Global adaptive regulation of feedforward nonlinear time‐delay systems by output feedback

Abstract

SUMMARYThe problem of global adaptive state regulation is investigated via output feedback for uncertain feedforward nonlinear time-delay systems. Compared with existing results, our control schemes can be applicable to more general nonlinear time-delay systems because of combining the low-gain scaling approach with the backstepping method. In particular, we allow that there exist uncertain output function and uncertain growth rate imposed on nonlinear terms. Also, one considers a class of nonlinear systems with main-axis delay. By the Lyapunov-Krasovskii theorem, delay-independent controllers are proposed by constructing novel lowgain observers driven by system input, to regulate the states of original system while all the closed-loop signals are globally bounded. Furthermore, two examples are given to illustrate the usefulness of our results.

Quantized feedback control for nonlinear feedforward systems with unknown output functions and unknown control coefficients

“…Remark The input and output quantizations are simultaneously involved in system , making it more challenging but more practically meaningful than the controlled feedforward systems without quantization …”

“…Subsequently, inspired by the low‐gain observers used in the feedforward systems and the observer form used in the lower‐triangular system, a time‐varying low‐gain observer is designed for system , ie, where constants c ≥ b with b being defined in Equation , β ∈( p ,1). By the work of Praly and Jiang, the positive values satisfy where k is a positive constant, P ∈ R n × n is a positive definite matrix, and …”

“…In addition, the considered system models in this paper have unknown output functions, unknown control coefficients, and unknown time‐varying growth rates. ii.Although the feedback control schemes for nonlinear feedforward systems without quantization have been developed in the work of Jia et al and Zhu and Wang, they cannot be directly applied to the system concerned in this paper because the quantization errors may lead to the deterioration of system performance and even cause instability. Particularly, using the stability condition that the Lipschitz unknown output function belongs to a given sector mentioned in the work of Zhu and Wang can only deal with the uncertainty of the output function but cannot handle the error caused by the input quantization.…”

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

“…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.…”