This article explores a new strategy for designated time stabilization of stochastic time-varying nonlinear systems. Conventional prescribed-time stabilization has limitations in practical engineering due to singularities induced by infinite control amplitude and a lack of manipulation of the state response after a prescribed time. To address these challenges, we build a hybrid stabilization controller using state-scale techniques and a finite-time stabilization process that is bounded in probability over the full range, guaranteeing that the closed-loop system has a solution that is almost surely unique at a designated time. Compared to the current prescribed stabilization results, the proposed strategy not only ensures that the state of the system converges in probability to a compact set at a designated time and belongs to the set after which it eventually enjoys fast finite-time convergence. Finally, the effectiveness of the strategy is verified by simulating a real mass-spring mechanical system.

This paper tackles the consensus tracking control challenge for a category of uncertain nonlinear multi-agent systems subject to unknown time-varying disturbances and output constraints. Even if only a portion of followers can directly receive the leader’s information, by developing a new barrier Lyapunov function and integrating it with the backstepping technique, a distributed robust adaptive state feedback controller is developed, which not only guarantees that the system outputs remain within prescribed constraints but also ensures that the output error between any two followers and the tracking error converge to the origin asymptotically. Neither control design nor theoretical analysis relies on eigenvalue information of Laplacian, thus eliminating the demand for global information and enhancing the utilization efficiency of local communication resources. The effectiveness of the control strategy is ultimately demonstrated through a practical example of single-link manipulators.

An adaptive neural networks event-triggered secure strategy is investigated to explore stochastic networked nonlinear systems with Denial-of-Service (DoS) attacks and unknown dead zone. In order to alleviate the negative effects of DoS attacks, a state estimator is constructed to approximate the immeasurable states. And the unknown dead zone input function is described as a bounded disturbance and a time-varying nonlinear function to offset the unknown dead zone effect. To defend against DoS attacks while ensuring system stability, an adaptive event-triggered prescribed performance controller is designed, ensuring that all signals of the closed-loop system are bounded in probability, and the tracking error tends to the designed performance bound within a predefined finite time. Meanwhile, this secure strategy can completely eliminate potential Zeno behavior. Subsequently, the modified average dwell time (ADT) approach was integrated with Lyapunov stability theory to establish the stability of the system. Eventually, two simulation results are utilized to prove the effectiveness of the developed strategy.

This paper investigates event-triggered prescribed-time stabilization for time-varying nonlinear systems. The motivation arises from three challenging issues: the singularity resulting from infinite control gains at the prescribed time instant, the management of infinity of implicit time variation, and trade-off between control effort and triggering intervals. Using a delicate trick that the finite value of a new time-varying function remains unchanged once all state variables of the system hit zero, we create an event-triggered strategy incorporating a sophisticated switching trigger rule equipped with a time-dependent threshold, based on the continuous feedback domination method with a series of integral functions containing nested sign functions. Better than existing results on prescribed-time stabilization, the scheme presented in this paper not only guarantees that states converge to zero precisely within the prescribed time and sustains non-truncated controller operation, but also uniquely tackles the prevention of the Zeno phenomenon. At last, the stabilization of tunnel diode circuit is conducted to confirm the validity and the effectiveness of our strategy.

This article explores the problem of prescribed-time stabilization for a class of high-order polynomial nonlinear systems with unknown time-varying nonlinearities. The key technique behind the proposed strategy involves fixing the time-varying components to their bounded values before the prescribed time and establishing a new lemma to suppress the time-varying continuous functions in the investigated system. We design a continuous bounded feedback controller to address the singularities induced by infinite control gains at the prescribed time and to suppress the implicit effects of time variations. Superior to the existing prescribed-time stabilization results, our strategy achieves the states' convergence within the prescribed-time and the nontruncated run of controller simultaneously. We employ the wing rock motion to demonstrate the practicality and superiority of the developed strategies.

In this study, an event-driven fuzzy adaptive control strategy is introduced to address the tracking control problem in a class of stochastic nonstrict-feedback systems under conditions of input delay, unknown control directions and full-state constraints. First, a model for a class of stochastic nonlinear control systems is established based on a ship maneuvering system. Subsequently, the system model is generalized further to obtain more complex nonstrict-feedback systems with unknown control directions. Next, the system is preprocessed to facilitate the design of control strategy. Through the introduction of an intermediate variable, Pade approximation principle is employed and the impact of input delay is eliminated. Subsequently, a nonlinear mapping approach is employed to transform the issue of full-state constraints into an unconstrained problem. This circumvents the complexities caused by the utilization of barrier Lyapunov functions effectively. Furthermore, the principles of fuzzy approximation and adaptive control theory are introduced. Based on the properties of the exponential function, an event-triggered control strategy is designed meticulously to ensure the semiglobal boundedness of all signals in the closed-loop system.

