For multi-agent systems (MASs) subject to input delays and time-varying state constraints, this work proposes a predefined-time consensus control scheme. The state constraints, input delays, and additional delays caused by event triggering are obstacles that affect the control performance and practicality of MASs. To achieve predefined-time consensus while strictly satisfying the state constraints, the scheme first tackles two key obstacles: input delays and unknown system nonlinearities. Specifically, the Pade approximation technique is adopted to reconstruct the input delay into a new error variable, and then adaptive neural networks (NNs) are used to compensate for both the delay-induced error and the unknown nonlinearities. Meanwhile, by leveraging an asymmetric barrier Lyapunov function (ABLF) and a predefined-time stability framework, the scheme fundamentally ensures that the MASs achieve state consensus within a predefined time and strictly satisfy the time-varying state constraints. Further, to solve the inherent communication burden problem in networked MASs and improve the applicability of the scheme, a dynamic event-triggered mechanism (DETM) is designed as a complementary optimization: based on a dynamically evolving internal variable, the DETM only triggers communication when necessary, thereby significantly reducing the number of control updates and inter-agent data transmissions. At the same time, the scheme eliminates the requirement for agents to continuously monitor their states to determine triggering conditions, further enhancing the practicality of the scheme. Simulation results verify the effectiveness of the proposed method.

This study investigates reinforcement-learning-based fixed-time optimal formation control for multiple nonholonomic mobile robots with prescribed performance constraints. First, the constrained formation error dynamics is established using a leader-follower approach. Meanwhile, a barrier function is employed to transform the constrained formation error dynamics into an unconstrained form. Then, an adaptive control technique and a critic-only reinforcement learning strategy are utilized to design a fixed-time optimal control law for the unconstrained error dynamics. Rigorous theoretical derivations demonstrate that the proposed control law guarantees that the constrained formation error converges to near zero within a fixed time, optimizing the performance index while satisfying the prescribed performance requirement. Finally, the feasibility of the proposed method is verified through simulations and experiments.

This paper investigates a fixed-time consensus control problem of nonlinear multi-agent systems under full-state constraints. First, by designing corresponding constraint functions for system transformation, state-dependent asymmetric time-varying constraints are realized. The feasibility conditions of the system are eliminated, and the requirements on the constraint boundary are relaxed. Meanwhile, a prescribed performance function is designed for the constraints on synchronization deviation, which helps to improve the transient and steady-state performance of the system and ensure rapid consensus convergence on a fixed-time framework. Additionally, considering the frequent communication between the controller and actuator and to decrease the controller update frequency to save system bandwidth, an adaptive threshold event-triggered mechanism is developed. A dynamic parameter is introduced into the triggered mechanism to adjust the triggered threshold, thereby overcoming the issue that static parameters might cause excessive or insufficient event-triggered and avoiding Zeno behavior. Finally, the effectiveness of the proposed strategy is verified through simulation. Note to Practitioners—In complex modern engineering systems, the consensus control of multi-agent systems has become a research hotspot. In practical industrial applications, given the requirements for safety and production efficiency, it is crucial for systems to effectively constrain states and ensure performance. This study employs the prescribed performance strategy within the fixed-time framework to construct the control method. The constraints of the system’s full states are achieved by transforming a constrained system into an unconstrained one. Meanwhile, the use of event-triggered mechanisms saves communication resources. The proposed method not only ensures rapid consensus convergence under full-state constraints but also enhances the control performance of multi-agent systems, closely connected to the needs of practical applications. Future research will continue to investigate how to apply it to practical engineering applications.

A prescribed time fuzzy adaptive consensus control method is constructed for multiagent systems with sensor faults and dead-zone input. Sensor faults inevitably occur in actual engineering systems and may distort the state information. Besides, the control effect would be further dramatically affected when systems exist dead-zone input. Thus, a fuzzy adaptive compensation strategy is established by the bounded adaptive optimized method to eliminate the impact of the above constraints. Furthermore, a given performance consensus control method is investigated with the aid of nonlinear transformation. Meanwhile, combined with the prescribed time technology, it further achieves that the systems settling time can be preselected while the performance of the systems is given. Finally, some simulation experiments are adopted to demonstrate the feasibility and effectiveness of the investigated control method.Note to Practitioners—This work studies the consensus problem for multiagent systems, which is important in engineering collaborative applications. Due to measurement noise and electronic damage, sensor faults inevitably happen in industrial applications. Besides, dead-zone input often occurs in actual systems as physical properties of electronic components. Based on the bounded adaptive optimized method, a fuzzy adaptive compensation strategy is constructed to deal with those issues. To further improve the control performance in the collaborative process, prescribed time technology and given performance strategy are applied to construct the control method. The investigated approach can be useful in multiagent systems to achieve more steady consensus operation, which is more in line with the application requirements.

