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The standard backstepping control scheme has inherently computational complexity explosion problem, and consequently, becomes prohibitive as the order increases. This paper contributes to command filtered adaptive fuzzy control (AFC) of fractional-order nonlinear systems (FNSs) by using fractional backstepping control method. To approximate the virtual input, a fractional-order command filter (FCF) is proposed. Filtering approximation errors that affect the performance of the controller during the filtering process are solved by an error compensation mechanism (ECM). The simulation results verify the validity of the theoretical results.

This article considers the problem of finite-time command-filtered control for switched nonlinear systems with input quantization and output constraints. The unmeasurable state is estimated by designing a switched state observer. During the design process, to overcome the chattering problem effectively, the hysteresis quantization is designed as two bounded nonlinear functions. Furthermore, in order to restrict the output to an expected range, the barrier Lyapunov function approach is introduced. The “explosion of complexity” and the error compensation problems in the backstepping design are solved by using a finite-time command-filtered approach. A first-order Levant differentiator is used instead of the general command filter in this paper, which can not only filter the intermediate signals accurately to get the differential signals, but also ensure the finite-time stability of the filter. Stability of the closed-loop system in the sense of semi-global practical finite-time stability (SGPFS) is proved by exploring a multiple Lyapunov functions approach. Finally, a simulation example is provided to verify the validity of the presented control method.

This paper investigates the tracking control problem for fractional-order (FO) nonlinear systems with model uncertainties and external disturbances under full-state constraints. An adaptive fuzzy control strategy based on a command filter is proposed, where the asymmetric Barrier Lyapunov Function is adopted to ensure that the states do not violate their constraints, and a fuzzy logic system is used to approximate the unknown nonlinear terms. Additionally, a FO command filter is implemented to approximate the virtual control signals and their derivatives, effectively addressing the explosion of complexity problem, while an error compensation function is incorporated to compensate for the filtering errors. Overall, the stability analysis is conducted based on the Lyapunov method to ensure the boundedness of all signals. Ultimately, the performance of the proposed controller is demonstrated through two simulation examples.

In this article, the problem of fuzzy adaptive fixed-time control is addressed for nonstrict-feedback nonlinear systems with input saturation and dead zone. The universal approximation properties of fuzzy logic systems are employed to model the unknown nonlinear functions. A command filter-based fixed-time adaptive fuzzy control strategy is presented based on the backstepping framework and fixed-time control theory. The command filter technique is presented to address the “computational explosion” problem inherent in the backstepping scheme, and an error compensation mechanism is adopted to reduce the errors arising from command filters. Meanwhile, the non-smooth input saturation and dead zone nonlinearities are approximated using a non-affine smooth function, and they are transformed into an affine form based on the mean-value theorem. The fixed-time convergence of the tracking error and the boundedness of the closed-loop signals are proved using the fixed-time stability theory. Finally, simulation was performed to demonstrate the effectiveness of the presented method.

For pure-feedback stochastic nonlinear systems subject to asymmetric constraints, the current nonlinear term is constrained by linear, homogeneous growth conditions. In this work, an entirely new approach to the solution is proposed that removes completely these constraints. The approach begins with the formulation of a Barrier Lyapunov Function (BLF) that is predicated on the constrained states, thereby ensuring that the system’s state variables are maintained within the designated constraints. Subsequently, neural network techniques are employed to address unmodeled dynamics and stochastic disturbances, without imposing any growth conditions. By applying bounded command filtering technique, the analytical computation of the command signal derivatives is avoided successfully. The introduction of a dynamic event-triggered mechanism (DETM), with threshold parameters adjusted in real-time, serves to guarantee the boundedness of all signals within the closed-loop system and enables the system output to track accurately a predefined signal within a finite-time. Finally, numerical and robot manipulator system simulations are offered to augment and validate our theoretical analysis results.

This paper focuses on the decentralized finite-time prescribed performance control problem for a class of large-scale nonlinear interconnected systems with input dead zone using an adaptive fuzzy approach. Specifically, fuzzy logic systems are utilized to approximate unknown nonlinear system functions and a finite-time prescribed performance control scheme is designed by taking advantage of both the adaptive technique and backstepping scheme. By introducing two smooth functions and utilizing the command filter backstepping design, the ‘explosion of complexity’ problem inherent in the conventional backstepping control is overcome, while the associated problems due to unknown interconnections are solved. The proposed control scheme guarantees that all signals within the closed-loop controlled system are bounded and the output tracking error falls within a small range predefined by the prescribed performance within a finite time. Two simulation examples are given to verify the high effectiveness of the presented control approach.

