Semiglobal ISpS disturbance attenuation with output tracking via direct adaptive design

Direct adaptive partial state feedback control is presented to achieve semiglobally input-to-state practically stable (ISpS) disturbance attenuation with output tracking for a class of uncertain time-varying nonlinear systems in which the unmeasured dynamics do not possess a constant disturbance attenuation level (CDAL). Identifying a necessary condition for the existence of a CDAL, direct adaptive neural networks (NNs) control is developed, where the universal approximation property of NNs and the domination design are employed together to overcome the difficulties due to the lack of state information, unknown system nonlinearities, and unknown state-dependent disturbance attenuation gain. The proposed method is coherent in the sense that it is applicable to the case in which a CDAL exists.