Nonlinear networked systems (NSs) subject to actuator faults are addressed in this paper through proposed fault diagnosis (FD) and fault-tolerant control (FTC) schemes. The nonlinear NSs are represented by an interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model with mismatched membership functions (MFs), in which uncertainties are described as a fuzzy interval with upper and lower bounds. To concurrently estimate system states and actuator faults, an interval type-2 (IT2) T-S fuzzy fault diagnosis observer is developed, serving to improve the system’s resilience against uncertainties and external disturbances. Following the observer’s fault estimation, an FTC strategy is formulated to guarantee asymptotic stability andH∞performance in the closed-loop system. The proposed framework employs Lyapunov stability theory, with sufficient conditions for the FD observer and FTC gain matrices derived via linear matrix inequalities. Finally, through simulation experiments, the effectiveness and practicality of the designed FD and FTC strategies are validated.

This article develops an event-triggered safe critic learning control (ESCLC) algorithm for nonlinear systems subject to asymmetric state constraints by integrating a safe critic learning control (SCLC) framework with an event-triggering mechanism. The SCLC algorithm innovatively incorporates control barrier functions into the safe value function design, addressing the challenge of deriving optimal control policies that guarantee system safety. Convergence of the SCLC algorithm is rigorously established within the value iteration framework, along with a criterion for assessing the admissibility of control policies. To enhance the application value of the algorithm in resource-constrained scenarios, an event-triggering mechanism is incorporated into the SCLC framework, yielding the ESCLC algorithm. The resulting closed-loop system under the ESCLC algorithm is proved to be asymptotically stable, and an upper bound on the actual value function is derived to ensure bounded performance degradation. In addition, a policy improvement method based on particle swarm optimization is designed that eliminates dependence on the system control matrix. Finally, the effectiveness of the ESCLC algorithm is verified through simulation experiments on a torsion pendulum system and a ball-and-beam system.

In this article, a multiagent adaptive critic control algorithm is developed for the multivariable control problem of wastewater treatment plants. The wastewater treatment plant is regarded as a type of decentralized interconnected system in this algorithm. To reduce the design difficulty of control strategies, multiple agents are created, and each agent is only responsible for optimizing the control strategy of a single subsystem. In addition, based on a well-designed Q-function, the agent considers the impact on other subsystems while optimizing its own control strategy. Therefore, the control algorithm exhibits good performance in both the implementation difficulty and the control accuracy. To ensure the initial performance of the control algorithm, the prior control strategy with expert knowledge is integrated into the control algorithm. Considering the disturbance factors in wastewater treatment plants, the direct control strategy is modified into an incremental control strategy, which improves the anti-interference performance of the control algorithm. The stability of the proposed algorithm is proved by constructing Lyapunov functions. The superiority of the control algorithm is verified through quantitative comparison results with other control algorithms.

Multitasking optimization (MTO), addressing multiple optimization problems synchronously, has achieved significant success in the field of evolutionary computation. However, in practice, few tasks are accomplished synchronously due to asynchronous initialization. In this article, an asynchronous MTO (AMTO) paradigm is proposed, which aims to deal with multiple optimization problems with asynchronous arrivals. Due to the asynchronous characteristic of tasks, there is multiple tenses knowledge in an AMTO environment. Transferring multitense knowledge may accelerate the optimization process of the target task. Also, an AMTO algorithm is proposed to transfer multitense knowledge. The past-tense knowledge is transferred by an initialization strategy, which selects effective knowledge to deal with mismatched tenses. And the present-tense knowledge is transferred by knowledge reuse, which aligns convergence intervals to handle mismatched evolutionary states. Finally, several AMTO test problem sets and a practical problem are designed to verify the performance of the proposed algorithm. The experimental results show that the performance of the algorithm can be improved by multitense knowledge transfer.

