CMAC-Based SMC for Uncertain Descriptor Systems Using Reachable Set Learning

This article introduces a novel sliding mode control (SMC) law to achieve trajectory tracking for a class of descriptor systems with unknown uncertainties. It approximates the uncertainties by a cerebellar model articulation control (CMAC) neural network. We formulate the problem of training the CMAC as a scheme of estimating a reachable set for a discrete-time nonlinear system. A new online learning algorithm based on output feedback control of reachable set estimation is developed and the approximation error is bounded in an ellipsoidal reachable set. In order to dispel the effect of the approximation error of the CMAC, we develop a compensation controller by using the reachable set bounds. Controller gains and parameters of the learning algorithm are obtained via linear matrix inequalities (LMIs). Our computer simulation results show that the proposed CMAC-based SMC technique can achieve convergent tracking errors. The technique is applied to a salient permanent magnet synchronous motor (PMSM) in our lab and demonstrates excellent performance.