Concise adaptive neural control of uncertain nonlinear systems with periodically nonlinear time-varying parameterized disturbances

This note makes effort at the problem of robust adaptive control for uncertain nonlinear systems with periodically nonlinear time-varying parameterized disturbances with known common period. A concise adaptive neural control scheme is developed by fusion of the Backstepping method and a novel MLN (minimum learning network) technique. In the control scheme, the intermediate variables, i.e., the virtual controls, do not appear in the finally actual control effort, and only one neural network is introduced to compensate sum of the uncertainties in the whole system. Thus, the outstanding advantage of the corresponding scheme is that the control law with a concise structure is model-independent and easy to implement in the process industries due to less computational burden. Based on the Lyapunov synthesis, it is proven that with the developed concise adaptive controller, all the signals in the closed-loop system converge to a small neighborhood of zero. Finally, three comparison examples demonstrate the effectiveness of the proposed algorithm.