For wastewater treatment process (WWTP), mechanism model for activated sludge process (ASP) is unsuitable for estimating the effluent COD (Chemical Oxygen Demand) as the parameters of ASM (Activated Sludge Model) series models are varying with operating conditions. This paper presents an integrated model to predict the effluent COD. The model consists of two sub-models which are simplified mechanism model of ASP and RBFNN (RBF Neural Network) with variable structure (VSRBFNN). ASP model can express the dynamic biochemical reactions occurred in WWTP, and VSRBFNN is used to reduce the prediction error of the ASP model as an error compensation model. To reduce the complexity of the mechanism model of ASP, the parameters of mechanism model are fixed. The layout and the parameters of VSRBFNN can be adjusted according to the training data, and the stable learning algorithm can restrict the modeling error of VSRBFNN within a bounded domain. The output value of the integrated model is weighted sum of those of two sub-models, where the weights denote the contributions of the two “sub-models” to the prediction error of integrated model and are rectified according to the relative prediction error online. The structure of the integrated soft sensor is concise and real-time capability is improved. Simulations show that the presented soft sensor has satisfactory prediction accuracy under various operating characteristics.

This paper focuses on the stabilization problem of continuous-time Markovian jump systems with controller failures. Here, the controller with a fault or not corresponds to a controller useful or not. First, a controller experiencing a fault or not is proposed, whose dwell times of controller useful or not are different constants and taken into account. Since the designed controller could bear faults in alternate intervals, it is named as a fault-tolerant controller here. Then, by constructing a Lyapunov function depending on such two states in terms of controller useful or not, concise conditions for the existence of controller are obtained and could be solved easily, in which the dwell times are included. Finally, a practical example is given to illustrate the effectiveness of the proposed methods. INDEX TERMS Markovian jumping systems, controller failure, fault-tolerant controller, Lyapunov function, dwell times.

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