Optimal Control of Nonlinear Processes

Dynamic optimization is rocket science and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in 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. The authors celebrate Pontryagin s Maximum Principle that crowning intellectual achievement of human understanding. Yet they go further, pushing 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.

This volume is designed to be a lively introduction to the mathematics of this rapidly advancing subject, and a bridge to a number of hot topics in the economics of crime for current scholars.

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.