This paper investigates the preset trajectory tracking control problem of vehicular platoon systems (VPS) with state constraints and preassigned performance requirements using reinforcement learning (RL). Specifically, both velocity and acceleration constraints are simultaneously considered along with performance requirements, thus providing a more comprehensive guarantee of system safety and stability. Existing approaches based on barrier Lyapunov functions (BLF) can tackle these issues but are prone to nonlinear growth and singularity problems, which complicates controller design. To overcome these limitations, a novel two-step state transformation strategy is proposed. First, a nonlinear mapping function (NMF) is employed to reconstruct the states, embedding velocity and acceleration constraints directly into the transformed state space. Second, a preset-trajectory-based preassigned performance control (PPC) strategy is adopted to convert the performance requirements into a tracking task. This strategy effectively mitigates nonlinear growth and singularity issues, simplifying controller design and stability analysis. On this basis, a simplified RL algorithm based on neural networks (NNs) within the actor–critic framework is integrated with the backstepping method, to enhance the overall control performance. The proposed method guarantees internal stability and string stability of the platoon. Simulation results validate the effectiveness and advantages of the proposed method.

This article investigates the secure consensus control problem for multi-unmanned aerial vehicles (uncrewed aerial vehicles (UAVs)) attitude system under channel fading. By decomposing the attitude system, an attitude privacy protection scheme is proposed, enhancing communication security through the transmission of only partial attitude angles. Under UAV channel fading, a distributed observer incorporating a detection factor and compensation mechanism is proposed to ensure both transmission accuracy and observation precision. Furthermore, to enhance tracking performance, a secure prescribed performance control (PPC) strategy based on preset trajectory is proposed. This strategy achieves the PPC without relying on complete information of UAVs. Ultimately, a simulation example involving UAVs demonstrates the feasibility and effectiveness of the proposed control scheme.

This paper investigates constrained multi-autonomous underwater vehicle (AUV) systems with hysteresis output. First, two novel shift functions are proposed to construct new state variables, addressing the issue of initial position and velocity variables of AUVs exceeding predefined boundaries. Based on these new state variables and combined with a coordinate transformation method, asymmetric time-varying full-state constraints independent of the initial conditions are achieved. Moreover, an innovative predefined-time convergence criterion is introduced. Based on this criterion, the proposed strategy ensures robust consensus within a predefined time under asymmetric full-state constraints, while effectively handling external disturbances, hysteresis, and saturation issues. A novel scaling inequality related to the hyperbolic tangent function is also proposed. Based on this scaling inequality, the sign function is replaced with the hyperbolic tangent function in the controller, and the proposed control scheme completely avoids issues of singularity and chattering. By leveraging neural networks (NN) and adaptive parameters to manage uncertainties and complex terms, the proposed control scheme successfully avoids the explosion of complexity. Notably, through adaptive parameter estimation, the negative impacts on system stability caused by deviations of the neural network weight matrix from its optimal value and approximation errors introduced by the neural network are mitigated. The closed-loop system is proven to be predefined-time stable. In addition, the sensitivity of the system to measurement noise is analyzed, and a NN-based observer is proposed to significantly mitigate the adverse effects caused by noise. Finally, the effectiveness of the proposed control scheme is validated through numerical simulation.

This article formulates a gain self-adjustment state observer-based performance self-recovery control (GASO-based PSrC) strategy for the industrial process system subject to actuator faults, and the main contributions of the GASO-based PSrC strategy can be summarized as its adaptability to external environmental variations, its capability to suppress faulty performance, and its plasticity in the postfault operation scenario, manifested in adjustable convergence rate and regulation precision for damaged process performance. Therein, a novel gain self-adjustment state observer (GASO) is constructed for estimating the disturbance and process states, thereby completing GASO gain update and maintenance as well as the accommodation of environment variation. To constrain sustained performance decay and steady-state evolution performance, a two-stage performance function with transient response and steady-state convergence is developed. An activation instruction based on the correntropy criterion is designed to detect faults and enable the guaranteed performance control scheme in the postfault operation scenario. Then, the proposed GASO-based PSrC framework is established to realize the scheduled process regulation level. Extensive experiment validations are accomplished on a micro-wastewater treatment process, and the regulation results on the dissolved oxygen (DO) concentration illustrate that the proposed control strategy can guarantee the user-defined performance requirement while mitigating the detriment of faults and disturbance.