A fixed-time fuzzy control (FTFC) scheme is suggested for uncertain nonlinear systems with prescribed performance (PP) and event-triggered communication. First, the original system with PP constraints is transformed into an unconstrained one using a coordinate transformation. Next, fuzzy logic systems (FLSs) are introduced to estimate the uncertain nonlinear functions, and an event-triggered mechanism (ETM) is designed to reduce the update frequency of the control signal. Then, a fixed-time fuzzy controller is proposed to ensure that the tracking error converges within a fixed time. Rigorous theoretical analysis shows that the proposed control scheme can achieve the fixed-time convergence of the tracking error according to the PP requirement. At the same time, communication resources are saved compared to traditional time-triggered control methods. Finally, the validity of the theoretical results is verified by simulation results.

The fixed-time formation control problem for uncertain nonlinear multiagent systems (MASs) with time-varying actuator failures is investigated. Actuator failures would have a huge impact on the system performance, especially when the actuator failures are time-varying, which may even cause system insecurity. In order to cope with time-varying actuator failures, a fixed-time convergence approach is proposed based on adaptive fuzzy control technology. Simultaneously, solving the above problems would aggravate the occupation of communication resources of the system. Therefore, a periodic adaptive event-triggered control scheme is developed, in which the triggering period can be adjusted adaptively. Furthermore, the convergence time of formation errors can be preset by applying the fixed-time control method. The convergence velocity can be accelerated immensely. Eventually, theoretical analysis and simulation illustrate that the proposed method can effectively compensate the time-varying actuator failures, and the MASs can achieve formation within a fixed time by using less communication resources.

The issue of practical fixed-time control is investigated for a category of uncertain nonlinear systems with input dead-zone constraint. Many practical control systems are subject to the constraint of communication resources and input dead zone, which affects the system’s performance and even results in system instability. To handle the above problems, an extended radial basis function neural networks (ERBFNNs) adaptive event-triggered control method is developed to enable the online compensation of input dead zone and schedule the update of control signals. On this foundation, based on the fixed-time stability theorem, a practical fixed-time event-triggered controller is established by the backstepping technique. Technically, the controller can guarantee that the tracking error converges into a small and adjustable set in a fixed time under different initial states, and the boundary of convergence time is dependent on the adjustable design parameters. Meanwhile, all the closed-loop signals are bounded, the communication resources are saved, and the Zeno behavior is also avoided. Finally, some simulation examples are given to illustrate the validity of the presented strategy.

A fixed‐time event‐triggered consensus control method is proposed for uncertain nonlinear multiagent systems with actuator failures. Since actuator failures, external disturbances and control gains are time‐varying and completely unknown, the effects of these system constraints on the system are completely unknown, which makes the implementation of fixed‐time tracking control challenging. To deal with these system constraints, radial basis function neural networks (RBFNNs) are applied to approximate the uncertain dynamics, and a boundary estimation method is presented to achieve adaptive compensation for them. Furthermore, considering that the implementation of this boundary estimation method requires a large number of communication resources, an event triggering mechanism is designed to reduce the update frequency of the controller. It is theoretically confirmed that using the proposed control scheme, all the followers can track the leader with sufficient accuracy in a predetermined time, and all the closed‐loop signals are bounded. Finally, the simulation experiments verify the theoretical results.

The fast finite-time event-triggered consensus control is investigated for a category of uncertain nonlinear multiagent systems (MASs) with full-state constraints. The uncertainty of the system is estimated by the radial basis function neural networks (RBFNNs). Furthermore, to achieve the fast finite-time stability and not violate the full-state constraints, a fast finite-time event-triggered consensus control method is proposed. The proposed control method can achieve the fast finite-time stability of the system, and all the followers can track the output signal of the leader. Meanwhile, the system states do not exceed the boundaries of the full-state constraints, and the communication resources of the system can be saved. Finally, some simulation examples are provided to verify the feasibility of the proposed approach.

For a class of uncertain nonlinear systems with actuator failures, the event-triggered prescribed settling time consensus adaptive compensation control method is proposed. The unknown form of actuator failures may occur in practical applications, resulting in system instability or even control failure. In order to effectively deal with the above problems, a neural network adaptive control method is developed to ensure that the system states rapidly converge in the event of failure and compensate for the failures of actuator. Meanwhile, a nonlinear transformation function is introduced to make sure that the tracking error converges for the predefined interval within a prescribed settling time, which makes that the convergence time can be preset. Furthermore, a finite-time event-triggered compensation control strategy is established by the backstepping technology. Under this strategy, the system not only can rapidly stabilize in finite time but also can effectively save network bandwidth. In addition, the states of the system are globally uniformly bounded. Finally, the theoretical analysis and simulation experiments validate the effectiveness of the proposed method.

