embedded identifier in the hybrid system by using a feed-forward neural network (FFNN). The hybrid systems are modelled by the differential-algebraic-impulsive-switched (DAIS) structure. The FFNN is used to identify the full dynamics of the hybrid system. Moreover, the partial derivatives of an objective function J with respect to the parameters are estimated by the proposed identifier. Then, it is applied for the identification and estimation of the non-smooth nonlinear dynamic behaviors due to a saturation limiter in a practical engineering system.