This study focuses on addressing the challenge of global output feedback control problem for a class of time-varying stochastic nonlinear systems subject to multiple uncertainties. The primary challenge concerns how to construct time-varying functions to counteract the effects of unmeasurable error coming from system output as well as the persistently increasing nonlinearities. By employing a full-order state observer and the dual gain approach, we design an output feedback regulator over the entire time domain to guarantee the existence and uniqueness of the closed-loop system’s solution and the almost sure asymptotic convergence of the state. This methodology achieves both the domination of the unknown growth rate and the unified system design, irrespective of sensor sensitivity. Finally, practical and numerical simulation examples demonstrate the feasibility of the presented approach.

This article explores the tracking issue for dc-dc buck power converter with stochastic disturbance, specifically focusing on how output voltage tracks to a desired voltage in a finite-time when the load changes. Meanwhile, considering unmodeled dynamics and nonaffine inputs, we propose an innovative finite-time fuzzy prescribed performance switching tracking algorithm to achieve tracking goal. For realizing the requirements of performance, the algorithm converts the tracking error to a new state by means of a coordinate transformation via the tangent function. In addition, the universal approximation capacity of the fuzzy-logic system is utilized to estimate the unknown nonlinear term effectively. On this basis, the designed adaptive dynamic event-triggered controller can not only ensure that all the signals for the closed-loop system remain bounded in probability but also guarantee that the tracking error will converge to a predetermined small neighborhood. Meanwhile, different piecewise functions are added into the controller to characterize prescribed performance and avoid singularity problems, respectively. Finally, the effectiveness of the tracking control algorithm is fully demonstrated by the simulations of the dc-dc buck power converter.

This article is concerned with the global fast finite-time adaptive stabilization for a class of high-order uncertain nonlinear systems in the presence of serious nonlinearities and constraint communications. By renovating the technique of continuous feedback domination to the construction of a serial of integral functions with nested sign functions, this article first proposes a new event-triggered strategy consisting of a sharp triggered rule and a time-varying threshold. The strategy guarantees the existence of the solutions of the closed-loop systems and the fast finite-time convergence of original system states while reaching a compromise between the magnitude of the control and the trigger interval. Quite different from traditional methods, a simple logic is presented to avoid searching all the possible lower bounds of trigger intervals. An example of the maglev system and a numerical example are provided to demonstrate the effectiveness and superiority of the proposed strategy.

The motivation of this study is to solve the challenges posed by the nonstrict feedback structure and multiple timedelays factors in stochastic systems, which significantly complicate the structure of system structure and make the procedure of controller design more difficult. Firstly, a new LyapunovKrasovskii function is constructed in this study. A method is devised based on this function, which incorporates the characteristic of kernel functions in fuzzy logic systems and the concept of variable separation to effectively tackle challenges posed by complex system structures and time-delay factors, as well as reducing the burden of updating dynamic gains. Additionally, the application of the Nussbaum function technique efficiently resolves the issue of unknown control direction while ingeniously leveraging the distinctive properties of the Nussbaum function and the stochastic Barbalat's lemma. This approach provides a complete theoretical proof of the boundedness of the system signals and guarantees the asymptotically stable in probability. Ultimately, the proposed approach is validated by the exceptional performance of the simulation results for an electromechanical control system.

This article extends the finite-time adaptive tracking control to stochastic nonlinear systems with multiple uncertainties, including output constraints, unknown parameters, unmodeled dynamics, and external disturbances. Most relevant results in literature have two main restrictions: 1) uncertainties and unknown items in the systems; 2) the matter of “explosion of complexity.” By integrating an improved technique of adding fuzzy logic systems to estimate unknown parameters with a bounded command filter method, a systematic tracking control scheme is developed that eliminates both of the above restrictions. To alleviate the serious uncertainties caused by the constraints, a quartic asymmetric time-varying barrier Lyapunov function is utilized when the control coefficient is known. Subsequently, an event-triggered controller is constructed that enables boundedness and finite-time convergence of all closed-loop signals. Eventually, to validate the effectiveness of the proposed adaptation strategy, this new method is applied to ship maneuvering systems that encounters multiple uncertainties arising from disturbances, such as wind, waves, and ocean currents.

This article aims to solve two intricate problems in nonlinear control: 1) the zero-division of the control by requiring its differentiability and 2) the finite-time stabilization via adaptive feedback for a class of uncertain nonlinear systems with asymmetric output constraints. The issue is how to control the system states to converge to the origin quickly while not violating the output constraints. This article develops an adaptive stabilizing controller constituting a piecewise tangent-type barrier function and a series of non-negative integral functions with sign functions, which is bounded over the whole time horizon and ensures the fast convergence of the system states. The innovation is two-fold: a technical lemma is proposed for the first time to make the designed controller completely decoupled from the first state variable of the system. The proposed strategy can handle both constrained and unconstrained systems without reconstructing barrier functions associated with the output constraint. Finally, the stabilization of a liquid-level system is investigated to demonstrate the effectiveness of the control scheme.

