An Improved Estimation Method for Unmodeled Dynamics Based on ANFIS and Its Application to Controller Design

By representing nonlinear systems as a combination of linear part and unmodeled dynamics, in this paper, an improved estimation algorithm using an adaptive neuro-fuzzy inference system (ANFIS) for unmodeled dynamics is presented. At first, the unmodeled dynamics is divided into two parts using the differential expansion of the control input at the last time instant; then, the two parts are estimated by the ANFIS. It has been shown that the proposed algorithm overcomes the problem that the unknown control input is embedded in unmodeled dynamics, which makes the true value of unmodeled dynamics difficult obtain. Moreover, the method improves the precision of the estimation of unmodeled dynamics. Second, under the assumption that the growth rate of unmodeled dynamics does not exceed its input vector, the “one-to-one mapping” and “regularization technique” are adopted to deal with the input and output data and the unmodeled dynamics, respectively. As a result, the data vector can be guaranteed to lie inside a compact set, which ensures the use of the universal approximation property of the ANFIS. On the other hand, it has been shown that datum of a system can be fully used to obtain the parameters (centers, widths) in membership functions and the network connection weights in the ANFIS by offline training. These parameters are tuned online to improve the estimation convergence rate of the unmodeled dynamics. The effectiveness of the proposed estimation method is illustrated by comparing it with the simulation results that are obtained from the other existing methods. Finally, the proposed estimation method is applied to the nonlinear switching control design. Both simulation and theoretical analysis have confirmed that the nonlinear switching control which adopts the proposed estimation method cannot only guarantee the stability and convergence of the system but can exhibit a desired dynamic performance for the closed-loop system as well.