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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.

In this paper, the tracking problem of four-Mecanum-wheel omnidirectional mobile robots is discussed. A fixed-time extended-state-observer-based transient-performance-guaranteed adaptive fuzzy controller based on the backstepping technique is designed under the assumption that the viscous friction coefficients are unknown. Firstly, fuzzy approximators are employed to approximate the unknown dynamics. Secondly, error transformation functions are introduced to guarantee the transient performance of tracking errors. Thirdly, fixed-time extended state observers are applied to estimate the external disturbances. Finally, the stability of the designed controller is proven by the practical fixed-time stability theory. Comparative simulations are carried out, and the simulation results verify the effectiveness of the designed controller.

This paper investigates the distributed leader–follower tracking problem for a team of flexible spacecraft over an undirected communication network with uncertain parameters subject to various actuator and measurement limitations. Assuming that at least one team member can receive information from the virtual leader, three scenarios are considered: (i) all the states of the flexible spacecraft can be completely measured and driven, (ii) only the rigid part of the flexible spacecraft can be driven with full state feedback and (iii) only the rigid part of the flexible spacecraft can be measured and driven. In the first case, a continuous adaptive control law is designed by building a unified architecture based on the linear-in-parameter property. In the second case, a distributed adaptive control algorithm is developed with a discontinuous parameter update law by treating the team of flexible spacecraft as two cascading subsystems. In the third case, a distributed adaptive control law is established with feedback from the generalized coordinates, generalized velocities and generalized accelerations of the rigid part of the spacecraft. It is theoretically proved that the closed-loop systems under the three designed adaptive control laws are all convergent to the target states. Finally, three numerical examples are presented to illustrate the effectiveness of the three proposed control laws.

In this paper, an adaptive fast terminal sliding mode control technique combined with a global sliding mode control scheme is investigated for the tracking problem of uncertain nonlinear third-order systems. The proposed robust tracking controller is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Under the uncertainty and nonlinearity effects, the reaching phase is removed and the chattering phenomenon is eliminated. This scheme guarantees robustness against nonlinear functions, parameter uncertainties and external disturbances. The derivative of the state variable is replaced by a delay term in the form of an Euler approximation of the derivative function. Furthermore, the knowledge of upper bounds of the system uncertainties is not required, which is more flexible in the real implementations. Simulation results are presented to show the effectiveness of the suggested method.

This study investigates an adaptive fixed-time tracking problem of nonlinear interconnected high-order systems with unknown control direction and stochastic disturbances. Under the framework of adaptive feedback, the backstepping method and fuzzy logic system are utilized to handle the stochastic disturbances and the packaged unknown nonlinearities. By utilizing the Nussbaum gain technique, an adaptive fixed-time controller is proposed to overcome the difficulties associated with unknown control directions. Distinguishing from the most existing results, a modified fixed-time control scheme is presented to deal with the positive odd integer terms from the interconnected high-order system with the help of adding a power integrator method. The designed control strategy guarantees that the tracking error converges within a fixed settling time and all signals of the closed-loop system are fixed-time stable. Simulation results validate the designed control approach.

Symmetry is widely present in science and daily life. And the internal structure of surface-mounted permanent magnet synchronous motors (PMSMs) has good symmetry. This article is dedicated to studying the tracking problem of PMSMs with adaptive and backstepping control methods. The research objective of this study is to design new adaptive controllers Uq and Ud, which enable the state of the motor position servo system to asymptotically and stably track the given signals of the system. They can suppress the impact of changes in B, J, and TL and can also enhance the robustness of the system. (i) The strongly coupled current and speed, variation of parameters over time, and nonlinearity of motor torque objectively pose significant challenges in the design of adaptive tracking controllers for PMSMs. (ii) Adaptive control technology and backstepping control methods are used for designing controllers for the PMSMs. (iii) After rigorous reasoning, an intelligent adaptive tracking control strategy for the PMSMs has been derived, which is for the direct axis current and the angle. (iv) The new adaptive tracking controllers are superior to existing controllers in that they can strongly suppress the disturbance of system parameters J, TL, and B, make the system state asymptotically stable, and achieve good tracking performance for the given signals. The results of the simulation indicate the validity of the designed control strategy.