A robust data-driven model predictive control (RDD-MPC) with a soft constrained strategy is proposed in this article. This method is designed to address model predictive control (MPC) constraint violations caused by external disturbances and outliers arising from measurement errors. First, a robust data-driven prediction model is constructed using kernel functions, and its parameters are updated via the soft-margin-based iterative quadratic programming (SMIQP) algorithm. This algorithm introduces a model slack variable (MSV) to tolerate the negative effects of outliers. This algorithm improves the robustness of the prediction model against outliers and ensures that the model can capture the complex dynamic characteristics of the system. Second, an enhanced soft constrained method (SCM) is designed to handle constraint violations. Unlike SCMs with a single slack variable, which may lead to excessive or insufficient constraint relaxation, this method employs two controller slack variables (CSVs) for coordinated constraint relaxation, thereby ensuring optimization feasibility. Combined with an adaptive weight penalty term, the proposed SCM maintains acceptable control performance in the presence of disturbances. Third, the input-to-state stability (ISS) of the proposed RDD-MPC method is rigorously proven. Finally, experimental results on classic nonlinear systems demonstrate that the proposed method can effectively improve both control performance and robustness. In addition, this method is evaluated on the Benchmark Simulation Model No. 1 (BSM1) for wastewater treatment processes (WWTPs). The experimental results further validate the effectiveness of the RDD-MPC method for systems engineering applications.

Wastewater treatment plays a meaningful role in environmental protection, water recycling and public health, and its optimal control offers significant economic and social value. However, the wastewater treatment plant is a large-scale nonlinear system, and its own operation is affected by a series of uncontrollable factors such as the flow rate and composition of the incoming wastewater. This makes it extremely challenging for traditional control methods to realize precise control. To address these issues, this paper proposes a novel knowledge-guided policy optimization control method by integrating policy transfer and adaptive dynamic programming. First, an adaptive critic policy transfer framework based on the source domain knowledge selection method is introduced to construct knowledge extraction and data mining structures to enhance the learning efficiency of the target domain agent. Second, a source domain knowledge selection module is proposed to adaptively adjust the knowledge extracted by the target domain agent. Third, an adaptive termination module is designed to determine when the immature policy in the source domain should terminate during the target domain learning process. Finally, the theoretical stability of the method in this paper is demonstrated by designing a reasonable Lyapunov function. The system performance of the wastewater treatment plant under dry, rainy, and stormy weather conditions is evaluated, ultimately demonstrating the superior performance and adaptability of the proposed method.

For unknown nonlinear systems, a safe optimal tracking control algorithm is developed based on multi-step critic learning. By integrating the control barrier function into the critic learning framework, the algorithm ensures that the tracking error is kept within a safe region and converges to zero with the minimal cost. Utilizing historical operational data of the system, a model network is established to identify the unknown system dynamics. By constructing feedforward control, the tracking problem of the original system is transformed into a regulation problem of the error system. To enhance the convergence speed of the algorithm, a critic learning framework with multi-step policy evaluation is designed. Furthermore, a criterion is developed to determine the admissibility of the safe tracking control policy at each iteration step. The convergence of the proposed algorithm is also proved. Finally, the simulation results demonstrate effectiveness of the algorithm and the validity of the theoretical results.

A robust soft constrained model predictive control (RSCMPC) method is proposed to address the effects of unknown disturbances for wastewater treatment processes (WWTPs). The disturbances involving inflow fluctuation and noises from WWTPs may result in the constraints violation of MPC due to its uncertainty of bioprocess, which may degrade the performance of the steady state. First, the artificial steady state is introduced to mimic the nearest feasible steady state when the reference steady state is not feasible. The deviation caused by disturbances between the artificial steady state and the reference steady state is also penalized to ensure that the output of MPC converges to the reference steady state. Second, the soft constraints, incorporating two slack variables and a penalty term, are designed to relax the state constraints of MPC and continuously mitigate the constraint violation, thereby ensuring its stability. Third, the input state stability (ISS) under disturbances is analyzed. Finally, the simulation tested on Benchmark simulation model 1 verifies the effectiveness of the proposed RSCMPC. The results demonstrate that RSCMPC improves the robustness of the system to maintain the stable operation of the WWTPs. Note to Practitioners—The external disturbances of wastewater treatment processes (WWTPs) will result in the constraints violation of model predictive control (MPC) and degrade the steady state performance. To overcome the influence of external disturbances, a robust soft constrained model predictive control (RSCMPC) method is designed. This method mainly includes three contributions: First, the artificial steady state is constructed with the prediction derived from fuzzy neural network, which is to mimic the nearest feasible steady state when the reference steady state is not feasible under disturbances. Second, the soft constrained method relaxes the state constraints of MPC through two slack variables to compensate the effects of disturbances and restore the feasibility of the controller. Third, the input state stability under disturbances is analyzed. Finally, the effectiveness of the proposed RSCMPC method is evaluated on a pilot platform of a real WWTPs. The experimental results show that RSCMPC can improves the control accuracy and robustness of the system under external disturbances. The proposed RSCMPC method can help practitioners improve the reliability of WWTPs operation.

