Fractional-order sliding mode control with a predefined-time observer for VTVL reusable launch vehicles under actuator faults and saturation constraints

Self Cite

This article studies the predefined-time observation problem of generalized strict-feedback second-order systems commonly encountered in practice.A nonaffine control input, a matched perturbation, and nonlinear functions satisfying the Hölder growth condition are considered. A class of adaptive predefined-time observers (PTOs) is designed to reconstruct unknown states and lumped perturbations based on a barrier function and specific time-varying functions. Distinct from existing observers for strict-feedback systems, the PTO accomplishes a complete reconstruction in a predefined time with trivial peaking observation errors. Furthermore, the upper bound of the settling time of the PTO is tightly and explicitly predefined by only one design parameter, and is irrelevant to the initial conditions. Hence, tuning procedures for the physically realizable temporal demands become less conservative and more straightforward. Moreover, the adaptive coefficients of the PTO are self-adjusted along with the magnitude of perturbation, efficiently improving the transient performance under wide-range perturbations. Finally, numerical simulations on a robot manipulator system demonstrate the effectiveness of the PTO. K E Y W O R D Sadaptive coefficients, adaptive predefined-time observer, generalized strict-feedback second-order system, peaking observation error, upper bound of the settling time Jixing Lv and Xiaozhe Ju contributed equally to this work.

“…Remark The boundedness assumption of

\dot{\Delta}

can be seen in References 25 and 40. Although a precise upper bound of

\dot{\Delta}

is difficult to obtain, acquiring a rough value of

W

is practical.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Note that it is convenient to find examples of

𝕂^{2}

functions, of which the selection range of

\alpha

can be directly obtained through L'Hôpital's rule 40 as follows:

h(r)=1/\left({r}_1-r\right)

\alpha \ge 1

h(r)=1/{\left({r}_1-r\right)}^2

\alpha \ge 0.5

h(r)=\sec \left(\pi r/2{r}_1\right)

\alpha \ge 1

. …”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Remark The PTOs 42,43 are incompetent for strict‐feedback systems with time‐varying

{\theta}_1\left({x}_1\right)

and Hölder growing nonlinear functions. The PTOs 25,40,41 work for double‐integrator systems or nonholonomic systems. Moreover, the PTO 25 employs

{\sec}^2\left(\pi t/2{t}_f\right)

{\sec}^4\left(\pi t/2{t}_f\right)

, and

{\sec}^6\left(\pi t/2{t}_f\right)

, where

\sec \left(\pi t/2{t}_f\right)

belongs to class‐

𝕂^{2}

.…”

Section: Pto Design and Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

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Robust approximate optimal control for air‐breathing hypersonic vehicle

Xiao

Liu

Fan

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This paper investigates the robust approximate optimal control problem for air-breathing hypersonic vehicle (AHV). By input-output linearzation and introducing auxiliary variables, the high-order nonlinear AHV dynamics are transformed to a second-order feedback decoupling model. Then a virtual command is designed by back-stepping strategy to guarantee the practical finite-time convergence of tracking error. In order to drive the AHV with uncertainties to follow the virtual command, a robust approximate optimal controller based on adaptive dynamic programming (ADP) is proposed. Different from the conventional robust method, both the robustness and the input cost are taken into consideration in the proposed controller, which can optimize the control actions and hence avoid the chattering. Besides, the proposed controller adopts a single critic network design instead of actor-critic structure, which ensures the stability of the system autonomously and simplifies the implementation procedure. The simulation results show the effectiveness of the proposed scheme.

Adaptive safe control for tethered aircrafts with input and output constraints

Song

Zhang

Huang

et al. 2023

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