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This study addresses the adaptive tracking control problem for a class of time-delay systems in strict-feedback form with unknown control gains and uncertain actuator non-linearity. The actuator non-linearity can be either backlash or dead zone, and the proposed approach does not require the knowledge of the bounds of non-linearity parameters. By applying an appropriate Lyapunov–Krasovskii functional and utilising the property of the well-defined trigonometric functions, the problems of time delay and controller singularity are avoided. The feasibility of using a static neural network to attenuate the effect of actuator non-linearity is proved with the aid of intermediate value theorem. Furthermore, it is proved that all closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Two simulation examples are provided to demonstrate the effectiveness of the designed method.

This study investigates the finite-time attitude-tracking problem for rigid spacecraft. A novel non-singular terminal sliding-mode control (NTSMC) law is designed to provide finite-time convergence and fast, high control precision even though inertia uncertainties and external disturbances affect the spacecraft systems under actuator failures and saturations. The proposed NTSMC scheme is chattering suppression and singularity-free. Simulation results are presented to demonstrate the efficiency of the proposed method.

This study is concerned with the tracking control problem for nonlinear uncertain robotic systems in the presence of unknown actuator nonlinearities. A novel adaptive sliding controller is designed based on a robust disturbance observer without any prior knowledge of actuator nonlinearities and system dynamics. The proposed control strategy can guarantee that the tracking error eventually converges to an arbitrarily small neighborhood of zero. Simulation results are included to demonstrate the effectiveness and superiority of the proposed strategy.

Active suspension systems have received increased importance for improving automotive safety and comfort. In active suspensions, actuators are placed between the car body and wheel-axle, and are able to both add and dissipate energy from the system, which enables the suspension to control the attitude of the vehicle, to reduce the effects of the vibrations, and then to increase ride comfort and vehicle road handling. However, the attained benefits are paralleled with the increasing possibility of component failures. In this study, a fault-tolerant control approach is proposed to deal with the problem of fault accommodation for unknown actuator failures of active suspension systems, where an adaptive robust controller is designed to adapt and compensate the parameter uncertainties, external disturbances and uncertain non-linearities generated by the system itself and actuator failures. Comparative simulation studies are then given to illustrate the effectiveness of the proposed controllers.

Electrically stimulated lower limb systems contain higher order nonlinearities and uncertainties in their physical parameters. Takagi-Sugeno (TS) fuzzy models are used to model nonlinear systems. Techniques such as parallel distributed compensation (PDC) are dependent on the membership functions that constitute the TS fuzzy model. When the exact representation approach is used to electrical stimulation applications, the system’s performance under PDC control can be deteriorated, because the membership functions may be uncertain, besides a high computational cost be required to compute them. In this paper, we propose a robust switched control subject to actuator saturation and fault (RSwASF) that effectively handles system uncertainties and nonidealities, such as fatigue, spasms, tremor, and muscle recruitment. Control techniques based on TS fuzzy modeling (PDC and robust PDC), as well as other approaches, such as sliding-mode control, backstepping, super-twisting, gain-scheduling, and proportional-integral-derivative (PID) control were compared to RSwASF through the root-mean-squared error (RMSE). The results indicate that RSwASF minimizes the influence of the parametric uncertainties and presents the lowest RMSE for healthy and paraplegic individuals.

This study addresses the input-to-state stability (ISS) of non-linear impulsive and switched delay systems. Based on the piecewise Lyapunov–Krasovskii functional method, the authors show that when only some of the constituent subsystems are ISS, the ISS property still can be retained for the non-linear impulsive and switched delay system, if the dwell time of the ISS subsystems satisfies a lower bound condition and the activation time of the non-ISS subsystems satisfies an upper bound condition, respectively. In common parlance, some of the intervals must be overly long, whereas the others must be short enough between impulses. Compared with existing results on related problems, the theory can be applied to a larger class of systems. The proposed approach also enables us to give the analysis of systems involving actuator failure, controller failure or temporary uncertain switching signal. As an example, the authors employ the method to analyse the problem of reliable control for a mechanical rotational cutting process.

This paper presents an adaptive optimal control method to suppress the oscillation of a floating platforms system in random seas. The system consists of multiple modules which are connected by flexible connectors with strong geometrical nonlinearity. To cope with the uncertain waves, a disturbance estimator is introduced to assess the actual wave excitation. This adaptive scheme of the estimator is integrated with an optimal control method subject to a limitation on the control outputs of actuators, where the optimal control process is carried out by the sequential quadratic program method. In numerical experiments, a floating platform with five semi-submersible modules is considered. Control process deals with 20 control variables to stabilize the surge, sway and yaw motions of a 30-DOF floating system, subject to unknown irregular waves and limitation of control output. Numerical results have verified the efficiency of the control strategy and show that the proposed control method performs very well.

The development of control approaches for systems preceded with hysteresis non-linearities has received great attentions in recent decades. The most common approach is the construction of an inverse model as the compensator to mitigate hysteresis effects. However, most of the developed schemes are state-based, requiring the availability of states of systems, which may not be the case for some practical systems. In this study, output control with inverse compensation will be addressed. By using the inverse as a feedforward compensator for the model described by the modified generalised Prandtl–Ishlinskii model, an corresponding analytical expression of the inverse compensation error is first obtained. Then, an observer-based robust adaptive output feedback controller is developed. It is shown that the proposed output feedback control scheme can not only guarantee the stability of the control systems, but also can achieve the desired tracking accuracy.

The problem of robust stabilization of a class of uncertain multi-input time-delayed systems with deadzone nonlinearity in the actuator is considered. To achieve a stable uncertain multi-input system, sliding mode control (SMC) is adopted in the controller design. The proposed controller guarantees the global reaching condition of the sliding mode in the uncertain multi-input system. In the sliding mode, the investigated time-delayed systems with deadzone nonlinearity still possess the insensitivity to the uncertainties and/or disturbances, which can be seen in the systems with linear inputs. In addition, the proposed controller can work effectively for systems no matter whether sector nonlinearity and/or deadzone exists in the actuator or not. However, such property cannot be obtained by the controller design through traditional SMC for the systems without input nonlinearity. Besides, the traditional SMC controller might produce limit cycles once the system contains deadzone in the input. Furthermore, the presented controller ensures the system trajectories globally exponentially converged in the sliding mode. Finally, two examples are illustrated to demonstrate the effectiveness of the proposed sliding mode controller.