An adaptive output regulation design method is proposed for a class of output feedback systems with nonlinear exosystem and unknown parameters. A new nonlinear internal model approach is developed in the present study that successfully converts the global robust output regulation problem into a robust adaptive stabilization problem for the augmented system. Moreover, an output feedback controller is achieved based on a type of state filter which is designed for the transformed augmented system. The adaptive control technique is successfully introduced to the stabilization design to ensure the global stability of the closed-loop system. The result can successfully apply to a tracking control problem associated with the well known Van der Pol oscillator.
This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm can be used in many applications, e. g. active vibration control, and the avoidance of nonharmonic distortion in nonlinear circuits. An example is shown that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol circuit.
This paper treats the question of robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output regulation problem for the modified FitzHugh-Nagumo neuron model are all satisfied. Then we apply the obtained output regulation results to the control problem for modified FitzHugh-Nagumo neuron model. Finally, an output feedback control law is designed for the modified FitzHugh-Nagumo neuron model to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is shown that the proposed algorithm can completely reject the external electrical stimulation generated from a Van der Pol circuit.