In view of the difficulty in obtaining the membrane bioreactor (MBR) membrane flux in real time, considering the disadvantage of the back propagation (BP) network in predicting MBR membrane flux, such as the local minimum value and poor generalization ability of the model, this article introduces tent chaotic mapping in the standard sparrow search algorithm (SSA), which improves the uniformity of population distribution and the searching ability of the algorithm (used to optimize the key parameters of the BP network). The tent sparrow search algorithm back propagation network (Tent-SSA-BP) membrane fouling prediction model is established to achieve accurate prediction of membrane flux; compared to the BP, genetic algorithm back propagation network (GA-BP), particle swarm optimization back propagation network (PSO-BP), sparrow search algorithm extreme learning machine(SSA-ELM), sparrow search algorithm back propagation network (SSA-BP), and Tent particle swarm optimization back propagation network (Tent–PSO-BP) models, it has unique advantages. Compared with the BP model before improvement, the improved soft sensing model reduces MAPE by 96.76%, RMSE by 99.78% and MAE by 95.61%. The prediction accuracy of the algorithm proposed in this article reaches 97.4%, which is much higher than the 48.52% of BP. It is also higher than other prediction models, and the prediction accuracy has been greatly improved, which has some engineering reference value.

This article studies the distributed fault-tolerant bipartite output synchronization problem of discrete-time linear multiagent systems (MASs) with process faults under a general directed signed graph. The reference signal is generated by an autonomous exosystem, which can also be seen as a leader. All followers are divided into two subgroups with antagonistic interactions, and the followers in each subgroup are cooperative. We aim to solve the bipartite fault-tolerant control (FTC) problem via the output regulation theory such that bipartite output synchronization can be achieved in the presence of process faults, that is, the outputs of followers with different subgroups can approach the output of exosystem with the same magnitude and the opposite sign regardless of process faults. To estimate the states and the faults of each follower, a simultaneous state and fault estimator based on the neighboring signed output estimation error and the standard discrete-time algebraic Riccati equation (ARE) is designed. Besides, a new exosystem observer with two classes of convergence conditions relying on the respective solutions of standard and modified AREs is provided. All eigenvalues of the exosystem matrix can lie completely outside the unit circle. Based on these estimations, we present a distributed fault-tolerant output feedback controller, which can overcome the no-loops constraint. Finally, simulation results are given to demonstrate the analytic results.

The problem of observer‐based decentralized robust H_∞ output tracking control with preview action in a class of uncertain and disturbed nonlinear interconnected systems is investigated in this study. The considered interconnected system consists of several subsystems with nonlinear interconnections, parametric uncertainties, and external disturbances. Based on the augmented error system approach combined with Lyapunov stability theory and special matrix inequality linearization techniques, a sufficient condition for the existence of a decentralized observer‐based robust H_∞ output feedback preview controller is derived for the original interconnected system in terms of linear matrix inequality (LMI) formulations. The gain matrices of the tracking controller and state observer are derived using only a one‐step LMI procedure, which overcomes the drawbacks of some multistep iterative algorithms. Finally, the effectiveness of the proposed control scheme is validated using a numerical example.

Optimal containment preview analysis and distributed design for multi-agent systems with general continuous-time linear dynamics and directed acyclic communication topology are considered. Firstly, the state augmentation technique and topology reconstruction method are applied to formulate the original problem as a set of internal-model based local optimal output regulation problem. Secondly, the linear superposition principle is employed to obtain the preview feed-forward compensations corresponding to multiple leaders. Thirdly, by expressing each preview compensation term as a form about the current state of the leader, the solvability of the local optimal output regulation problem, as well as the optimal regulation problems, are proved. On this basis, the sufficient conditions and the distributed optimal control strategy are derived, which ensure the convergence of the containment preview problem. Finally, the effectiveness of the distributed design is illustrated by a numerical experiment.