This article addresses the problem of adaptive prescribed-time distributed consensus tracking with dynamic full-state and input triggering for a class of uncertain state-constrained strict-feedback multiagent systems with external disturbances. The primary contribution lies in developing of a novel prescribed-time disturbance observer-based adaptive chainlike filter, capable of generating smooth estimates of intermittently triggered state-feedback signals while compensating for external disturbances and unknown nonlinearities within a predefined convergence time. The multiagent systems are nonlinearly transformed to address state constraints, without needing feasibility conditions on virtual control laws in the recursive design. The dynamic triggering variables are introduced using a prescribed-time adjustment function and distributed tracking errors. Based on the state variables of the adaptive chainlike filters, a prescribed-time distributed consensus tracking strategy is established to guarantee the prescribed-time convergence of filtering errors, disturbance observation errors, leader estimation errors, and consensus tracking errors, without requiring continuous state-feedback measurements. The shared use of neural networks across chainlike filters, disturbance observers, and controllers reduces computational complexity. The practical prescribed-time stability and satisfaction of state constraints in the closed-loop system are proven through a rigorous technical lemma. Finally, simulation results validate the effectiveness and robustness of the proposed control scheme.

We propose a prescribed-time nonlinear disturbance observer (PTNDO) approach for adaptive prescribed-time tracking of state-constrained strict-feedback systems with unmatched disturbances and nonlinearities. In contrast to existing control methods that address the state constraint problem, the key contribution of this article is the development of a neural-network-based adaptive PTNDO to compensate for unmatched disturbances within a prescribed time while dealing with unknown nonlinearities in the field of the adaptive prescribed-time tracking. Based on a nonlinear transformation function technique that eliminates the conventional feasibility conditions of virtual control laws in recursive design steps, the original state-constrained system is transformed into an unconstrained system. Subsequently, by deriving a practical prescribed-time adjustment function and its related stability lemma, a PTNDO-based adaptive control strategy is established to guarantee that the disturbance observation and tracking errors converge to the adjustable bound, including zero at a prescribed settling time, while maintaining state constraints. Simulation results verify the resulting approach.

This article explores a guaranteed network connectivity problem during moving obstacle avoidance within a distributed formation tracking framework for uncertain nonlinear multiagent systems with range constraints. We investigate this problem based on a new adaptive distributed design using nonlinear errors and auxiliary signals. Within the detection range, each agent regards other agents and static or dynamic objects as obstacles. The nonlinear error variables for formation tracking and collision avoidance are presented, and the auxiliary signals in formation tracking errors are introduced to maintain network connectivity under the avoidance mechanism. The adaptive formation controllers using command-filtered backstepping are constructed to ensure closed-loop stability with collision avoidance and preserved connectivity. Compared with the previous formation results, the resulting features are as follows: 1) the nonlinear error function for the avoidance mechanism is considered an error variable, and an adaptive tuning mechanism for estimating the dynamic obstacle velocity is derived in a Lyapunov-based control design procedure; 2) network connectivity during dynamic obstacle avoidance is preserved by constructing the auxiliary signals; and 3) owing to neural networks-based compensating variables, the bounding conditions of time derivatives of virtual controllers are not required in the stability analysis.

We investigate the distributed time-varying formation tracking of networked quadrotors with input saturation and moving obstacles. The quadrotors’ position and attitude models are subjected to unknown external disturbances. This study has two main contributions. First, we develop filter-based distributed desired profiles and extended state observers (ESOs) for state-transformed nonlinear quadrotors to achieve time-varying formation tracking without requiring the velocity and acceleration information of the leader, followers, and moving obstacles. This achievement holds even in the presence of input saturation. Second, the proposed approach guarantees collision avoidance with moving obstacles, including adjacent quadrotors and unknown objects, by using only the relative distance from the obstacle, irrespective of external disturbances. This is accomplished by designing error functions for avoiding moving obstacles and including auxiliary signals in the formation tracker design. Based on the distributed profiles and the signals estimated using the ESOs, we design a collision-free time-varying formation tracker. The Lyapunov stability theory is utilized to prove that all signals of the proposed closed-loop formation tracking system are bounded, and the tracking errors converge to an adjustable bound that includes the origin. Finally, simulation results are provided to demonstrate the effectiveness of the proposed method.

