Knowledge-Data Driven Optimal Control for Nonlinear Systems and Its Application to Wastewater Treatment Process.

Optimal control is developed to guarantee nonlinear systems run in an optimum operating state. However, since the operation demands of systems are dynamically changeable, it is difficult for optimal control to obtain reliable optimal solutions to achieve satisfying operation performance. To overcome this problem, a knowledge-data driven optimal control (KDDOC) for nonlinear systems is designed in this article. First, an adaptive initialization strategy, using the knowledge from historical operation information of nonlinear systems, is employed to dynamically preset parameters of KDDOC. Then, the initial performance of KDDOC can be enhanced for nonlinear systems. Second, a knowledge guide-based global best selection mechanism is used to assist KDDOC in searching for the optimal solutions under different operation demands. Then, dynamic optimal solutions of KDDOC can be obtained to adapt to flexible changes in nonlinear systems. Third, a knowledge direct-based exploitation mechanism is presented to accelerate the solving process of KDDOC. Then, the demand response speed of KDDOC can be improved to ensure nonlinear systems with optimal operation performance in different states. Finally, the performance of KDDOC is validated on a simulation and a practical process. Several experimental results illustrate the effectiveness of the proposed optimal control for nonlinear systems.

Sampled-Data H∞ Dynamic Output-Feedback Control for NCSs With Successive Packet Losses and Stochastic Sampling.

The problem of sampled-data H∞ dynamic output-feedback control for networked control systems with successive packet losses (SPLs) and stochastic sampling is investigated in this article. The aim of using sampled-data control techniques is to alleviate network congestion. SPLs that occur in the sensor-to-controller (S-C) and controller-to-actuator (C-A) channels are modeled using a packet loss model. Additionally, it is assumed that stochastic sampling follows a Bernoulli distribution. A model is established to capture the stochastic characteristics of both the SPL model and stochastic sampling. This model is crucial as it allows us to determine the probability distribution of the sampling interval between successive update instants, which is essential for stability analysis. An exponential mean-square stability condition for the constructed equivalent discrete-time stochastic system, which also guarantees the prescribed H∞ performance, is established by incorporating probability theory. The desired controller is designed using a step-by-step synthesis approach, which may offer lower design conservatism compared to some existing methods. Finally, our designed approach using a networked F-404 engine system model is validated and its merits relative to existing results are discussed. The proposed method is finally validated by employing a networked model of the F-404 engine system. Furthermore, the advantages of our method are presented in comparison to previous results.

A Novel Set-Based Discrete Particle Swarm Optimization for Wastewater Treatment Process Effluent Scheduling.

With the escalating severity of environmental pollution caused by effluent, the wastewater treatment process (WWTP) has gained significant attention. The wastewater treatment efficiency and effluent quality are significantly impacted by effluent scheduling that adjusts the hydraulic retention time. However, the sequential batch and continuous nature of the effluent pose challenges, resulting in complex scheduling models with strong constraints that are difficult to tackle using existing scheduling methods. To optimize maximum completion time and effluent quality simultaneously, this article proposes a restructured set-based discrete particle swarm optimization (RS-DPSO) algorithm to address the WWTP effluent scheduling problem (WWTP-ESP). First, an effective encoding and decoding method is designed to effectively map solutions to feasible schedules using temporal and spatial information. Second, a restructured set-based discrete particle swarm algorithm is introduced to enhance the searching ability in discrete solution space via restructuring the solution set. Third, a constraint handling strategy based on violation degree ranking is designed to reduce the waste of computational resources. Fourth, a Sobel filter based local search is proposed to guide particle search direction to enhance search efficiency ability. The RS-DPSO provides a novel method for solving WWTP-ESP problems with complex discrete solution space. The comparative experiments indicate that the novel designs are effective and the proposed algorithm has superior performance over existing algorithms in solving the WWTP-ESP.

Foreground Capture Feature Pyramid Network-Oriented Object Detection in Complex Backgrounds.