This study proposes a nonlinear adaptive optimal control method, the adaptive H2 control method, applied to the trajectory tracking problem of the wheeled mobile robot (WMR) with four-wheel mecanum wheels. From the perspective of solving mathematical problems, finding an analytical adaptive control solution that satisfies the adaptive H2 performance criterion for the trajectory tracking problem of the WMR with four-wheel mecanum wheels is an extremely challenging task due to the high complexity of the dynamic system. To analytically derive the control law and adaptive control law for this trajectory tracking problem, a proportional-derivative (PD) type transformation is employed to formalize the trajectory tracking error dynamics between the WMR and the desired trajectory (DT). Based on an in-depth analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from the highly complex nonlinear dynamic system equations. This control law provides a solution to the trajectory tracking problem of the WMR while satisfying the adaptive H2 performance criterion. The proposed adaptive nonlinear control method offers a simple control structure and advantages such as improved energy efficiency. Finally, simulations and experimental implementations were conducted to verify the performance of the proposed adaptive H2 control method and the H2 control method in tracking the DT. The results demonstrate that, compared to the H2 control method, the adaptive H2 control method exhibits superior trajectory tracking performance, particularly in the presence of significant model uncertainties.

Recently, the integration of renewable energy sources, specifically photovoltaic (PV) systems, into power networks has grown in significance for sustainable energy generation. Researchers have investigated different control algorithms for maximum power point tracking (MPPT) to enhance the efficiency of PV systems. This article presents an innovative method to address the problem of maximum power point tracking in photovoltaic systems amidst swiftly changing weather conditions. MPPT techniques supply maximum power to the load during irradiance fluctuations and ambient temperatures. A novel optimal model reference adaptive controller is developed and designed based on the MIT rule to seek global maximum power without ripples rapidly. The suggested controller is also optimized through two popular meta-heuristic algorithms: The genetic algorithm (GA) and the whale optimization algorithm (WOA). These meta-heuristic approaches have been exploited to overcome the difficulty of selecting the adaptation gain of the MRAC controller. The reference voltage for MPPT is generated in the study through an adaptive neuro-fuzzy inference system. The suggested controller’s performance is tested via MATLAB/Simulink software under varying temperature and radiation circumstances. Simulation is carried out using a Soltech 1sth-215-p module coupled to a boost converter, which powers a resistive load. Furthermore, to emphasize the recommended algorithm’s performance, a comparative study was done between the optimal MRAC using GA and WOA and the conventional incremental conductance (INC) method.

For the trajectory tracking problem of a single-particle train dynamics model under the condition of partial loss of power in the train power unit due to actuator failure during the operation of the EMU, considering the situation where the system exists with uncertain dynamics from the model and unknown external disturbers, a control method based on fuzzy adaptive fault-tolerant control method for EMU is proposed. Under the framework of the backstepping method, the fuzzy system is used to approach the system function, and a fuzzy adaptive controller is designed. It is proved that the designed control law can enable the train system to track the given speed and displacement trajectory under partial power loss. Using the CRH3 train as the research object, the results show that the designed controller can complete the trajectory tracking control task.

In this paper, we consider the observer-based adaptive consensus tracking problem for a class of nonlinear time-delay multi-agent systems in the presence of input saturation. Under the assumption that the communication topology is directed and connected, a distributed adaptive consensus controller is developed based on the dynamic surface control technique. By constructing the nonlinear observer, the unmeasurable agents dynamics can be estimated. Input saturation problem is solved by a smooth function combined with an auxiliary variable. With the help of prescribed performance functions, the synchronization errors converge to the prescribed sets, which are characterized as a neighborhood of zero. According to Lyapunov stability theory, it is shown that with the proposed distributed consensus tracking approach, the consensus errors are cooperatively semi-globally uniformly ultimately bounded. Finally, a simulation example is provided to show the effectiveness of the proposed algorithm.