Cooperative rendezvous between the autonomous surface vehicle (ASV) and uncrewed underwater vehicle (UUV) constitutes a core support for the marine Internet of Things (MIoT). However, the communication between two vehicles is vulnerable to denial-of-service (DoS) attacks, which may lead to rendezvous failure. To address this challenge, this study develops a safe resilient rendezvous control method with dynamic event-triggered mechanism. An adaptive neural parameter compression algorithm is incorporated to approximate heterogeneous system uncertainties and external disturbances with fewer adaptive parameters, effectively alleviating computational burdens. To further ensure a safe rendezvous, a prescribed performance control (PPC)-based scheme is proposed to regulate the UUV’s ascending trajectory, thereby facilitating a smooth ascent. Considering that communication between the ASV and UUV may be disrupted by DoS attacks, a second-order resilient filter is proposed to estimate the unavailable virtual leader states in real time. To optimize onboard communication usage, a dynamic event-triggered mechanism is embedded within the control design, enabling a more flexible control for cooperative rendezvous. The closed-loop stability is provided under DoS attacks, with simulation results and comparisons demonstrating the effectiveness of the proposed rendezvous approach.

This article investigates the problem of disturbance attenuation for autonomous surface vehicles (ASVs) subject to asymmetric time-varying saturation. To address this challenge, we propose a novel event-triggered (ET) zero-sum (ZS) differential game framework that integrates a barrier function and a nonquadratic value function, enabling simultaneous achievement of safety control and disturbance attenuation. Initially, by designing a barrier function, the control problem of the asymmetric time-varying saturated ASV system is transformed into an unsaturated form. Afterward, a nonquadratic value function is designed, and ZS games are employed to obtain the saturated-optimal control policy and the worst-case disturbance policy. Then, the ET method is introduced into policy execution and critic neural network learning. The scheme in this article ensures the safety and stability of the ASV while reducing computational burden and meeting the needs of disturbance attenuation. Finally, theoretical analysis and simulation experiments verify the feasibility of the ET ZS differential game approach.

This paper proposes a novel dynamic event-triggered control method for a class of completely unknown nonaffine hierarchical differential games, incorporating asymmetric boundaries in both system states and control strategies. To tackle this problem, dynamic feedback and mapping functions are first introduced to construct an unconstrained affine augmented system. Then, integral reinforcement learning techniques are used to derive the Hamilton-Jacobi equation without the original system dynamics. Furthermore, dynamic event-triggered control is employed to alleviate the network transmission burden. During the algorithm implementation, critic neural networks are designed for each agent. Analysis results show that the states and weights are ultimately uniformly bounded. Finally, simulation results using the torsional pendulum system and RLC circuit system validate the effectiveness of the present method.

In this article, an integral reinforcement learning (IRL) method is developed for dynamic event-triggered nonzero-sum (NZS) games to achieve the Nash equilibrium of unmanned surface vehicles (USVs) with state and input constraints. Initially, a mapping function is designed to map the state and control of the USV into a safe environment. Subsequently, IRL-based coupled Hamilton-Jacobi equations, which avoid dependence on system dynamics, are derived to solve the Nash equilibrium. To conserve computational resources and reduce network transmission burdens, a static event-triggered control is initially designed, followed by the development of a more flexible dynamic form. Finally, a critic neural network is designed for each player to approximate its value function and control policy. Rigorous proofs are provided for the uniform ultimate boundedness of the state and the weight estimation errors. The effectiveness of the present method is demonstrated through simulation experiments.

The quadratic program (QP) with equality constraint is widely involved in science and engineering fields. Numerous solutions to the equality-constrained QP (ECQP) have been reported, particularly the zeroing neural network (ZNN) for the time-dependent ECQP. However, such solutions can be severely affected by the harmonic noise and may lose their efficacy. This study aims to address the above limitation by proposing the new ZNN model against harmonic noise with the only known frequency. Such a model, called the harmonic noise rejection ZNN (HNR-ZNN) model, is established by incorporating the dynamics of the harmonic signal (from which the unknown information for the signal's amplitude and phase can be eliminated). Theoretical analysis indicates that the proposed HNR-ZNN model effectively determines the optimal solution of time-dependent ECQP under harmonic noise interference. Comparative computer simulations and real-world robot applications further indicate the validity, excellence, and practicality of the presented HNR-ZNN model.