Feature pyramids are widely adopted in visual detection models for capturing multiscale features of objects. However, the utilization of feature pyramids in practical object detection tasks is prone to complex background interference, resulting in suboptimal capture of discriminative multiscale foreground semantic features. In this article, a foreground capture feature pyramid network (FCFPN) for multiscale object detection is proposed, to address the problem of inadequate feature learning in complex backgrounds. FCFPN consists of a foreground dual attention (FDA) module and a pathway aggregation (PA) structure. Specifically, the FDA mechanism activates top-down foreground channel responses and lateral spatial foreground location features, so that channel and spatial foreground features are adequately captured. Then, the PA module adaptively learns the fusion weights of multiscale features at different levels of the feature pyramid, which enhances the complementarity of semantic information between different levels of the foreground feature maps. Since the fusion weights are learned adaptively based on different pyramid levels, the detection model accordingly retains the gained information of feature sizes and suppresses the conflicting information. The evaluations on public datasets and the self-built complex background dataset demonstrate that the detection average precision (AP) and the feature learning performance of the proposed method are superior compared with other FPNs, which proves the effectiveness of the proposed FCFPN.

Evaluation of Open-Source Large Language Models for Metal-Organic Frameworks Research.

Along with the development of machine learning, deep learning, and large language models (LLMs) such as GPT-4 (GPT: Generative Pre-Trained Transformer), artificial intelligence (AI) tools have been playing an increasingly important role in chemical and material research to facilitate the material screening and design. Despite the exciting progress of GPT-4 based AI research assistance, open-source LLMs have not gained much attention from the scientific community. This work primarily focused on metal-organic frameworks (MOFs) as a subdomain of chemistry and evaluated six top-rated open-source LLMs with a comprehensive set of tasks including MOFs knowledge, basic chemistry knowledge, in-depth chemistry knowledge, knowledge extraction, database reading, predicting material property, experiment design, computational scripts generation, guiding experiment, data analysis, and paper polishing, which covers the basic units of MOFs research. In general, these LLMs were capable of most of the tasks. Especially, Llama2-7B and ChatGLM2-6B were found to perform particularly well with moderate computational resources. Additionally, the performance of different parameter versions of the same model was compared, which revealed the superior performance of higher parameter versions.

Diversified Knowledge Transfer Strategy for Multitasking Particle Swarm Optimization.

Evolutionary multitasking optimization (EMTO) has capability of performing a population of individuals together by sharing their intrinsic knowledge. However, the existed methods of EMTO mainly focus on improving its convergence using parallelism knowledge belonging to different tasks. This fact may lead to the problem of local optimization in EMTO due to unexploited knowledge on behalf of the diversity. To address this problem, in this article, a diversified knowledge transfer strategy is proposed for multitasking particle swarm optimization algorithm (DKT-MTPSO). First, according to the state of population evolution, an adaptive task selection mechanism is introduced to manage the source tasks that contribute to the target tasks. Second, a diversified knowledge reasoning strategy is designed to capture the knowledge of convergence, as well as the knowledge associated with diversity. Third, a diversified knowledge transfer method is developed to expand the region of generated solutions guided by acquired knowledge with different transfer patterns so that the search space of tasks can be explored comprehensively, which is favor of EMTO alleviating local optimization. Finally, the performance of the proposed algorithm is evaluated in comparison with some other state-of-the-art EMTO algorithms on multiobjective multitasking benchmark test suits, and the practicality of the algorithm is verified in a real-world application study. The results of experiments demonstrate the superiority of DKT-MTPSO compared to other algorithms.

Double-Closed-Loop Robust Optimal Control for Uncertain Nonlinear Systems.

Optimal control methods have gained significant attention due to their promising performance in nonlinear systems. In general, an optimal control method is regarded as an optimization process for solving the optimal control laws. However, for uncertain nonlinear systems with complex optimization objectives, the solving of optimal reference trajectories is difficult and significant that might be ignored to obtain robust performance. For this problem, a double-closed-loop robust optimal control (DCL-ROC) is proposed to maintain the optimal control reliability of uncertain nonlinear systems. First, a double-closed-loop scheme is established to divide the optimal control process into a closed-loop optimization process that solves optimal reference trajectories and a closed-loop control process that solves optimal control laws. Then, the ability of the optimal control method can be improved to solve complex uncertain optimization problems. Second, a closed-loop robust optimization (CL-RO) algorithm is developed to express uncertain optimization objectives as data-driven forms and adjust optimal reference trajectories in a close loop. Then, the optimality of reference trajectories can be improved under uncertainties. Third, the optimal reference trajectories are tracked by an adaptive controller to derive the optimal control laws without certain system dynamics. Then, the adaptivity and reliability of optimal control laws can be improved. The experimental results demonstrate that the proposed method can achieve better performance than other optimal control methods.

Robust Multiobjective Particle Swarm Optimization With Feedback Compensation Strategy.

