A second-order sliding mode (SOSM) control method is developed for the regulation problem of a DC-DC buck converter. By taking into account the model uncertainties and external disturbances in the mathematical model, a sliding variable with relative of degree two is first constructed. Then, a new SOSM controller is developed such that the output voltage will well track the desired reference voltage. Theoretical analysis shows that the resulting closed-loop system is globally finite-time stable, while similar SOSM control results only give the proof for finite-time convergence. The way on how to implement the proposed SOSM algorithm is also presented. The theoretical findings are verified by extensive simulations and experiments.

This article investigates the adaptive fuzzy tracking control design for uncertain nonstrict-feedback nonlinear systems with time-varying constraints and asymmetric input saturations. It is known that time-varying output constraint, time-varying error constraints, and input saturations are commonly seen issues in many practical engineering systems due to inherent physical limitations and performance requirements. To deal with these problems and improve the convergence rate of the control system, a novel fixed-time convergent adaptive fuzzy control scheme is proposed for the considered uncertain nonlinear systems via the time-varying barrier Lyapunov function (BLF) technique. First, to deal with the unknown nonlinearities and uncertainties in the system dynamic model, fuzzy logic systems are utilized to approximate the unknown functions of the considered model. Then, the problem of asymmetric input amplitude and rate saturations is handled by constructing a unified smooth characterizing function and an innovative auxiliary design signal system. Subsequently, considering physical limitations and performance requirements, a novel time-varying BLF-based adaptive fuzzy backstepping control scheme is designed for the uncertain nonstrict-feedback nonlinear systems to realize superior tracking performances and keep the states staying in predefined time-varying compact regions during operations. Further, rigorous theoretical analyses have been conducted to show that the proposed control scheme achieves fixed-time convergence of all signals in the closed-loop control system. Finally, representative simulation results verify the effectiveness of the proposed control scheme.

This paper presents a novel fixed-time sliding mode disturbance observer (SMDO)-based robust backstepping cruise tracking control scheme with closed-loop finite-time convergence for flexible air-breathing hypersonic vehicles (FAHVs). In order to enhance the control system's robustness, a fixed-time SMDO is designed to compensate for the flexibility effects, model uncertainties, and external disturbances in FAHVs. In consequence, fixed convergence time of disturbance observation is achieved independently of initial estimation errors. Furthermore, velocity and altitude continuous finite-time tracking controllers are constructed by incorporating the SMDO and nonsmooth backstepping technique. To solve the problem of ``explosion of complexity'' in the conventional backstepping approach, nonsmooth filters are specifically constructed to generate the derivatives of virtual control laws. A Lyapunov-based stability analysis is conducted to show the finite-time convergence of the closed-loop FAHV control system. Finally, several representative numerical simulations are given to illustrate the effectiveness and superiority of the proposed control strategy.

Uncertainty and measurement noise are main obstacles that limit the tracking control performances of flexible air-breathing hypersonic vehicles (FAHVs). In this paper, we propose a novel fixed-time convergent nonsmooth backstepping control scheme for FAHV via augmented sliding mode observers (ASMOs) to overcome these obstacles. The ASMOs are first designed for the FAHV dynamics by employing the measured states corrupted by noises as inputs. On one hand, the ASMOs can simultaneously estimate the uncertainties and filter out the measurement noises. On the other hand, the observation error of each ASMO can be convergent within a fixed time independent of its initial observation error. Then, based on the estimation results, the altitude and velocity tracking controllers are developed by using fixed-time nonsmooth backstepping technique. Afterwards, a Lyapunov-based stability analysis is given to illustrate the fixed-time convergence of the closed-loop signals of the FAHV control system. Finally, comparative simulations are conducted to illustrate the superiority of the proposed control scheme.

In this article, an extended state observer (ESO)-based controller with a model predictive governor is designed for 3-D trajectory tracking of underactuated underwater vehicles. The proposed control scheme takes three primary challenges including underactuated property, velocity constraint, and lumped disturbance into consideration. With respect to the model predictive governor, an underactuated kinematic tracking error model is utilized to produce reference velocities. Meanwhile, a heading angle compensation mechanism is utilized to avoid the steady tracking errors resulting from dynamics coupling of the vehicle. Besides, an ESO is designed to estimate the lumped disturbances and unmeasured velocity states. Based on the ESO, a kinetic controller is offered to accomplish the precise velocity tracking only in virtue of the position and orientation information. Note that this article details both the design process of the control scheme and rigorous theoretical analysis. Eventually, simulation and experimental results demonstrate the feasibility and superiority of the proposed method. Notably, this work lays the foundation for the underactuated trajectory tracking control in complicated and turbulent underwater environments.

It is commonly believed that uncertainties are obstacles to the tracking performances of flexible air-breathing hypersonic vehicles (FAHVs). In addition, the estimation of unmeasured states in FAHV makes this issue much more complicated. To deal with these difficulties, this paper explores a novel adaptive fuzzy nonsmooth backstepping output-feedback control scheme for FAHV with closed-loop finite-time convergence. Firstly, to approximate the unknown dynamics of FAHV, some function approximators are constructed by utilizing interval type-2 fuzzy logic system (IT2-FLS). On this basis, a fixed-time convergent adaptive IT2 fuzzy observer is designed to estimate the unmeasured flight path angle and angle of attack of FAHV accurately and rapidly. Consequently, the estimation errors of the designed observer are convergent in a fixed time independent of their initial estimation errors. Furthermore, based on the estimated states, velocity and altitude tracking controllers are designed by using finite-time adaptive IT2 fuzzy nonsmooth backstepping control technique, which avoids the problem of “explosion of complexity” in traditional backstepping methods. Subsequently, rigorous Lyapunov stability analysis is conducted to show the finite-time convergence of the closed-loop signals of FAHV control system. Finally, the robustness and superiority of the proposed control scheme is validated by several simulations in representative scenarios.