This article presents an efficient method for solving the optimal tracking control policy of unmanned surface vehicles (USVs) using a hybrid adaptive dynamic programming (ADP) approach. This approach integrates data-driven integral reinforcement learning (IRL) and dynamic event-driven (DED) mechanisms into the solution of the control policy of the established augmented system while obtaining both the feedforward and feedback components of the tracking controller. For the USV model and the reference trajectory, an augmented system is established, and the tracking Hamilton-Jacobi-Bellman (HJB) equation is derived based on IRL, aiming to fully utilize system data information and reduce model dependency. For the solution of the tracking HJB equation, the DED-based controller update rule is used to further reduce the burden of network transmission. In implementing the ADP method, the DED experience replay-based weight update rule is utilized to recycle data resources. Experiments show that compared with the static event-driven (SED) approach, the DED approach reduces the sample size by 78% and increases the average interval by about four times.

An event-triggered adaptive dynamic programming (ADP) algorithm is developed in this article to solve the tracking control problem for partially unknown constrained uncertain systems. First, an augmented system is constructed, and the solution of the optimal tracking control problem of the uncertain system is transformed into an optimal regulation of the nominal augmented system with a discounted value function. The integral reinforcement learning is employed to avoid the requirement of augmented drift dynamics. Second, the event-triggered ADP is adopted for its implementation, where the learning of neural network weights not only relaxes the initial admissible control but also executes only when the predefined execution rule is violated. Third, the tracking error and the weight estimation error prove to be uniformly ultimately bounded, and the existence of a lower bound for the interexecution times is analyzed. Finally, simulation results demonstrate the effectiveness of the present event-triggered ADP method.

In this article, an event-triggered$H_{\infty }$control method is proposed based on adaptive dynamic programming (ADP) with concurrent learning for unknown continuous-time nonlinear systems with control constraints. First, a system identification technique based on neural networks (NNs) is adopted to identify completely unknown systems. Second, a critic NN is employed to approximate the value function. A novel weight updating rule is developed based on the event-triggered control law and time-triggered disturbance law, which reduces controller execution times and guarantees the stability of the system. Subsequently, concurrent learning is applied to the weight updating rule to relax the demand for the traditional persistence of excitation condition that is difficult to implement online. Finally, the comparison between the time-triggered method and event-triggered method in simulation demonstrates the effectiveness of the developed constrained event-triggered ADP method.

In this article, an event-triggered adaptive dynamic programming (ADP) method is proposed to solve the robust control problem of unmatched uncertain systems. First, the robust control problem with unmatched uncertainties is transformed into the optimal control design for an auxiliary system. Subsequently, to reduce controller executions and save computational and communication resources, an event-triggering mechanism is introduced. By using a critic neural network (NN) to approximate the value function, novel concurrent learning is developed to learn NN weights, which avoids the requirement of an initial admissible control and the persistence of excitation condition. Moreover, it is proven that the developed event-triggered ADP controller guarantees the robustness of the uncertain system and the uniform ultimate boundedness of the NN weight estimation error. Finally, by using the F-16 aircraft and the inverted pendulum with unmatched uncertainties as examples, the simulation results show the effectiveness of the developed event-triggered ADP method.

This article reviews the recent development of adaptive dynamic programming (ADP) with applications in control. First, its applications in optimal regulation are introduced, and some skilled and efficient algorithms are presented. Next, the use of ADP to solve game problems, mainly nonzero-sum game problems, is elaborated. It is followed by applications in large-scale systems. Note that although the functions presented in this article are based on continuous-time systems, various applications of ADP in discrete-time systems are also analyzed. Moreover, in each section, not only some existing techniques are discussed, but also possible directions for future work are pointed out. Finally, some overall prospects for the future are given, followed by conclusions of this article. Through a comprehensive and complete investigation of its applications in many existing fields, this article fully demonstrates that the ADP intelligent control method is promising in today's artificial intelligence era. Furthermore, it also plays a significant role in promoting economic and social development.

In this paper, the zero-sum game problem is considered for partially unknown continuous-time nonlinear systems, and an event-triggered adaptive dynamic programming (ADP) method is developed to solve the problem. First, an identifier neural network (NN) and a critic NN are applied to approximate the drift system dynamics and the optimal value function, respectively. Subsequently, an event-triggered approach is developed based on ADP, which samples the states and updates the weights of NNs at the same time when the event-triggering condition is violated, such that the computational complexity is reduced. It is proved that the states and the error of NN weights are uniformly ultimately bounded. Finally, the effectiveness of the developed ADP-based event-triggered method is verified through simulation studies.