This study investigates a quantized feedback design problem for distributed adaptive leader-following consensus of uncertain strict-feedback nonlinear multiagent systems with state quantizers. It is assumed that all system nonlinearities of followers are unknown and heterogeneous, all state variables of each follower are quantized by a uniform state quantizer, and quantized states of followers are only communicated under a directed network. Compared with previous approximation-based distributed consensus tracking methods for uncertain lower triangular multiagent systems, the main contribution of this article is addressing the distributed quantized state communication problem in the adaptive leader-following consensus tracking field of uncertain lower triangular multiagent systems. A quantized-states-based local adaptive control law for each follower is derived by designing quantized-signals-based weight tuning laws for neural-network-based function approximators. By analyzing the boundedness of the local quantization errors, it is shown that the total closed-loop signals are uniformly ultimately bounded and the consensus tracking errors converge to a sufficiently small domain around the origin. Finally, simulation examples, including multiple ship steering systems, are considered to verify the effectiveness of the proposed theoretical approach.

This article proposes a neural-network-based adaptive asynchronous event-triggered design strategy for the distributed consensus tracking of uncertain lower triangular nonlinear multi-agent systems under a directed network. Compared with the existing event-triggered recursive consensus tracking designs using multiple neural networks for each follower and continuous communications among followers, the primary contribution of this study is the development of an asynchronous event-triggered consensus tracking methodology based on a single-neural network for each follower under event-driven intermittent communications among followers. To this end, a distributed event-triggered estimator using neighbors' triggered output information is developed to estimate a leader signal. Subsequently, the estimated leader signal is used to design local trackers. Only a triggering law and a single-neural network are used to design the local tracking law of each follower, irrespective of unmatched unknown nonlinearities. The information of each follower and its neighbors is asynchronously and intermittently communicated through a directed network. Thus, the proposed asynchronous event-triggered tracking scheme can save communicational and computational resources. From the Lyapunov stability theorem, the stability of the entire closed-loop system is analyzed and the comparative simulation results demonstrate the effectiveness of the proposed control strategy.

This paper investigates a minimal-function-approximation (MFA)-based decentralized event-triggered tracking problem for uncertain interconnected systems with completely unknown nonaffine nonlinearities. It is assumed that events are triggered to transmit state variables in the sensor-to-controller channel. The existing approximation-based event-triggered control schemes for single lower-triangular nonlinear systems require multiple neural-network-based or fuzzy-based function approximators and multiple event-triggering conditions that are equal to the order of the system. Thus, all error surfaces using virtual control laws should be computed to verify the triggering conditions in the sensor part. To overcome the complexity in using these multiple function approximators and event-triggering conditions, we propose an event-triggered tracking strategy using one function approximator and one event-triggering condition for each subsystem in the decentralized control framework, regardless of the order of pure-feedback nonlinear subsystems. The proposed strategy is based on the MFA design technique and thus one event-triggering condition using a local tracking error is established for the local tracking law of each subsystem. Using the impulsive system approach and the Lyapunov stability theorem, the total closed-loop stability is analyzed rigorously and the minimum interevent times for each subsystem are derived to exclude the unexpected Zeno behavior.

This article addresses a filter-driven-approximation (FDA)-based design problem for the distributed containment control of multi-input-multi-output pure-feedback multiagent systems with completely unknown nonlinearities. Local filter-driven approximators are designed to compensate for unknown nonaffine nonlinear functions lumped in the local controller design procedure where the first-order filtered signals of the error surfaces, state variables, and control inputs are linearly combined for the design of the filter-driven approximators. A containment control scheme using the filter-driven function approximators is recursively constructed to ensure that the outputs of the followers converge to the convex hull spanned by multiple time-varying leaders. Compared with existing containment control results using adaptive neural-network-based or fuzzy-based approximators, the proposed FDA-based containment control scheme depends only on the relative output information among agents and does not require any adaptive techniques. Thus, the proposed control structure can be simplified. It is shown that the closed-loop signals, including approximation errors are semi-globally uniformly ultimately bounded. Simulation examples are provided to validate the effectiveness of the proposed theoretical strategy.

A neural-network-based dynamic surface design strategy against sensor and actuator deception attacks is presented to design a delay-independent adaptive resilient control scheme of uncertain nonlinear time-delay cyberphysical systems in the lower triangular form. It is assumed that all nonlinearities, time-varying delays, and sensor and actuator attacks are unknown. In the concerned problem, since the state information measured by sensors is compromised by additional attack signals, the exact state variables are not available for feedback. Thus, a memoryless adaptive resilient control design using compromised state variables is developed by employing the neural-network-based function approximation technique and designing the attack compensator. The resulting control scheme ensures the robust stabilization in the presence of unknown deception attacks and time-varying delays. It is shown from the Lyapunov stability analysis that all closed-loop signals are uniformly ultimately bounded and the stabilization errors converge to an adjustable neighborhood of the origin.

