Semiglobal fixed‐time output feedback stabilization for a class of nonlinear systems

Abstract

In this article, the fixed‐time output feedback stabilization for a class of lower‐triangular nonlinear systems only subject to Hölder continuous condition is investigated. First, a fixed‐time state observer is designed to estimate the unmeasured system states. Then, a fixed‐time full‐state feedback controller is designed under the assumption that all system states are measurable. Finally, a fixed‐time output feedback controller is designed by integrating the fixed‐time full‐state feedback controller with the fixed‐time state observer. Rigorous theoretical analysis for the semiglobal fixed‐time stability of the resulting closed‐loop system is provided. Numerical simulations are performed on a flexible‐joint single‐link robotic manipulator with a DC motor to illustrate the effectiveness and superiority of the proposed control method.

Adaptive predefined‐time observer design for generalized strict‐feedback second‐order systems under perturbations

“…Consequently, parameters need to be tuned by trial and error for a specific temporal demand. (ii) Perturbations were not considered in References 26‐31 and 35, or the observation errors did not vanish under perturbations 32‐34 . In other words, the FTOs and FxTOs 26‐35 are theoretically infeasible for a complete reconstruction if perturbations exist.…”

“…Nonlinear terms are required to satisfy the Hölder growth condition over a short time interval, which is more general than the conventional assumption of consistent Hölder or Lipschitz growing nonlinearities. A class of adaptive PTOs is designed to completely reconstruct states and perturbations of a generalized strict‐feedback second‐order system. The UBST is tightly predefined by only one design parameter, making tuning procedures for time‐critical scenarios more straightforward and less conservative than those of FTOs and FxTOs 26‐35 Correction terms governing the transient process of the PTO are adaptively adjusted following the magnitude of perturbation, which outperform nonadaptive correction terms of observers 25‐35,40‐43 by significantly improving the transient performance under wide‐range time‐varying perturbations. Prior information on the Hölder growth constant is not needed.…”

“…The UBST is tightly predefined by only one design parameter, making tuning procedures for time‐critical scenarios more straightforward and less conservative than those of FTOs and FxTOs 26‐35 Correction terms governing the transient process of the PTO are adaptively adjusted following the magnitude of perturbation, which outperform nonadaptive correction terms of observers 25‐35,40‐43 by significantly improving the transient performance under wide‐range time‐varying perturbations. Prior information on the Hölder growth constant is not needed. Furthermore, large peak observation errors are efficiently prevented during the fast observation process of the PTO. …”

Fixed‐time output feedback stabilization of a class of high‐order planar nonlinear systems

“…The fixed‐time control can be regarded as a special case of finite‐time control, whose settling time is bounded and does not rely on the initial conditions of the system states. Until recently, some relevant results have been reported for the fixed‐time output feedback stabilization of double integrator systems, 19,20 chained integrator systems, 21 perturbed planar nonlinear systems, 22 nonholonomic nonlinear systems, 23,24 and lower‐triangular nonlinear systems 25 . In the works, 26,27 a fixed‐time second‐order sliding mode controller was designed for the stabilization of nonlinear systems subject to output constraints.…”

“…Until recently, some relevant results have been reported for the fixed-time output feedback stabilization of double integrator systems, 19,20 chained integrator systems, 21 perturbed planar nonlinear systems, 22 nonholonomic nonlinear systems, 23,24 and lower-triangular nonlinear systems. 25 In the works, 26,27 a fixed-time second-order sliding mode controller was designed for the stabilization of nonlinear systems subject to output constraints. Nevertheless, all of the above controllers were only focused on the stabilization of nonlinear systems with orders equal to one.…”