This book intends to report new optimal control results with critic intelligence for complex discrete-time systems, which covers the novel control theory, advanced control methods, and typical applications for wastewater treatment systems. Therein, combining with artificial intelligence techniques, such as neural networks and reinforcement learning, the novel intelligent critic control theory as well as a series of advanced optimal regulation and trajectory tracking strategies are established for discrete-time nonlinear systems, followed by application verifications to complex wastewater treatment processes. Consequently, developing such kind of critic intelligence approaches is of great significance for nonlinear optimization and wastewater recycling. The book is likely to be of interest to researchers and practitioners as well as graduate students in automation, computer science, and process industry who wish to learn core principles, methods, algorithms, and applications in the field of intelligent optimal control. It is beneficial to promote the development of intelligent optimal control approaches and the construction of high-level intelligent systems.