This article investigates the distributed adaptive optimization of multiagent systems with uncertain nonlinearities, utilizing a dynamic event-triggered mechanism. Distinct from existing algorithms that assume healthy operation, the proposed dynamic event-triggered strategy not only saves communication resources but also ensures convergence to a small neighborhood of the global minimizer even in the presence of actuator faults, thereby effectively avoiding the loss of optimality or optimization failure caused by malfunctions. Furthermore, considering that practical systems often possess only measurable outputs and exhibit complex nonlinear characteristics, a state observer is developed to estimate the unmeasured state variables. On this basis, by incorporating the backstepping design technique from the nonlinear fault-tolerant control theory, an adaptive event-triggered output feedback fault-tolerant control strategy is designed to compensate for actuator faults. Meanwhile, a high-order filter is introduced to resolve the incompatibility between the signal derivative discontinuity induced by event-triggering and the differentiability requirements of backstepping design. Thereby, the controller design and stability analysis can proceed within a continuous-time framework. Theoretical analysis demonstrates that the proposed method guarantees that all signals in the resulting closed-loop system are bounded. The validity of the proposed control strategy is further verified through a simulation.
Yonglin Yu, Xudong Zhao, Ben Niu et al.· IEEE Transactions on Reliabi...· 0 citations
Maintaining the concentration of dissolved oxygen at predefined levels is critical for the efficient operation of biological wastewater treatment processes, which are inherently complex and subject to disturbances. In this article, an intelligent online learning framework for optimal tracking control is established, which eliminates the reliance on an explicit mathematical model of the process and synergistically integrates prior knowledge with the action-dependent heuristic dynamic programming algorithm. First, a data-driven actor-critic framework is designed by integrating the disturbance network to counteract process interferences, achieving robust tracking for the dissolved oxygen concentration. Second, an intelligent integrated control input is developed, which dynamically combines the online-learned policy from the action network with a prior control policy derived from existing knowledge, regulated by an adaptive weight function to enhance initial learning and stability. Third, neural networks are implemented for the critic, action, and disturbance components to facilitate online learning. Furthermore, the stability is analyzed in detail, which proves that both the weight errors of neural networks and the closed-loop tracking error are uniformly ultimately bounded. Finally, simulations on the benchmark simulation model No. 1 platform under diverse weather conditions demonstrate that the proposed method achieves superior self-learning capability, high tracking accuracy, and robustness compared to related methods, verifying its favorable tracking control performance. Note to Practitioners—Effective wastewater treatment process is an integral component of promoting environmental protection and cost reduction. A key challenge for operators is maintaining the dissolved oxygen concentration at its optimal setpoint despite frequent and unpredictable changes in incoming wastewater, flow rates, and weather conditions. Traditional control methods often struggle with these complexities, leading to inefficient operation, excess energy consumption, and potential non-compliance with effluent standards. This paper presents a novel data-driven intelligent controller designed to address this practical problem. Unlike methods that require a perfect mathematical model of wastewater treatment processes, the optimal control policy can be obtained adaptively through online learning. It is specifically designed to be robust against the unknown disturbances common in real plants. Furthermore, the existing operational knowledge is incorporated to ensure safe and stable performance, improving the control efficiency and accuracy of the algorithm. The significant benefit is an adaptive system that self-optimizes to precisely track setpoints of dissolved oxygen concentration, leading to reduced energy costs, improved treatment quality, and less required operator intervention. Simulation results on a widely accepted BSM1 platform under various weather scenarios confirm these advantages over existing methods. This makes the proposed framework a promising and practical tool for enhancing the automation and intelligence of wastewater treatment processes.
Ding Wang, Jin Ren, Mingming Zhao et al.· IEEE Transactions on Automat...· 0 citations
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