Multiobjective particle swarm optimization (MOPSO) has been proven effective in solving multiobjective problems (MOPs), in which the evolutionary parameters and leaders are selected randomly to develop the diversity. However, the randomness would cause the evolutionary process uncertainty, which deteriorates the optimization performance. To address this issue, a robust MOPSO with feedback compensation (RMOPSO-FC) is proposed. RMOPSO-FC provides a novel closed-loop optimization framework to reduce the negative influence of uncertainty. First, Gaussian process (GP) models are established by dynamically updated archives to obtain the posterior distribution of particles. Then, the feedback information of particle evolution can be collected. Second, an intergenerational binary metric is designed based on the feedback information to evaluate the evolutionary potential of particles. Then, the particles with negative evolutionary directions can be identified. Third, a compensation mechanism is presented to correct the negative evolution of particles by modifying the particle update paradigm. Then, the compensated particles can maintain the positive exploration toward the true PF. Finally, the comparative simulation results illustrate that the proposed RMOPSO-FC can provide superior search capability of PFs and algorithmic robustness over multiple runs.

Self-Organizing Robust Fuzzy Neural Network for Nonlinear System Modeling.

Fuzzy neural network (FNN) is a structured learning technique that has been successfully adopted in nonlinear system modeling. However, since there exist uncertain external disturbances arising from mismatched model errors, sensor noises, or unknown environments, FNN generally fails to achieve the desirable performance of modeling results. To overcome this problem, a self-organization robust FNN (SOR-FNN) is developed in this article. First, an information integration mechanism (IIM), consisting of partition information and individual information, is introduced to dynamically adjust the structure of SOR-FNN. The proposed mechanism can make itself adapt to uncertain environments. Second, a dynamic learning algorithm based on the α -divergence loss function ( α -DLA) is designed to update the parameters of SOR-FNN. Then, this learning algorithm is able to reduce the sensibility of disturbances and improve the robustness of Third, the convergence of SOR-FNN is given by the Lyapunov theorem. Then, the theoretical analysis can ensure the successful application of SOR-FNN. Finally, the proposed SOR-FNN is tested on several benchmark datasets and a practical application to validate its merits. The experimental results indicate that the proposed SOR-FNN can obtain superior performance in terms of model accuracy and robustness.

Spatial oblivion channel attention targeting intra-class diversity feature learning.

Convolutional neural networks (CNNs) have successfully driven many visual recognition tasks including image classification. However, when dealing with classification tasks with intra-class sample style diversity, the network tends to be disturbed by more diverse features, resulting in limited feature learning. In this article, a spatial oblivion channel attention (SOCA) for intra-class diversity feature learning is proposed. Specifically, SOCA performs spatial structure oblivion in a progressive regularization for each channel after convolution, so that the network is not restricted to a limited feature learning, and pays attention to more regionally detailed features. Further, SOCA reassigns channel weights in the progressively oblivious feature space from top to bottom along the channel direction, to ensure the network learns more image details in an orderly manner while not falling into feature redundancy. Experiments are conducted on the standard classification dataset CIFAR-10/100 and two garbage datasets with intra-class diverse styles. SOCA improves SqueezeNet, MobileNet, BN-VGG-19, Inception and ResNet-50 in classification accuracy by 1.31%, 1.18%, 1.57%, 2.09% and 2.27% on average, respectively. The feasibility and effectiveness of intra-class diversity feature learning in SOCA-enhanced networks are verified. Besides, the class activation map shows that more local detail feature regions are activated by adding the SOCA module, which also demonstrates the interpretability of the method for intra-class diversity feature learning.

Decentralized adaptively weighted stacked autoencoder-based incipient fault detection for nonlinear industrial processes.

Modern industrial processes often exhibit large-scale and nonlinear characteristics. Incipient fault detection for industrial processes is a big challenge because of the faint fault signature. To improve the performance of incipient fault detection for large-scale nonlinear industrial processes, a decentralized adaptively weighted stacked autoencoder (DAWSAE) -based fault detection method is proposed. First, the industrial process is divided into several sub-blocks and local adaptively weighted stacked autoencoder (AWSAE) is established for each sub-block to mine local information and obtain local adaptively weighted feature vectors and residual vectors. Second, the global AWSAE is established for the whole process to mine global information and obtain global adaptively weighted feature vectors and residual vectors. Finally, local statistics and global statistics are constructed based on local and global adaptively weighted feature vectors and residual vectors to detect the sub-blocks and the whole process, respectively. The advantages of proposed method are verified by a numerical example and Tennessee Eastman process (TEP).