A fast finite-time adaptive fuzzy tracking control algorithm is proposed for stochastic nonlinear systems (SNSs) under an event-triggered mechanism. Unlike the traditional finite-time control of SNSs, for this article, the drift and diffusion terms can be completely unknown. First, a fuzzy-logic system has been implemented to approximate the uncertain functions of SNSs. Second, a novel theorem of a fast finite-time adaptive control mechanism of deterministic systems is presented by revamping the fast finite-time stability in the mean square. Next, the complex explosion issue caused by the backstepping technique is effectively avoided based on command filtering feedback control. Compared with the standard backstepping technique, which has avoided the analytical computations of the derivatives of virtual control functions and has dramatically reduced the computational burden. Finally, an example of the one-link manipulator with motor dynamic systems is provided to verify the theoretical analysis.

In this note, finite-time adaptive tracking control is studied for nonlinear systems with unmodeled dynamics, asymmetric time-varying output constraints, and uncertain disturbances. Without any growth conditions, fuzzy logic systems are applied to tackle the unknown complicated functions. A novel backstepping approach is developed by combining barrier Lyapunov functions and bounded finite-time command filter. By regulating the threshold parameters online, a new dynamic event-triggered controller is established to ensure that all the signals of the closed-loop system are bounded and the output can follows the preset signal in finite time. Meanwhile, the output is always staying in an asymmetric time-varying interval all the time. The feasibility of the proposed control algorithm is verified with a numerical example and a practical application.

This study concentrates on the tracking control problem for nonlinear systems subject to actuator saturation. To improve the performance of the controller, we propose a fixed-time tracking control scheme, in which the upper bound of the convergence time is independent of the initial conditions. In the control scheme, first, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. Then, the effect of input saturation is compensated by introducing an auxiliary system. Furthermore, a fixed-time adaptive neural network control method is given with the help of fixed-time control theory, in which the dynamic order of controllers is reduced to a certain extent since there is only one updating law in the entire control design. Through rigorous theoretical analysis, it is concluded that the proposed control scheme can guarantee that: 1) the output tracking error can converge to a small neighborhood near the origin in a fixed time and 2) all signals in the closed-loop system are bounded. Finally, a numerical example and a practical example based on the single-link manipulator are provided to verify the effectiveness of the proposed method.

In this article, the problem of global fixed-time stabilization for a class of high-order uncertain nonlinear systems has been investigated. Quite different from traditional methods, a novel finite-time control scheme is presented for the first time based on a serial of exponential functions and fractional power integration with nested sign functions, which can guarantee that the convergent time of the states of the closed-loop systems is finite and independent of any initial conditions by the simple choice of design parameters. The remarkable contribution of this article lies in the fact that it provides an alternative to manipulate the possibility of initial states being far from the origin. As a practical application, the finite-time stabilizing design of maglev systems is provided to demonstrate the effectiveness and the superiority of the proposed strategy.

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

This article is concerned with the improvement of robust control methodology and its application in stabilizing a class of high-order nonlinear systems with multiple unknown time-varying sensitivities, and discusses how to use the proposed control strategy on humanoid robot manipulation. The novel design approach successfully breaks through the limitation of the neural network technique; that is, state variables must be located in some compact sets. The remarkable feature of the systems under investigation lies in the presence of measurement sensitivities and higher powers, which makes the nonlinear systems essentially different from the related works. By reductio and the introduction of a modified tuning function, an appropriate controller is constructed to render that all the state variables belong to a predetermined bounded set. Finally, an example is provided to illustrate the effectiveness of the proposed control strategy.

This article reports this article on the problem of adaptive fuzzy output tracking control for a category of high-order nonlinear systems with input saturation, output constraint, and serious uncertainties. A high-order barrier Lyapunov function and an auxiliary Hyperbolic Tangent function is employed to deal with output constraint and input saturation, respectively. By incorporating a backstepping design technique, adaptive fuzzy control, and adding a power integrator, a novel control scheme is designed to ensure that all states in the resulting closed-loop system are bounded and the tracking error converges to a bounded compact set. Moreover, two simulations are conducted to verify the effectiveness of the design method.

This article reports our study on the issue of finite-time adaptive fuzzy tracking control for a class of uncertain nonlinear systems with the prescribed performance. A novel finite-time prescribed performance control approach, in which fuzzy systems are employed to approximate completely unknown nonlinear functions, is proposed by incorporating the technique of prescribed performance control with the method of command filtered design. Based on the finite-time stability theory, all the signals of the closed-loop system can be bounded and the output tracking error can converge to a prescribed small region within a finite-time by the proposed scheme; meanwhile, the problem of complexity explosion can be avoided. The effectiveness of the presented method is verified by two examples.