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In this paper, a fixed-time dynamic surface high-order sliding mode control approach is presented for chaos suppression and voltage stabilization in three-bus power system via design of current source converter-based static synchronous compensator controller. The proposed control strategy constructs two high-order sliding mode surfaces to achieve control objective. By combining backstepping idea with dynamic surface control (DSC) technique, high-order sliding mode controller is designed and the inherent problem of “explosion of complexity” in backstepping design is avoided. Further, a new stability concept is introduced into DSC design to achieve semi-global uniform ultimate boundedness of the signals in high-order sliding mode system within finite time independent of initial condition. In addition, stability analysis is provided to show that the proposed control scheme can achieve semi-globally fixed-timely uniformly ultimately bounded stabilization. Finally, simulation results are given to demonstrate the effectiveness of the proposed control scheme and the superior performance over conventional DSC.

The flight control problem of a flexible air-breathing hypersonic vehicle is presented in the presence of input constraint and aerodynamic uncertainty. A control-oriented model, where aerodynamic uncertainty and the strong couplings between the engine and flight dynamics are included, is derived to reduce the complexity of controller design. The flexible dynamics are viewed as perturbations of the model. They are not taken into consideration at the level of control design, the influence of which is evaluated through simulation. The control-oriented model is decomposed into velocity subsystem and altitude subsystem, which are controlled separately. Then robust adaptive controller is developed for the velocity subsystem, while the controller which combines dynamic surface control and radial basis function neural network is designed for the altitude subsystem. The unknown nonlinear function is approximated by the radial basis function neural network. Minimal-learning parameter technique is utilized to estimate the maximum norm of ideal weight vectors instead of their elements to reduce the computational burden. To handle input constraints, additional systems are constructed to analyze their impact, and the states of the additional systems are employed at the level of control design and stability analysis. Besides, “explosion of terms” problem in the traditional backstepping control is circumvented using a first-order filter at each step. By means of Lyapunov stability theory, it is proved theoretically that the designed control law can assure that tracking error converges to an arbitrarily small neighborhood around zero. Simulations are performed to demonstrate the effectiveness of the presented control scheme in coping with input constraint and aerodynamic uncertainty.

This paper devotes to proposing a robust adaptive fault-tolerant tracking control scheme for a class of output-constrained uncertain nonlinear systems with unknown time-varying powers. The motivation is to enable the tracking accuracy and the settling time to be arbitrarily prescribed while constructing a compact set large enough in which the approximation of any unknown continuous function by neural networks (NNs) is effective. Using a serial of time-varying gain filters and scaling time-varying functions, an exquisite controller is constructed by integrating NNs approximation and the dynamic surface control (DSC) technology. The designed controller is not only strongly robust to compensate external disturbances and actuator faults, but also drives the tracking error to enter a prescribed neighborhood of the origin within an arbitrarily prescribed time while satisfying the prescribed time-varying output constraint without constructing the barrier functions. Finally, two practical examples are provided to demonstrate the application of the proposed strategy.

The article addresses the output-feedback control issue for a class of multi-input multi-output (MIMO) uncertain nonlinear systems with multiple event-triggered mechanisms (ETM). Compared to previous event-triggering studies, this paper aims to trigger both the output and filtered signals. Unknown nonlinear dynamics are approximated using fuzzy logic systems (FLSs). Then, a novel kind of state observer has been designed to deal with unmeasurable state problems using the triggered output signal. The sampled estimated state, the triggered output signal, and the filtered signal are utilized to propose an event-triggering mechanism that consists of sensor-to-observer (SO) and observer-to-controller (OC). An event-triggered output feedback control approach is given inside backstepping control, whereby the filter may be employed to circumvent the issue of the virtual control function not being differentiable at the trigger time. It is testified that, according to the Lyapunov stability analysis scheme, all closed-loop signals and the system output are ultimately uniformly constrained by our control method. Finally, the simulation examples are performed to confirm the theoretical findings.

A new problem of observer-based fractional adaptive type-2 fuzzy backstepping control for a class of fractional-order MIMO nonlinear dynamic systems with dead-zone input nonlinearity is considered in the presence of model uncertainties and external disturbances where the control scheme is constructed by combining the backstepping dynamic surface control (DSC) and fractional adaptive type-2 fuzzy technique. First, a linear state observer estimates immeasurable states. Second, the unknown nonlinear functions of the uncertain system are approximated with interval type-2 fuzzy logic systems. Third, to avoid the complication of backstepping design process, the DSC is used. Fourth, by using the fractional adaptive backstepping, fractional adaptive laws are constructed, the proposed method is applied to a class of uncertain fractional-order nonlinear MIMO system. In order to have a better control performance in reducing tracking error, the controller parameters are tuned by using the PSO algorithm. Stability of the system is proven by the Mittag-Leffler method. It is presented that the proposed design guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the zero. The simulation examples are given to show the efficiency of the proposed controller.