The issue of neural adaptive self-triggered tracking control for uncertain nonlinear systems with input hysteresis is considered. Combining radial basis function neural networks (RBFNNs) and adaptive backstepping technique, an adaptive self-triggered tracking control approach is developed, where the next trigger instant is determined by the current information. Compared with the event-triggered control mechanism, its biggest advantage is that it does not need to continuously monitor the trigger condition of the system, which is convenient for physical realization. By the proposed controller, the hysteresis's effect can be compensated effectively and the tracking error can be bounded by an explicit function of design parameters. Simultaneously, all other signals in the closed-loop system can be remaining bounded. Finally, two examples are presented to verify the effectiveness of the proposed method.

This article investigates a fuzzy adaptive two-bit-triggered control for uncertain nonlinear systems with actuator failures and dead-zone constraint. Actuator failures and dead-zone constraint exist frequently in practical systems, which will affect the system performance greatly. Based on the improved fuzzy-logic systems (FLSs), a fuzzy adaptive compensation control is established to address these issues. The approximation error is introduced to the control design as a time-varying function. In addition, for the limited transmission resources of the practical system, a two-bit-triggered control mechanism is proposed to further save system transmission resources. It is proved that the proposed method can guarantee the system tracking performance and all the signals are bounded. Its effectiveness is verified by the simulation examples.

In this paper, an adaptive neural network control for stochastic nonlinear systems with uncertain disturbances is proposed. The neural network is considered to approximate an uncertain function in a nonlinear system. And computational burden in operation is reduced by handling the norm of the neural-network vector. However, it will arise chattering issue, which is a challenge to avoid it from the symbolic operation. Further, traditional schemes often view error of estimate as bounded constant, but it is a time-varying function exactly, which may lead control schemes cannot conform to practical situation and guarantee stability of systems. Thus, backstepping technology and the neural network technology combined to stabilize stochastic nonlinear systems together to handle the aforementioned issues. It is proved that the proposed control scheme can guarantee the satisfactory asymptotic convergence performance and predetermined transient tracking error performance. From simulation results, the proposed control scheme is verified that can guarantee the satisfactory effectiveness.

Hysteresis exists ubiquitously in physical actuators. Besides, actuator failures/faults may also occur in practice. Both effects would deteriorate the transient tracking performance, and even trigger instability. In this paper, we consider the problem of compensating for actuator failures and input hysteresis by proposing a fuzzy control scheme for stochastic nonlinear systems. Compared with the existing research on stochastic nonlinear uncertain systems, it is found that how to guarantee a prescribed transient tracking performance when taking into account actuator failures and hysteresis simultaneously also remains to be answered. Our proposed control scheme is designed on the basis of the fuzzy logic system and backstepping techniques for this purpose. It is proven that all the signals remain bounded and the tracking error is ensured to be within a preestablished bound with the failures of hysteretic actuator. Finally, simulations are provided to illustrate the effectiveness of the obtained theoretical results.

In this paper, the uncertain direct of the hysteretic system component will be considered. Besides, the effect of stochastic disturbance inevitably exists in many practical systems, which would cause the instability. Simultaneously, it is significant to guarantee the perfect error tracking performance for the uncertain nonlinear hysteresis systems when operation suffers the failure. To ensure the maintaining acceptable system performance in reality, the new properties of the Nussbaum function are proposed, and an auxiliary virtual controller is designed through the neural network (NN) universal approximator. Furthermore, it is challenged to save the system-limited transmutation resource for nonlinear systems, especially for stochastic nonlinear systems, with unknown hysteresis input and actuator failures. The coupling effect of the system communication resource constrains has to arise the issue of the mutual coupling function, which makes that the tracking control design is more complicated. Using the proposed event-triggered controller and back-stepping technology, a new optimization algorithm is proposed to ensure that the states of the closed-loop system and the tracking error remain bounded in probability. Finally, to illustrate the effectiveness of our proposed adaptive NN control method with the event-triggered strategy, some numerical examples are provided.

In this paper, event trigger fuzzy adaptive compensation control for the uncertain stochastic nonlinear system with actuator failures is considered. Although great strides have been made in the accommodating nonlinear system recently, it remains a challenge to establish an event-triggered-based controller for the uncertain stochastic nonlinear system with actuator failures, especially to ensure asymptotic tracking performance. In this paper, we propose a new relative event trigger adaptive fuzzy controller established by utilizing the techniques of robust approach to address the actuator failures and stochastic interference. It is proven that the proposed scheme guarantees the bounding of all closed-loop signals and the asymptotic convergence performance of tracking error. Simulation results demonstrate that our proposed control scheme for compensating the stochastic nonlinear system guarantees effectiveness.