In order to ensure effluent quality compliance with standards and enhance operational efficiency, the optimal control of wastewater treatment process (WWTP) has been regarded as crucial. However, the excellent control performance and low operational energy consumption are often maintained through the continuous adjustment of controller parameters, which results in an increased computational burden. Therefore, the dual-triggered adaptive fuzzy robust optimal tracking control method is proposed in WWTP. Firstly, based on the optimal framework, the designed adaptive collaborative controller not only can track and control the dissolved oxygen and nitrate nitrogen concentrations simultaneously, but also can ensure a balance between the effluent quality and energy consumption. Secondly, based on the designed dual dynamic trigger thresholds, the proposed event-triggering mechanism is used to selectively update network parameters, which is able to reduce unnecessary computational resource consumption. Then, the technique of actuator saturation processing is introduced to improve the robustness for adaptive optimal controller. Finally, the stability of the proposed controller of WWTP is rigorously analyzed using Lyapunov theory and the effectiveness is validated through simulation experiments.

Effluent quality (EQ) and energy consumption (EC) are two critical indicators concerned in wastewater treatment process (WWTP). Because of the nonlinear uncertainty characteristic exhibited in biochemical reaction, it is perceived as a challenge to design an effective optimal controller. Thus, the constraint structure-based adaptive fuzzy adjustable optimal control method is proposed for WWTP. First, considering the conflict between EC and EQ, the fuzzy neural network-based optimal control framework is selected to track and control the objective in WWTP. Second, the dynamic adjustment mechanism is designed into the control framework, which can avoid the peak value of key indicators exceed the effluent standard. Meanwhile, the asymmetric constraint structure is constructed into the design of adaptive controller, in which not only the concentrations of dissolved oxygen and nitrate nitrogen, but also the tracking errors are all ensured in the desired ranges. Finally, the stability of the control system is proved, and the effectiveness of the designed controller is evaluated via benchmark simulation model I.

To obtain the effective purification performance in wastewater treatment process (WWTP), the optimal control is an important method to guarantee the effluent quality reaching the standard and improve the treatment efficiency. The concentrations of dissolved oxygen (DO) and nitrate nitrogen (NO$_{\text{3}}$-N) are primary metrics that impact effluent quality, which is needed to be stably tracking controlled for achieving optimal performance in WWTP. Therefore, the double-layer fuzzy neural network (FNN)-based optimal control method with multivariable is proposed. First, considering the dynamic characteristic of WWTP, the FNN-based actor network is exploited to approximate the unknown dynamic information. Subsequently, the FNN-based critic network is integrated to minimize the cost function of DO and NO$_{\text{3}}$-N concentrations, which is composed of the control error and the control variable. Then, to guarantee the stability of the optimal controller, the Lyapunov function is constructed through backstepping method to analyze the control system performance. Finally, the optimality and effectiveness of the control system with multivariable are verified via the simulation experiments in benchmark simulation model 1.

Recently, the wastewater treatment process has become an effective tool to improve the ecological environment. Due to the inevitable actuator faults, the load capacity of the equipment and the purification efficiency of the wastewater are reduced. How to improve the purification and economic efficiency is a huge challenge. Therefore, a prescribed performance-based fault-tolerant optimal control method with multivariable is designed in this article. First, the error transformation function-based prescribed performance is introduced to achieve stable tracking control. Second, the fault approximation based adaptive control method is used to solve the problem of unavoidable actuator faults. Subsequently, the multivariable optimal controller is structured to guarantee the control accuracy and equipment energy consumption simultaneously. Finally, the steady state and transient performance are analyzed and the optimality is verified by some experiments.

The activated sludge method is one of the most commonly used methods for the wastewater treatment process (WWTP). Among them, the dissolved oxygen (DO) concentration is a key factor affecting microbial metabolism and wastewater treatment effectiveness. However, due to the nonlinearity and dynamicity of WWTP, it is difficult to precisely control the DO concentration by traditional control methods. To solve this problem, the online-growing pipelined recurrent wavelet neural network (OG-PRWNN) control is proposed to improve the DO control accuracy. First, the online growing mechanism is designed to adjust the number of modules of the controller by measuring the control performance. Then, the structure of the controller is automatically determined to meet the different operating conditions of the WWTP. Second, the online algorithm of parameters incorporating adaptive learning rates is designed to train the OG-PRWNN to meet the control requirements. In addition, the stability of the OG-PRWNN controller is analyzed by the Lyapunov stability theorem. Finally, the performance of the controller is verified by the benchmark simulation model of WWTP. Simulation results show that the OG-PRWNN controller can obtain better control accuracy.

