Data-driven safe adaptive dynamic programming with hybrid lifelong learning in wastewater treatment processes

The wastewater treatment process (WWTP) is a critical component driving sustainable industrial development. The monitoring and control of the dissolved oxygen (DO) concentration play a vital role in the WWTP. An adaptive utility function, a control barrier function, and an adaptive dynamic programming approach based on a lifelong learning mechanism are constructed in this paper to realize the online control of the DO concentration. First, the magnitude of the tracking error is adopted for control input modulation to enhance the adaptability of the utility function. Second, an adjustable control barrier function is employed to constrain the tracking error within a specific range. Then, a constraint term is introduced into the process of updating the weights by using weights of the critic and action networks from the previous time step, which enhances the approximation performance of the proposed controller. A stability criterion related to the learning law is also established and the uniform ultimate boundedness of the weight estimation error is proven. Finally, the established method is applied to the WWTP and its tracking performance is validated under various weather conditions. • An adaptive incremental utility function is developed to enhance adaptability. • Adjustable nonnegative CBF confines tracking error to balance accuracy and safety. • LL mechanism embeds prior knowledge in weight updates for time-varying WWTP control.