This article studies the problem of dynamic-surface-based event-triggered adaptive tracking control for a class of strictly-feedback stochastic nonlinear systems with state constraints. Firstly, radial basis function neural networks (RBFNNs) are used to approximate unknown nonlinear continuous functions, and barrier Lyapunov functions (BLFs) are used to address state constraint problems. Then, the dynamic surface control (DSC) scheme is applied to solve the “explosion of complexity” issue, and error compensation signals are added to reduce the error caused by the filter to achieve a more effective control performance and optimize the algorithm. In addition, this research also considers the case of systems with relative threshold event-triggered mechanisms to save communication resources, and the existence of the lower bound of the minimum inter-event time is proved to exclude the Zeno behavior. Meanwhile, an adaptive tracking controller with the backstepping control strategy is designed, so that all signals in the closed-loop system are bounded and the tracking error converges to a small residual set of the origin in probability. Finally, the simulation examples are given to demonstrate the effectiveness of the control method.

Input saturation is one of the common phenomena in many practical systems, and it is main obstacles that limits the systems performance. In this paper, the adaptive neural network (NN) control problem has been discussed for a family of uncertain nonstrict-feedback systems with input saturation. The innovations are summarized as follows: (1) the auxiliary systems and the NN state observer are developed to eliminate the influence of input saturation and estimate unmeasurable states; (2) in order to against the drawback of “explosion of complexity\" for the traditional backstepping control technique (BCT), the dynamic surface control technique is used to reduce the excessive computation burden; (3) the proposed NN control approach for nonstrict-feedback systems only utilize the property of radial basis function-neural networks (RBF-NNs), instead of the restrictive assumption. Furthermore, unknown smooth functions are approximated by RBF-NNs in nonlinear systems. By employing the BCT, an adaptive output-feedback controller has been constructed. Meanwhile, all signals in closed-loop system are semi-globally uniformly ultimate bounded. An explicit function with the saturation error and designed parameters is obtained, which indicates the tracking error can be tuned through the saturation error and designed parameters. Finally, the superiority of the proposed control technique is validated by two examples.

In this article, the research team systematically developed a method to model the kinematics and dynamics of a 3-wheeled robot subjected to external disturbances and sideways wheel sliding. These models will be used to design control laws that compensate for wheel slippage, model uncertainties, and external disturbances. These control algorithms were developed based on dynamic surface control (DSC). An adaptive trajectory tracking DSC algorithm using a fuzzy logic system (AFDSC) and a radial neural network (RBFNN) with a fuzzy logic system were used to overcome the disadvantages of DSC and expand the application domain for non-holonomic wheeled mobile robots with lateral slip (WMR). However, this adaptive fuzzy neural network dynamic surface control (AFNNDSC) adaptive controller ensures the closed system is stable, follows the preset trajectory in the presence of wheel slippage model uncertainty, and is affected by significant amplitude disturbances. The stability and convergence of the closed-loop system are guaranteed based on the Lyapunov analysis. The AFNNDSC adaptive controller is evaluated by simulation on the Matlab/simulink software R2022b and in a steady state. The maximum position error on the right wheel and left wheel is 0.000572 (m) and 0.000523 (m), and the angular velocity tracking error in the right and left wheels of the control method is 0.000394 (rad/s). The experimental results show the theoretical analysis’ correctness, the proposed controller’s effectiveness, and the possibility of practical applications. Orbits are set as two periodic functions of period T as follows.

Dynamic surface control (DSC) is a recognized nonlinear control approach for high-order systems. However, as the complexity of the system increases and the first-order filter (FOF) is introduced, there exists a singularity problem, i.e., the control input will reach infinity. This limits the application of the DSC algorithm to a class of real-world systems with complex dynamics. To address the problem of singularity, we present a novel DSC approach called nonsingular dynamic surface control (NDSC), which completely avoids the singularity problem and significantly improves the overall control performance. NDSC includes a nonsingular hypersurface, which is constructed by the error between system states and virtual control inputs. Then the nonsingular hypersurface will be applied to derive the corresponding control law with the aid of the DSC approach to ensure the output of the system can track arbitrary desired trajectories. NDSC has the following novel features: (1) finite time asymptotic stabilization can be guaranteed; (2) the performance of NDSC is insensitive to the FOF’s parameter variation once the maximum tracking error of FOF is bounded, which significantly reduces reliance on the control sampling frequency. We thoroughly evaluate the proposed NDSC algorithm in an unmanned aerial vehicle (UAV) system with an underactuated nature. Finally, the simulation results illustrate and highlight the effectiveness and superiority of the proposed control algorithm.

In the presence of dynamic uncertainties, external time-varying disturbances, and limited inputs to the multi-point mooring system (MPMS) of a floating offshore platform (FOP), this paper proposes a robust adaptive dynamic surface (RADS) control method incorporating a disturbance observer. A disturbance observer is designed to estimate the unknown time-varying disturbance and apply feedforward compensation to the control variable. Simultaneously, the adaptive law of the σ-corrected leakage term is employed to estimate the bound of the disturbance observation error, thereby enhancing positioning accuracy. An auxiliary dynamic system (ADS) is then introduced to address input constraints, while the differential explosion problem associated with the traditional inversion method is resolved through the integration of the dynamic surface control (DSC) algorithm. The Lyapunov function is utilized to demonstrate that the controller ensures the consistent ultimate boundedness of all signals within the closed-loop system. Finally, a simulation experiment was conducted based on the eight-point mooring platform of the “Kantan3”, and the positioning accuracy reached 3%, which is higher than the specification requirements of the classification society. The results indicate that the designed controller achieves higher positioning accuracy and improved anti-interference performance and has been put into practical application on “Kantan3”.