In this paper, the p-th moment synchronization problem for a class of stochastic multi-layer neural networks with intra-layer and inter-layer connections is investigated. Due to the multiple connections with delays and stochastic noise, the typical methodologies that build a canonical linear or expanded matrix model to analyze its stability by constraining eigenvalues in the left-half plane, such as the Kronecker product method, linear matrix inequality and M -matrix approach are tough to tackle the problem. Consequently, a graph-theory-based Lyapunov functional is constructed by combining multiplicative principles and a graph-theoretic approach to help examine the effect of inter- and intra-layer connectivity on a unified framework. With the proposed adaptive fixed-time controller, sufficient conditions for the p-th moment synchronization in a fixed time are derived in terms of algebraic inequality. A corollary, together with a constant-gain fixed-time controller, is presented in case there is no delay. Finally, a confirmatory and two comparative simulations show the effectiveness and convenient implementation of the proposed control strategy.

An incremental iterative Q-learning algorithm (IIQLA) is proposed to tackle the optimal secure control problem for cyber-physical systems under false data injection attacks. Within a zero-sum game framework, the secure control problem is transformed into solving an iterative algebraic Riccati equation. To derive the optimal secure control policy from the equation, the IIQLA is developed, which does not require prior knowledge of the system dynamics. This algorithm utilizes two auxiliary variables to separate the behavior policy and the target policy, thereby improving the exploration of data. As a result, the devised control policies are more conservative, leading to solutions that are closer to the optimal policy. Moreover, by introducing an adaptive learning rate, the proposed IIQLA can accelerate the convergence speed and decrease the number of required iterations, thus alleviating the computation burden. The convergence of the proposed IIQLA with different learning rates is also analyzed. In addition, the closed-loop system is guaranteed to be asymptotically stable, and the exploration noise does not introduce bias into the optimal policies. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed approach.

This article delves into the semi-global robust output regulation of uncertain singular linear systems subject to input saturation and denial-of-services (DoSs) attacks. In the event of a DoS attack, the communication channel between the plant and the controller is blocked. To address the input saturation nonlinearity and to enhance robustness against uncertainty and Dos attacks, a post-processing internal model-based robust output feedback regulator is proposed. It employs the small gain techniques, incorporating two small positive parameters. The overall system is modeled as a hybrid system using hybrid formalism, for which a jump corresponds to the DoS attacks. It is shown that the proposed regulator exhibits robustness against certain DoS attacks and structure uncertainties. Consequently, the output error can asymptotically converge to the origin when the structured uncertainty is small enough, and the proposed constraint on the duration of DoS attacks is met. Finally, two numerical example are given to illustrate the effectiveness of the result.

This article aims at the leader-following secure consensus problem of nonlinear multiagent systems (MASs) with switching topologies, where the agents are not only suffered from the aperiodic malicious denial-of-service (DoS) attacks but also affected by instantaneous disturbance from the external environment. Due to the existing challenge of instantaneous disturbance about occurrence time being unknown, the impulsive-based switching network structure is put forward to tackle the impact of external instantaneous disturbance on MASs. Then, a novel hybrid event-triggered and impulsive control protocol is developed to guarantee that nonlinear MASs can resist DoS attacks and achieve the consensus control objective. Contrasted with the methods of continuous control, the developed hybrid event-triggered and impulsive control protocol using the discontinuous sampled state has certain merits saving control resources. Based on the Lyapunov theory, the stability of the closed-loop system is proven, and the Zeno behavior can be excluded successfully. An example is supplied to elicit the availability of the presented methodology.

