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Bridging the gap between introductory texts and the specialized research literature, this is one of the first truly rigorous yet accessible treatments of modern reinforcement learning. Written by three leading researchers with over a decade of teaching experience, the book uniquely combines mathematical precision with practical insights. It progresses naturally from planning (dynamic programming, MDPs, value and policy iteration) to learning (model-based and model-free algorithms, function approximation, policy gradients, and regret minimization). Each concept is developed from first principles with complete proofs, making the material self-contained. The modular chapter organization enables flexible course design. The book's website offers battle-tested exercises refined through years of classroom use. Combining mathematical rigor with practical applications, this definitive text is ideal for advanced undergraduate and graduate students as well as practitioners seeking a deep understanding of sequential decision-making and intelligent agent design.
Optimization is a foundational topic in mathematics, underpinning nearly all of our modern industrial and technological world. Assuming only basic knowledge of linear algebra and calculus, this book provides a rapid, yet thorough, overview of applied mathematical optimization for advanced undergraduates, beginning graduate students, or practitioners in engineering and science. The text opens with an 'Optimization Bootcamp', introducing methods at a beginning level, before progressing to deep-dives into advanced topics and research-ready methods. The focus throughout is on modern applications of machine learning, inverse problems, and control. Rich pedagogy includes Python code with simple working examples and advanced case studies. Every section is accompanied by YouTube lectures to encourage interaction with the material. Using intuitive explanations, this book makes the material as simple and interesting as possible, while still having the depth, breadth and precision required to empower use in research and real-world applications.
This book is designed for undergraduate and graduate students in engineering enrolled in courses on control systems and optimal control. It will also serve as a valuable reference for mathematics students studying control theory. It offers a rigorous and systematic treatment of both finite-dimensional and infinite-dimensional control systems. The volume opens with chapters on essential mathematical foundations, including mathematical modelling, linear algebra, and ordinary differential equations, establishing a solid framework for the study of control theory. Subsequent chapters provide an in-depth treatment of key topics such as controllability, observability, feedback control, state observer, optimal control, constrained control, stability, approximate controllability, and regularized control. The text concludes with comprehensive coverage of discrete-time systems and infinite-dimensional systems. Throughout the book, theoretical developments are supported by detailed mathematical proofs, illustrative examples, solved problems, and end-of-chapter exercises, making it suitable for both classroom use and self-study.