This paper focuses on the development of linear Switched Box–Jenkins (SBJ) models for approximating complex dynamical models of biological wastewater treatment processes. We discuss the adaptation of these processes to the SBJ framework, showing the model's generality and flexibility as a class of switched systems that can offer accurate predictions for complex and nonlinear dynamics. This approach of modeling enables real-time data reconciliation from experiments and allows the design of model-based control strategies. Through the extension of the Outer Bounding Ellipsoids (OBEs) algorithm, the paper introduces an online two-stage parameter identification algorithm that effectively handles bounded disturbances for SBJ models. Using the OBE method relaxes the stochastic assumptions on disturbances, which may not be satisfied in practice, particularly for biological and environmental fluctuations. The proposed decomposed OBE algorithm separately identifies the switching patterns and parameters of linear submodels, conducting parameter identification in two distinct phases for input/output and disturbance/output submodels. The efficacy of this approach is shown via simulation results validated against both ADM1 and PBM models, demonstrating the proposed algorithm's capability to accurately predict outputs from different biological wastewater treatment models.

Purple phototrophic bacteria (PPB) show an underexplored potential for resource recovery from wastewater. Raceway reactors offer a more affordable full-scale solution on wastewater and enable useful additional aerobic processes. Current mathematical models of PPB systems provide useful mechanistic insights, but do not represent the full metabolic versatility of PPB and thus require further advancement to simulate the process for technology development and control. In this study, a new modelling approach for PPB that integrates the photoheterotrophic, and both anaerobic and aerobic chemoheterotrophic metabolic pathways through an empirical parallel metabolic growth constant was proposed. It aimed the modelling of microbial selection dynamics in competition with aerobic and anaerobic microbial community under different operational scenarios. A sensitivity analysis was carried out to identify the most influential parameters within the model and calibrate them based on experimental data. Process perturbation scenarios were simulated, which showed a good performance of the model.

Dynamical systems and processes that either exhibit non-smooth behaviours (e.g. through logic control or natural phenomena) or work in different modes of operation are usually represented using hybrid systems models, i.e. mathematical models that combine continuous dynamics with discrete-event dynamics. Identification of a hybrid system includes finding switching patterns and identification of model parameters to obtain a data-driven model. This survey paper provides a systematic review of models (how to parameterize the system) and methods (how to identify unknown parameters) proposed for hybrid system identification with an exposition of recent advances and developments, and further research directions.