Neural Network-Based Adaptive Tracking Control for Denitrification and Aeration Processes With Time Delays.

Wastewater treatment process (WWTP), consisting of a class of physical, chemical, and biological phenomena, is an important means to reduce environmental pollution and improve recycling efficiency of water resources. Considering characteristics of the complexities, uncertainties, nonlinearities, and multitime delays in WWTPs, an adaptive neural controller is presented to achieve the satisfying control performance for WWTPs. With the advantages of radial basis function neural networks (RBF NNs), the unknown dynamics in WWTPs are identified. Based on the mechanistic analysis, the time-varying delayed models of the denitrification and aeration processes are established. Based on the established delayed models, the Lyapunov-Krasovskii functional (LKF) is used to compensate for the time-varying delays caused by the push-flow and recycle flow phenomenon. The barrier Lyapunov function (BLF) is used to ensure that the dissolved oxygen (DO) and nitrate concentrations are always kept within the specified ranges though the time-varying delays and disturbances exist. Using Lyapunov theorem, the stability of the closed-loop system is proven. Finally, the proposed control method is carried out on the benchmark simulation model 1 (BSM1) to verify the effectiveness and practicability.

Deterministic Learning-Based Adaptive Neural Control for Nonlinear Full-State Constrained Systems.

In this article, an adaptive neural learning method is introduced for a category of nonlinear strict-feedback systems with time-varying full-state constraints. The two challenging problems of state constraints and learning capability are investigated and solved in a unified framework. To obtain the learning of unknown functions and satisfy full-state constraints, three main steps are considered. First, an adaptive dynamic surface controller (DSC) based on barrier Lyapunov functions (BLFs) is structured to implement that the closed-loop systems signals are bounded and full-state variables remain within the prescribed time-varying intervals. Moreover, the radial basis function neural networks (RBF NNs) are used to identify unknown functions. The output of the first-order filter, instead of virtual control derivatives, is used to simplify the complexity of the RBF NN input variables. Second, the state transformation is used to obtain a class of linear time-varying subsystems with small perturbations such that the recurrence of the RBF NN input variables and the partial persistent excitation condition are actualized. Therefore, the unknown functions can be accurately approximated, and the learned knowledge is kept as constant NN weights. Third, the obtained constant weights are borrowed into an adaptive learning scheme to achieve the batter control performance. Finally, simulation studies illustrate the advantage of the reported adaptive learning method on higher tracking accuracy, faster convergence rate, and lower computational expense by reusing learned knowledge.

Transfer Learning Algorithm With Knowledge Division Level.

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.

Self-Organizing Interval Type-2 Fuzzy Neural Network Using Information Aggregation Method.

Interval type-2 fuzzy neural networks (IT2FNNs) usually stack adequate fuzzy rules to identify nonlinear systems with high-dimensional inputs, which may result in an explosion of fuzzy rules. To cope with this problem, a self-organizing IT2FNN, based on the information aggregation method (IA-SOIT2FNN), is developed to avoid the explosion of fuzzy rules in this article. First, a relation-aware strategy is proposed to construct rotatable type-2 fuzzy rules (RT2FRs). This strategy uses the individual RT2FR, instead of multiple standard fuzzy rules, to interpret interactive features of high-dimensional inputs. Second, a comprehensive information evaluation mechanism, associated with the interval information and rotation information of RT2FR, is developed to direct the structural adjustment of IA-SOIT2FNN. This mechanism can achieve a compact structure of IA-SOIT2FNN by growing and pruning RT2FRs. Third, a multicriteria-based optimization algorithm is designed to optimize the parameters of IA-SOIT2FNN. The algorithm can simultaneously update the rotatable parameters and the conventional parameters of RT2FR, and further maintain the accuracy of IA-SOIT2FNN. Finally, the experiments showcase that the proposed IA-SOIT2FNN can compete with the state-of-the-art approaches in terms of identification performance.

Multistate-Constrained Multiobjective Differential Evolution Algorithm With Variable Neighborhood Strategy.

