Adaptive dynamic CMAC neural control of nonlinear chaotic systems with L2 tracking performance

The advantage of using cerebellar model articulation control (CMAC) network has been well documented in many applications. However, the structure of a CMAC network which will influence the learning performance is difficult to select. This paper proposes a dynamic structure CMAC network (DSCN) which the network structure can grow or prune systematically and their parameters can be adjusted automatically. Then, an adaptive dynamic CMAC neural control (ADCNC) system which is composed of a computation controller and a robust compensator is proposed via second-order sliding-mode approach. The computation controller containing a DSCN identifier is the principal controller and the robust compensator is designed to achieve L2 tracking performance with a desired attenuation level. Moreover, a proportional–integral (PI)-type adaptation learning algorithm is derived to speed up the convergence of the tracking error in the sense of Lyapunov function and Barbalat’s lemma, thus the system stability can be guaranteed. Finally, the proposed ADCNC system is applied to control a chaotic system. The simulation results are demonstrated that the proposed ADCNC scheme can achieve a favorable control performance even under the variations of system parameters and initial point.