This paper investigates a distributed connectivity-preserving and collision-avoiding formation tracking problem of networked uncertain underactuated surface vessels (USVs) with heterogeneous limited communication ranges. All nonlinearities in the dynamic model are assumed to be completely unknown. Compared with the existing formation tracking results for USVs, our primary contribution is to develop a new nonlinearly transformed formation error for achieving the initial connectivity preservation, the collision avoidance, and the distributed formation tracking without switching the desired formation pattern and using any additional potential functions. In other words, these three objectives can be achieved by using only one transformed formation error surface. The local tracker design strategy using the nonlinearly transformed error is established under the direct graph topology, where the adaptive function approximation technique and the auxiliary variables are employed to compensate for uncertain nonlinearities and to deal with the underactuated problem of USVs, respectively. Finally, the Lyapunov stability analysis and simulations are performed to verify the effectiveness of the proposed theoretic result.

This paper addresses a distributed connectivity-preserving synchronized tracking problem of multiple uncertain nonholonomic mobile robots with limited communication ranges. The information of the time-varying leader robot is assumed to be accessible to only a small fraction of follower robots. The main contribution of this paper is to introduce a new distributed nonlinear error surface for dealing with both the synchronized tracking and the preservation of the initial connectivity patterns among nonholonomic robots. Based on this nonlinear error surface, the recursive design methodology is presented to construct the approximation-based local adaptive tracking scheme at the robot dynamic level. Furthermore, a technical lemma is established to analyze the stability and the connectivity preservation of the total closed-loop control system in the Lyapunov sense. An example is provided to illustrate the effectiveness of the proposed methodology.

This brief addresses a distributed connectivity-preserving adaptive consensus tracking problem of uncertain nonlinear strict-feedback multiagent systems with limited communication ranges. Compared with existing consensus results for uncertain nonlinear lower triangular multiagent systems, the main contribution of this brief is to present an error-transformation-based design methodology to preserve initial connectivity patterns in the consensus tracking field, namely, both connectivity preservation and consensus tracking problems are considered for uncertain nonlinear lower triangular multiagent systems. A dynamic surface design based on nonlinearly transformed errors and neural network function approximators is established to construct the local controller of each follower. In addition, a technical lemma is derived to analyze the stability of the proposed connectivity-preserving consensus scheme in the Lyapunov sense.

This paper presents a new approximation-based control approach for uncertain nonlinear pure-feedback systems. The main idea of this paper is to estimate unknown continuous nonlinear functions through a linear combination of first-order filtered signals of state variables and a control input in the nonadaptive control framework, instead of using conventional adaptive neural or fuzzy function approximators. Based on the proposed filter-driven approximation technique, we first present a state-feedback control scheme for pure-feedback systems with unknown nonaffine nonlinearities and a dead-zone input. Then, a filter-driven-approximation-based output-feedback control scheme is proposed via a system transformation and an observer to estimate unmeasurable state variables. Based on the Lyapunov stability theorem, the control errors and the filter-driven approximation errors are considered to prove that the controlled closed-loop system is semi-globally uniformly ultimately bounded. Finally, simulation results are provided to show that the proposed filter-driven-approximation-based controller and the existing function-approximation-based adaptive controllers have similar control performance for nonlinear pure-feedback systems.

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

This paper addresses a distributed fault detection and accommodation (DFDA) problem for uncertain nonlinear interconnected systems with faults in time-delayed nonlinearities. In contrast to existing DFDA works, we consider uncertain time-delayed interactions among subsystems and their faults, and additionally delays are assumed to be unknown. Under these conditions, a distributed memoryless local fault detection scheme consisting of a local detection estimator and its corresponding time-varying detection threshold is presented for each subsystem by using only output measurements. Then, a decentralized output-feedback control scheme for a local fault accommodation is designed based on this detection estimator and the adaptive approximation technique. The fault detectability and the stability of the proposed output-feedback DFDA scheme are thoroughly investigated in the Lyapunov sense. A simulation example is provided to illustrate the effectiveness of the proposed methodology.

A decentralized adaptive backstepping control design using minimal function approximators is proposed for nonlinear large-scale systems with unknown unmatched time-varying delayed interactions and unknown backlash-like hysteresis nonlinearities. Compared with existing decentralized backstepping methods, the contribution of this paper is to design a simple local control law for each subsystem, consisting of an actual control with one adaptive function approximator, without requiring the use of multiple function approximators and regardless of the order of each subsystem. The virtual controllers for each subsystem are used as intermediate signals for designing a local actual control at the last step. For each subsystem, a lumped unknown function including the unknown nonlinear terms and the hysteresis nonlinearities is derived at the last step and is estimated by one function approximator. Thus, the proposed approach only uses one function approximator to implement each local controller, while existing decentralized backstepping control methods require the number of function approximators equal to the order of each subsystem and a calculation of virtual controllers to implement each local actual controller. The stability of the total controlled closed-loop system is analyzed using the Lyapunov stability theorem.