Here, an adaptive radial basis function (RBF) neural network (NN) backstepping controller is proposed for a class of input‐constrained flexible joint robotic manipulators represented by strict‐feedback form with unknown terms, external stochastic disturbance, and output disturbance. The proposed approach is robust against both deterministic and stochastic uncertainties and disturbances and copes with the control input amplitude saturation. Moreover, by deploying the minimal learning parameter method and command filter technique, the computational burden of derivative terms and adaptive terms greatly decreases. Considering the mean‐value theorem assists us to avoid the need for having the input saturation bounds in prior. The suggested tracking control scheme mandates the closed‐loop system states to be semi‐globally bounded‐in‐probability. Also, a quartic Barrier Lyapunov function is utilized to force the tracking error to be confined within a pre‐chosen small region around the origin. Eventually, a numerical simulation of a flexible joint robot manipulator with a single link is performed to show the effectiveness and performance of the developed control method. An adaptive neural network backstepping controller is proposed for input‐constrained flexible joint robotic manipulators with unknown terms, external stochastic disturbance, and output disturbance. Deploying the minimal learning parameter and command filter techniques decreases the computational burden. Considering the mean‐value theorem avoids the pre‐need for input saturation bounds. The quartic Barrier Lyapunov function confines the tracking error and mandates semi‐globally bounded‐in‐probability.

The paper investigates the problem of adaptive fuzzy fixed-time output-feedback control for nonlinear switched systems subject to immeasurable states and arbitrary switching. The trouble of the uncertain nonlinearities is solved by employing fuzzy logic systems, and the problem of immeasurable states is settled by using state observer. In particular, a fixed-time command filter is proposed to solve the computational complexity problem resulted in the repetitive derivatives of the indirect controller. By utilizing the designed filter and the common Lyapunov function technology, an adaptive fuzzy fixed-time output-feedback control strategy is designed. The designed control strategy assures that all the states in the closed-loop system maintain bounded, and the tracking error and the state estimation error converge to a residual set in a fixed time, respectively. Furthermore, the singularity problem is effectively eliminated by utilizing L’Hospital’s rule. Eventually, the validity of the proposed control strategy is demonstrated by the numerical examples.

In this study, a finite-time adaptive prescribed performance control scheme is investigated for multi-input multi-output systems with input friction and backlash. The novel fixed-time neuro disturbance observer (Fix-TNDO) and fixed-time command filter (Fix-TCF) are constructed to ensure fast response of the controlled systems with settling time being determined regardless of initial states. The uncertainties caused by unknown smooth functions are handled by neural network approximators, then input friction and system disturbances are accurately compensated by Fix-TNDO. Meanwhile, the employed Fix-TCF is utilized to avoid repeated differentiation of virtual control signals during controller design. In particular, prescribed convergence of tracking errors for multi-input multi-output nonlinear system is ensured by finite-time performance function. Finally, simulation and experiment results demonstrate the feasibility and effectiveness of the proposed control strategy.

In this paper, a novel three‐dimensional fixed‐time integrated guidance and control (IGC) scheme with multi‐stage interconnected observers is proposed for cooperative attacks using multiple missiles against a maneuvering target under impact angle and input saturation constraints. External disturbances, modeling errors, and aerodynamic parameter variations are considered as system uncertainties and a three‐channel fully coupled IGC model for multiple missiles is established. The IGC system is designed optimally based on fixed‐time stability theory, sliding mode control, and the backstepping technique. Three inter‐cascaded fixed‐time disturbance observers based on an improved super‐twisting algorithm are designed to estimate and compensate for system uncertainties. Second‐order command filters are used to constrain virtual control signals, and additional filtering error subsystems are introduced to compensate for the tracking errors of filters. System stability and uniformly ultimately fixed‐time boundedness of all states are proven using the Lyapunov stability theory. Finally, the limits of the acceleration components of the maneuvering target perpendicular to the line of sight direction are derived. The effectiveness of the designed IGC scheme and the ability of multi‐stage interconnected observers to sense disturbances with each other are verified through simulations. There are three main points: the first one is to add the actuator factors to the existing multiple‐missile cooperative guidance law to consider the design of an integrated guidance and control scheme under multiple‐missile cooperative guidance; the second one is to design the disturbance observer with the ability to influence and sense each other on the basis of the existing fixed‐time disturbance observer based on the improved super‐twisting algorithm; and the third one is to derive the limits of a maneuvering target's acceleration perpendicular to the LOS direction under input saturation constraints.