Ever since the reinforcement learning (RL) method was proposed, the optimal control problem for multiagent systems (MASs) has been intensively explored in light of the limitation of the control resource. However, most of the consequences have overlooked the denial-of-service (DoS) attacks which are often encountered in engineering scenarios. Thus, the current investigation makes the first attempt to explore the optimized containment control issue with a dynamic event-triggered mechanism for heterogeneous stochastic MASs subject to DoS attacks. For the purpose of achieving optimal control, the optimized backstepping technique is developed by resorting to a simplified RL algorithm based on the identifier–critic–actor structure. Then, a novel dynamic event-triggered mechanism is put forward to update the control input signals only at triggering instants so as to reduce the communication burden. Furthermore, by means of stochastic Lyapunov stability theory, it is verified that all signals in the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in probability, in the simultaneous presence of disturbances and DoS attacks. Finally, the validation of the presented strategy is demonstrated via a simulation example.

This article focuses on the${H_\infty }$control for nonlinear two-time-scale systems with event-triggered mechanisms. Utilizing the Takagi–Sugeno fuzzy model, it is feasible to represent nonlinear two-time-scale systems as fuzzy two-time-scale systems. Event-triggered state feedback control strategy is designed for achieving the${H_\infty }$performance, which inevitably leads to the asynchronous phenomenon of the premise variables between continuous time and triggering instants. Under the consideration of the asynchronous phenomenon, based on a$\varepsilon$-dependent Lyapunov function, the fuzzy composite state feedback controller gains and the event-triggered parameters are codesigned in the form of linear matrix inequalities, and the upper bound of$\varepsilon$is provided as well. Furthermore, the proposed event-triggered mechanism ensures the exclusion of Zeno behavior. Finally, simulation results including comparison studies are shown to demonstrate the effectiveness of the proposed control strategy.

This article investigates the robust output regulation of linear uncertain singularly perturbed systems by output-feedback control. Due to the presence of extremely small perturbation parameters, numerical issues will arise when applying conventional robust regulator design techniques to the regular system. To handle the problem, a continuous-time output-feedback controller adopting the forwarding design technique is proposed by combining the internal model approach with singularly perturbed theory. In this manner, the circumvention of numerical issues and the resolution of robustness problems can be achieved. Additionally, the sampling of the transmissions between the plant and the controller is taken into account, leading to the proposed implementation of a dynamic output-based event-triggered strategy. As a result, the output regulation property becomes practical. To avoid Zeno behavior, the implementation ensures the existence of a strictly positive minimum intertime for the triggering instant sequence. The validity of the results is demonstrated through the presentation of a numerical example.

When realizing multiagent optimal consensus control, it may encounter the situation that malicious agents transmit false information. Besides, due to the unreliability of information interaction and the uncertainty of the system itself, the agent may not fully know its own cost function. In this article, an improved Bayesian graphical game method is proposed to solve the optimal consensus problem of linear dynamical networks in the presence of false information. The agent’s probabilistic estimate of the uncertainty is named belief, and the update of probability estimate is named belief update. An information tradeoff principle is designed to solve the belief update problem in the presence of malicious neighbors. The principle can not only reduce the loss caused by false information but also force malicious agents to switch from deception to cooperation. On this basis, a new belief update method with information tradeoff principle is established. It is proved that this new belief update method has a faster convergence rate than the Bayesian belief update method when malicious neighbors exist. As an illustrative example, the graphical game solution is applied to the formation tracking control problem of a quad-rotor unmanned aerial vehicle swarm. Theoretical proof and simulation comparisons can illustrate the proposed method’s advantages.

