Background -- Continuous-Time Dynamical Systems -- Applied Optimal Control -- Tour d'Horizon: Optimal Control -- The Path to Deeper Insight: From Lagrange to Pontryagin -- Multiple Equilibria, Points of Indifference, and Thresholds -- Advanced Topics -- Higher-Dimensional Models -- Numerical Methods for Discounted Systems of Infinite Horizon -- Extensions of the Maximum Principle -- Appendices -- Mathematical Background -- Derivations and Proofs of Technical Results.

Dynamic optimization is rocket science – and more. This volume teaches how to harness the modern theory of dynamic optimization to solve practical problems, not only from space flight but also in emerging social applications such as the control of drugs, corruption, and terror. These innovative domains are usefully thought about in terms of populations, incentives, and interventions, concepts which map well into the framework of optimal dynamic control. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. We celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding – and push its frontiers by exploring models that display multiple equilibria whose basins of attraction are separated by higher-dimensional DNSS "tipping points". That rich theory is complemented by numerical methods available through a companion web site. Ensdorsements: "An excellent synthesis of the richness of systems theory highlighted with strongly motivating applications and an outstanding text for a graduate-level course. The book provides a thorough background in the variety of mathematical foundations needed, recognizing that different readers will come with a diversity of backgrounds. Its applications to drug control, corruption, and terrorism represent creative modeling that provides important insights into subtleties that go beyond the normal linear thinking about these complex phenomena." Alfred Blumstein, winner of the 2007 Stockholm Prize in Criminology University Professor of Urban Systems and Operations Research H. John Heinz III School of Public Policy and Management Carnegie Mellon University, Pittsburgh "This carefully written book is a masterpiece that combines a rigorous exposition of non-linear dynamics with sophisticated and intriguing optimal control models of drugs, corruption, and terror. The chapter on numerical methods is a valuable added bonus. The book deserves a prominent place in the bookshelf of all serious researchers wishing to use the tools of dynamic optimization." Ngo Van Long James McGill Chair, and professor of economics Department of Economics McGill University Montreal "First of its kind devoted to the very timely topics of drugs, corruption and terror. A highly readable comprehensive treatment of controlled dynamical nonlinear systems involving such concepts as limit cycles, multiple equilibria, and DNSS points. Laced with beautiful graphics and supported by numerical computations. A delight from the beginning to the end." Suresh P. Sethi Charles & Nancy Davidson Distinguished Professor of Operations Management & Director of the Center for Intelligent Supply Networks The University of Texas at Dallas.