In this brief, we study the distributed consensus tracking control problem for multiple strict-feedback systems with unknown nonlinearities under a directed graph topology. It is assumed that the leader's output is time-varying and has been accessed by only a small fraction of followers in a group. The distributed dynamic surface design approach is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader. The function approximation technique using neural networks is employed to compensate unknown nonlinear terms induced from the controller design procedure. From the Lyapunov stability theorem, it is shown that the consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighborhood of the origin.

This brief proposes a simple control approach for a class of uncertain nonlinear systems with unknown time delays in strict-feedback form. That is, the dynamic surface control technique, which can solve the "explosion of complexity" problem in the backstepping design procedure, is extended to nonlinear systems with unknown time delays. The unknown time-delay effects are removed by using appropriate Lyapunov-Krasovskii functionals, and the uncertain nonlinear terms generated by this procedure as well as model uncertainties are approximated by the function approximation technique using neural networks. In addition, the bounds of external disturbances are estimated by the adaptive technique. From the Lyapunov stability theorem, we prove that all signals in the closed-loop system are semiglobally uniformly bounded. Finally, we present simulation results to validate the effectiveness of the proposed approach.

A decentralized adaptive methodology is presented for large-scale nonlinear systems with model uncertainties and time-delayed interconnections unmatched in control inputs. The interaction terms with unknown time-varying delays are bounded by unknown nonlinear bounding functions related to all states and are compensated by choosing appropriate Lyapunov-Krasovskii functionals and using the function approximation technique based on neural networks. The proposed memoryless local controller for each subsystem can simply be designed by extending the dynamic surface design technique to nonlinear systems with time-varying delayed interconnections. In addition, we prove that all the signals in the closed-loop system are semiglobally uniformly bounded, and the control errors converge to an adjustable neighborhood of the origin. Finally, an example is provided to illustrate the effectiveness of the proposed control system.

In this comment, we point out an error in [1], which will show that the main result of the paper cannot be generalized for nonlinearly parametric time-delay systems considered in [1]. In [1], the authors considered the problem of the adaptive control for a class of nonlinearly parametric time-delay systems and applied successfully the proposed approach to second-order nonlinear time-delay systems with the term x1(t - tau)x2(t - tau) used as simulation examples in Section VI. However, we show in this comment that the control approach presented in [1] cannot be generalized although it is realizable for nonlinear second-order time-delay systems with the term x1(t - tau ) x2(t - tau). In addition, we illustrate this error by one detail example. For simplicity, all the symbols in this comment are the same as those in [1].

In this paper, we propose a new robust output feedback control approach for flexible-joint electrically driven (FJED) robots via the observer dynamic surface design technique. The proposed method only requires position measurements of the FJED robots. To estimate the link and actuator velocity information of the FJED robots with model uncertainties, we develop an adaptive observer using self-recurrent wavelet neural networks (SRWNNs). The SRWNNs are used to approximate model uncertainties in both robot (link) dynamics and actuator dynamics, and all their weights are trained online. Based on the designed observer, the link position tracking controller using the estimated states is induced from the dynamic surface design procedure. Therefore, the proposed controller can be designed more simply than the observer backstepping controller. From the Lyapunov stability analysis, it is shown that all signals in a closed-loop adaptive system are uniformly ultimately bounded. Finally, the simulation results on a three-link FJED robot are presented to validate the good position tracking performance and robustness of the proposed control system against payload uncertainties and external disturbances.

A new method for the robust control of flexible-joint (FJ) robots with model uncertainties in both robot dynamics and actuator dynamics is proposed. The proposed control system is a combination of the adaptive dynamic surface control (DSC) technique and the self-recurrent wavelet neural network (SRWNN). The adaptive DSC technique provides the ability to overcome the "explosion of complexity" problem in backstepping controllers. The SRWNNs are used to observe the arbitrary model uncertainties of FJ robots, and all their weights are trained online. From the Lyapunov stability analysis, their adaptation laws are induced, and the uniformly ultimately boundedness of all signals in a closed-loop adaptive system is proved. Finally, simulation results for a three-link FJ robot are utilized to validate the good position tracking performance and robustness against payload uncertainties and external disturbances of the proposed control system.