Global adaptive output-feedback stabilization for a class of uncertain nonlinear systems with unknown growth rate and unknown output function

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

“…Remark 4. As can be seen from the right-hand side of the inequality (16), due to the existence of an unknown output function h(x 1 ), the integrability of the derivativeV + 1 is not only related to the Nusbaum function and the unknown control direction but also related to the derivative h ′ + (x 1 ), which is different from the simple case y = x 1 considered in the existing results. [7][8][9]11,12 This makes the stability analysis schemes proposed in the above existing results no longer feasible for the considered system (1) in this paper.…”

“…Hence, it is interesting to study the output feedback control for nonlinear systems with unknown output functions. In recent years, significant attention has been paid and several results have been achieved for such control problems. For instance, the global adaptive regulation problem for nonlinear feedforward systems was investigated in the work of Jia et al, the global adaptive output feedback stabilization for nonlinear systems with unknown growth rates was achieved in the work of Yan et al, and the quantized feedback control for nonlinear feedforward systems was addressed by Wang et al…”

“…The main contributions of this paper are summarized as follows: Compared with the existing output feedback control results, the restrictive conditions on the output function are relaxed. Particularly, the unknown output function involved in this paper only requires to have a generalized derivative (ie, the output function does not need to be differentiable as in other works), and the prior knowledge on the upper and lower bounds of the generalized derivative need not to be known. Although the feedback control schemes for nonlinear cascade systems with known output functions have been developed, they rely on the state information x 1 which is not available in the concerned control problem; thus, they cannot be directly applied to the system concerned in this paper. More importantly, when the unknown output function and the unknown control direction exist simultaneously, the analysis scheme provided in the work of Jiang et al and Wu et al will no longer be feasible since the integrability of the derivative of the Lyapunov function depends on the generalized derivative of the unknown output function.…”

“…In recent years, significant attention has been paid and several results [14][15][16][17] have been achieved for such control problems. For instance, the global adaptive regulation problem for nonlinear feedforward systems was investigated in the work of Jia et al, 15 the global adaptive output feedback stabilization for nonlinear systems with unknown growth rates was achieved in the work of Yan et al, 16 and the quantized feedback control for nonlinear feedforward systems was addressed by Wang et al 17 It is noteworthy that the aforementioned results of unknown output functions require to know either the control coefficients themselves or a priori knowledge about the control direction (ie, the sign of the control coefficient). As claimed by Chen et al, 18 the control direction which represents the motion direction of the system may not be known in some practical applications.…”

“…Compared with the existing output feedback control results, [7][8][9][10][11][12][13][14][15][16] the restrictive conditions on the output function are relaxed. Particularly, the unknown output function involved in this paper only requires to have a generalized derivative (ie, the output function does not need to be differentiable as in other works [14][15][16], and the prior knowledge on the upper and lower bounds of the generalized derivative need not to be known. 2.…”