Incremental multi-subreservoirs echo state network control for uncertain aeration process

It is a critical challenge to realize the control of dissolved oxygen (DO) in uncertain aeration process, due to the inherent nonlinearity, dynamic and unknown disturbances in wastewater treatment process (WWTP). To address this issue, the incremental multi-subreservoirs echo state network (IMSESN) controller is proposed. First, the echo state network (ESN) is employed as the approximator for the unknown system state, and the disturbance observer is constructed to handle the unmeasurable disturbances.Second, to further improve controller adaptability, the error-driven subreservoir increment mechanism is incorporated, in which the new subreservoirs are inserted into the network to enhance uncertainty approximation.Moreover, the minimum learning parameter (MLP) algorithm is introduced to update only the norm of output weights, significantly reducing computational complexity while maintaining control accuracy.Third, the Lyapunov stability theory is applied to demonstrate the semiglobal ultimate boundedness of the closed-loop signals. Under diverse weather conditions, the simulations on the benchmark simulation model no. 1 (BSM1) show that the proposed controller has outperformed existing methods in tracking accuracy and computational efficiency.