In this paper, we investigate the observer-based integral sliding mode security control problem for a class of time-delay nonlinear discrete-time disturbed cyber-physical systems (CPSs) subject to dual-channel aperiodic asynchronous denial-of-service (DoS) attacks. An adaptive event-triggered protocol (AETP) is proposed to save network resources, whose triggering threshold is dynamically adjusted. The DoS attacks are described by the occurrence frequency and the durations, and a corresponding neural network (NN)-based switched observer is employed to estimate the unmeasurable state of the original system. By means of this model, a novel switched system is constructed under the designed equivalent integral sliding mode controller. Sufficient conditions are given to ensure the input-to-state practically stability of the closed-loop system while achieving the desired security level. Furthermore, the explicit expressions for the gain matrices of the controller and the observer are derived with the help of solving linear matrix inequalities. In order to strengthen the robustness and suppress chattering of the system, a robust integral sliding mode control (RISMC) algorithm is developed under the reaching condition. Finally, a water supply distribution system is employed to verify the advantages of the developed control approach.Note to Practitioners—With the advancement of long-distance communication technologies, the open network environment poses an increasingly serious security threat to the operation of CPSs. In the context of communication scheduling, cyber attacks will lead to severe data sparsity problems, which inevitably deteriorate system performance. In addition, geographically dispersed CPSs tend to face more complex disturbances and nonlinearities than traditional systems. Therefore, developing resource-aware control algorithms and analysis techniques to comprehensively improve the security and robustness of CPSs are still a challenging problem. This article focuses on the observer-based event-triggered security and robust control of CPSs subject to dual-channel DoS attacks. For the sake of the burden of communication bandwidth, a novel AETP is developed to schedule data exchange so as that save network resources. In view of the threat of aperiodic DoS attacks and external disturbances to CPSs, an observer-based RISMC scheme is proposed. Subsequently, simulation results show that the proposed method can achieve the desired security performance with sufficient robustness.

The wastewater treatment process (WWTP) is of great significance to environmental protection. To improve the efficiency of the WWTP, it is crucial to ensure that the dissolved oxygen (DO) concentration tracks the set value efficiently. Due to the nonlinear and time-varying dynamics of the WWTP, traditional control methods cannot accurately control the DO concentration. To overcome these challenges, this article proposes an online transferred heuristic dynamic programming (TrHDP) control design by combining transfer learning with adaptive critic design. First, we use the historical sample data to construct a mathematical model of the WWTP and learn the prior knowledge from the model. Then, the online control process of the DO concentration is guided by utilizing the prior knowledge. In order to avoid negative transfer and save computing resources, we design a novel decay function with the truncation mechanism. In addition, we prove the stability of the TrHDP control scheme by constructing a Lyapunov function. Finally, the performance of the TrHDP scheme is verified by the Benchmark Simulation Model No. 1. Compared with other methods, the TrHDP method possesses higher control accuracy for the DO concentration and overcomes the disadvantage of low learning efficiency of general online methods.

In this article, recursive filtering is investigated for time-varying discrete sequential systems (DSSs) under weighted try-once-discard (WTOD) protocols, which are employed to govern the access authorization of a shared network in order to remit the communication burden. A transmission model, dependent on a Bernoulli distributed white sequence, is developed to describe the phenomenon of deception attacks. In light of the adopted protocol and the attack model, a recursive algorithm with the form of Riccati-like difference equations is developed to optimize the filtering performance in the mean square sense. Furthermore, by resorting to the mathematical induction, the convergence of the proposed recursive algorithm is discussed profoundly. Finally, a simulation example is presented to verify the availability of the designed recursive filter.

This paper investigates the exponential stability analysis issue for a class of delayed recurrent neural networks (RNNs) with semi-Markovian parameters. By constructing a stochastic Lyapunov functional and using some zoom techniques to estimate its weak infinitesimal operator, the exponential mean square stability criteria have been proposed for the Markovian neural networks with certain transition probabilities. We then generalize the homogeneous polynomial approach for the delayed Markovian RNNs with uncertain transition probabilities during the stability analysis. Theoretical results have obtained by introducing an appropriate technique for dealing with a large number of complex homogeneous polynomial matrix inequalities. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed technique.