Optimal Control Theory with Economic Applications
This book serves not only as an introduction, but also as an advanced text and reference source in the field of deterministic optimal control systems governed by ordinary differential equations. It also includes an introduction to the classical calculus of variations.
An important feature of the book is the inclusion of a large number of examples, in which the theory is applied to a wide variety of economics problems. The presentation of simple models helps illuminate pertinent qualitative and analytic points, useful when confronted with a more complex reality. These models cover: economic growth in both open and closed economies, exploitation of (non-) renewable resources, pollution control, behaviour of firms, and differential games. A great emphasis on precision pervades the book, setting it apart from the bulk of literature in this area. The rigorous techniques presented should help the reader avoid errors which often recur in the application of control theory within economics.
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Calculus of variations
Optimal control theory without restrictions on
35 other sections not shown
admissible functions admissible pair associated assume assumption calculus of variations candidate for optimality Chapter concave function conditions in theorem Consider problem Consider the problem constraint qualification continuous function continuously differentiable contradiction control functions control variable convex set corresponding criterion functional defined denote differential equation discontinuity economic Euler equation Exercise exist a number existence theorem finite first-order fixed given Hamiltonian Hence holds horizon problems implies inequality integral interval jump points Let x*(t maximizes Maximum Principle Moreover necessary conditions Note obtain one-sided limits optimal control problems optimal pair optimal solution optimal value function pair x(t parameters partial derivatives piecewise continuous pl(t positive constants proof of theorem prove pure state constraints quasi-concave replaced restrictions result Seierstad solves the problem strictly increasing subderivative sufficient conditions Suppose terminal conditions theorem 11 theorem 9 transversality conditions type-A type-B solution unique valid variational problem