One of the major challenges of transfer learning algorithms is the domain drifting problem where the knowledge of source scene is inappropriate for the task of target scene. To solve this problem, a transfer learning algorithm with knowledge division level (KDTL) is proposed to subdivide knowledge of source scene and leverage them with different drifting degrees. The main properties of KDTL are three folds. First, a comparative evaluation mechanism is developed to detect and subdivide the knowledge into three kinds-the ineffective knowledge, the usable knowledge, and the efficient knowledge. Then, the ineffective and usable knowledge can be found to avoid the negative transfer problem. Second, an integrated framework is designed to prune the ineffective knowledge in the elastic layer, reconstruct the usable knowledge in the refined layer, and learn the efficient knowledge in the leveraged layer. Then, the efficient knowledge can be acquired to improve the learning performance. Third, the theoretical analysis of the proposed KDTL is analyzed in different phases. Then, the convergence property, error bound, and computational complexity of KDTL are provided for the successful applications. Finally, the proposed KDTL is tested by several benchmark problems and some real problems. The experimental results demonstrate that this proposed KDTL can achieve significant improvement over some state-of-the-art algorithms.

Optimal control system has been considered as a valuable technique to enhance the reliability and security of wastewater treatment process (WWTP). However, due to the complex environments, it is difficult to realize the optimal control with changeable operational conditions in WWTP. To overcome this problem, an intelligent optimal control system with flexible objective functions (IOCS-FOF) was proposed in this paper. The main merits of this proposed IOCS-FOF were shown as follows. First, an optimal control system scheme was developed, where different time-scale operational objectives were detailed to describe the operational features. Second, a flexible objective strategy was designed to determine suitable objective functions, which could adapt to complex environments of WWTP. Third, a novel dynamic multiobjective optimization algorithm for flexible objectives (FO-DMOA) was developed to obtain the optimal solutions of IOCS-FOF. Finally, the proposed IOCS-FOF was applied in the benchmark simulation model No. 1 (BSM1) to confirm its technique capability. The results demonstrate that this proposed method can improve the operation performance of WWTP.

Many artificial networks in the real world have the power-law degree distribution. This feature causes a lot of difficulties in network design, such as robustness, reliability and other performance issues. In this paper, the congestion problem in power-law communication networks is focused. Since nodes with very large degree usually become the bottleneck in this kind of networks when shortest path routing is adopted, a new design of routing is proposed. A hybrid approach, that combines a genetic algorithm and a greedy approach, is designed to find the routing paths of the source-destination pairs. As shown by theoretical and simulation results, the transmission capacity can be improved with the new design which outperforms other existing routing schemes. It should also be emphasized that, though only scale-free network is discussed, the proposed approach is general and useful for other network types.

In this paper, a genetic algorithm (GA) is proposed to tackle with the constrained pinning control problem in complex networks. Based on a hierarchical chromosome structure, it is demonstrated that suitable pinned nodes can be selected with appropriate control gains, resulting in a better synchrony capability of the entire network. Simulation results verify the effectiveness of this method, and it is concluded that the proposed approach can outperform some other evolutionary algorithms and the conventional node selection approaches.

In this paper, a novel genetic algorithm (GA) is presented to tackle with the constrained pinning control problem for complex networks. The information of the node degree is incorporated in the design so that a set of pinned nodes can be duly obtained. In addition, the control strength of each selected node is assigned by the use of a decrease-and-conquer approach, satisfying the total control strength constraint of the problem. Simulation results confirm the effectiveness of the design and it outperforms other evolutionary algorithms and conventional node selection approaches.

This brief deals with the problem of stability analysis for a class of recurrent neural networks (RNNs) with a time-varying delay in a range. Both delay-independent and delay-dependent conditions are derived. For the former, an augmented Lyapunov functional is constructed and the derivative of the state is retained. Since the obtained criterion realizes the decoupling of the Lyapunov function matrix and the coefficient matrix of the neural networks, it can be easily extended to handle neural networks with polytopic uncertainties. For the latter, a new type of delay-range-dependent condition is proposed using the free-weighting matrix technique to obtain a tighter upper bound on the derivative of the Lyapunov-Krasovskii functional. Two examples are given to illustrate the effectiveness and the reduced conservatism of the proposed results.