Multiobjective differential evolution (DE) algorithm (MODE) has been widely used in multiobjective optimization problems. However, due to the complex feasible regions, the optimization efficiency of MODE may decrease when solving constrained multiobjective problems. It is challenging to promote the evolution of population with few feasible solutions. In this article, a multistate-constrained MODE with variable neighborhood strategy (MSCMODE-VNS) is proposed to enhance the optimization effectiveness with complex feasible regions. First, a variable neighborhood DE strategy, based on a specially designed convergence indicator, is designed to accelerate the generation of feasible solutions. Second, a multistate population updating strategy with a comprehensive solution evaluation mechanism is devised to update the population of the next generation to improve the performance of solutions. Third, the convergence analysis, based on the probability theory, is derived to verify the effectiveness of the proposed MSCMODE-VNS algorithm. Finally, experimental results indicate that MSCMODE-VNS can achieve a satisfactory performance on three benchmark test suites and two real-world-constrained multiobjective problems.

Multiobjective Integrated Optimal Control for Nonlinear Systems.

The multiobjective optimal control method optimizes the performance indexes of nonlinear systems to obtain setpoints, and designs a controller to track the setpoints. However, the stepwise optimal control method that independently analyzes the optimization process may obtain unfeasible and difficult to track setpoints, which will reduce the operation and control performance of the systems. To solve this problem, a multiobjective integrated optimal control (MIOC) strategy is proposed for nonlinear systems in this article. The main contributions of MIOC are threefold. First, in the framework of multiobjective model predictive control, an integrated control structure with a comprehensive cost function and a collaborative optimization algorithm is designed to achieve the coordinate optimal control. Second, for the time inconformity of setpoints and control laws caused by the characteristic of tracking control, the different prediction horizons are designed for the comprehensive cost function. Then, the collaborative optimization algorithm is proposed for the comprehensive cost function to achieve the integrated solution of setpoints and control laws to enhance the operation and control performance of nonlinear systems. Third, the stability and control performance analysis of MIOC is provided. Finally, the proposed MIOC method is applied for a nonlinear system to demonstrate its effectiveness.

Consensus of MASs With Input and Communication Delays by Predictor-Based Protocol.

In this article, the consensus problem of multiagent systems (MASs) affected by input and communication delays is investigated. A predictor-based state feedback protocol is used to reach the consensus of linear MASs by delay compensation. In order to analyze the maximum delay under the predictor-based protocol, the overall MASs are equivalent to the feedback interconnection system, including a linear time-invariant system and a time-delay operator, in view of the characteristic of the Laplacian matrix. Then, the maximum delay corresponding to the predictor-based protocol is evaluated by using the small gain theorem (SGT). Finally, two numerical examples are given to verify the effectiveness of the obtained consensus condition.

Data-Knowledge-Driven Self-Organizing Fuzzy Neural Network.

Fuzzy neural networks (FNNs) hold the advantages of knowledge leveraging and adaptive learning, which have been widely used in nonlinear system modeling. However, it is difficult for FNNs to obtain the appropriate structure in the situation of insufficient data, which limits its generalization performance. To solve this problem, a data-knowledge-driven self-organizing FNN (DK-SOFNN) with a structure compensation strategy and a parameter reinforcement mechanism is proposed in this article. First, a structure compensation strategy is proposed to mine structural information from empirical knowledge to learn the structure of DK-SOFNN. Then, a complete model structure can be acquired by sufficient structural information. Second, a parameter reinforcement mechanism is developed to determine the parameter evolution direction of DK-SOFNN that is most suitable for the current model structure. Then, a robust model can be obtained by the interaction between parameters and dynamic structure. Finally, the proposed DK-SOFNN is theoretically analyzed on the fixed structure case and dynamic structure case. Then, the convergence conditions can be obtained to guide practical applications. The merits of DK-SOFNN are demonstrated by some benchmark problems and industrial applications.

Adaptive NN Controller of Nonlinear State-Dependent Constrained Systems With Unknown Control Direction.

Various constraints commonly exist in most physical systems; however, traditional constraint control methods consider the constraint boundaries only relying on constant or time variable, which greatly restricts applying constraint control to practical systems. To avoid such conservatism, this study develops a new adaptive neural controller for the nonlinear strict-feedback systems subject to state-dependent constraint boundaries. The nonlinear state-dependent mapping is employed in each step of backstepping procedure, and the prescribed transient performance on tracking error and the constraints on system states are ensured without repeatedly verifying the feasibility conditions on virtual controllers. The radial basis function neural network (NN) with less parameters approach is introduced as an identifier to estimate the unknown system dynamics and reduce computation burden. For removing the effect of unknown control direction, the Nussbaum gain technique is integrated into controller design. Based on the Lyapunov analysis, the developed control strategy can ensure that all the closed-loop signals are bounded, and the constraints on full system states and tracking error are achieved. The simulation examples are used to illustrate the effectiveness of the developed control strategy.