Standard output regulation design techniques cannot be applied for linear two-time-scale systems subject to saturated inputs. In this work, a state feedback output regulation is first proposed based on a classical stabilizing composite state feedback controller. Nevertheless, the corresponding design is difficult to implement due to numerical issues. Thus, the method of asymptotic power series expansion is applied to provide an approximate solution to the regulator equation. Then, a time-continuous state feedback controller is designed by combining the Chang transformation approach and the low-gain feedback technique, which results in a semi-global bounded output regulation of the closed-loop system. Furthermore, to reduce control updates, a dynamic event-triggered control scheme is proposed which ensures the exclusion of Zeno behavior by maintaining a strictly positive time between any two triggering moments, regardless of the initial state of the system. Additionally, an observer-based event-triggered control scheme is proposed to cater to the practical scenario in which system state information is unavailable. Finally, to demonstrate the effectiveness of our proposed technique, two examples are presented.

This article investigates the synchronization problem of interconnected linear two-time-scale systems (TTSSs) with switching topology. By utilizing the Chang transformation, a distributed synchronization protocol is proposed with event-triggered communication. Static and dynamic event-triggered mechanisms are proposed successively, which both contain two separated event-triggering conditions corresponding to the slow and the fast subsystems. The existence of a strictly positive time period between any two successive transmissions is ensured regardless of the initial states. The main difficulty of this study lies in that the state jump and parametric uncertainty appear because of the system transformation. To overcome the difficulty, the system is first modeled as an uncertain hybrid system. Then, the control gain is properly designed by solving Riccati-like equations dependent on the rough bounds of the eigenvalues of communication graph Laplacians, and a piecewise quadratic Lyapunov function is proposed with which the jump caused by the switching topology is subtly evaluated. Sufficient conditions are thus established to achieve the event-triggered synchronization. Furthermore, the results are also extended to solve the synchronization problem of the interconnected impulsive linear TTSSs. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

This article proposes the design of an event-triggered control strategy for consensus of interconnected two-time scales systems with structured uncertainty. The control design under consideration ensures also that consensus is achieved with an overall guaranteed cost. Since each system involves processes evolving on both fast and slow time scales, two Zeno-free event-triggered mechanisms are designed to independently decide the sampling and transmission instants for the slow and fast states, respectively. As the first step, we design an event-triggering consensus protocol in the ideal/nominal case when the interconnected systems are not affected by uncertainties and the interactions happen over a fixed interaction network. Next, the results are extended in order to take into account structured uncertainties affecting the systems' dynamics. At this step, we go further and we provide sufficient conditions for event-triggering consensus with a guaranteed overall cost. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

In this paper, the leader-following output consensus problem for a class of uncertain nonlinear multiagent systems with unknown control directions is investigated. Each agent system has nonidentical dynamics and is subject to external disturbances and uncertain parameters. The agents are connected through a directed and jointly connected switching network. A novel two-layer distributed hierarchical control scheme is proposed. In the upper layer, to save the communication resources and to handle the switching networks, an event-triggered communication scheme is proposed, and a Zeno-free event-triggered mechanism is designed for each agent to generate the asynchronous triggering time instants. Furthermore, to avoid the continuous monitoring of the system states, a Zeno-free self-triggering algorithm is proposed. In the lower layer, to handle the unknown control directions problem and to achieve the output tracking of the local references generated in the upper layer, the Nussbaum-type function-based technique is combined with internal model principle. With the proposed two-layer distributed hierarchical controller, the leader-following output consensus is achieved. The obtained result is further extended to the formation control problem. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

In this paper, the global robust output regulation problem of a class of uncertain nonlinear systems is investigated by the event-triggered adaptive control law for the case of unknown control direction. The Nussbaum-type function-based technique is proposed to tackle the presence of unknown control direction. Then, by applying the adaptive control technique and the internal model principle, a new event-triggered adaptive control method is proposed. With the proposed corresponding event-triggered mechanism, the output regulation of the nonlinear systems can be realized regardless of the unknown control direction, meanwhile the Zeno behavior can be excluded. Finally, a numerical example is presented to verify the effectiveness of the proposed control law.