Optimal Control Theory with Economic ApplicationsThis 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. |
Contents
Calculus of variations | 1 |
Different types of terminal conditions | 31 |
7 | 45 |
Copyright | |
38 other sections not shown
Common terms and phrases
admissible functions assume assumption C¹-functions calculus of variations Chapter concave concave function conditions in theorem Consider problem Consider the problem constraint qualification continuous function control functions control variable convex convex set corresponding defined denote differential equation discontinuity economic Euler equation Exercise exist a number existence theorem finite fixed given Hamiltonian Hence holds horizon problems implies inequality infinite horizon integral interval jump points K₁ Let x*(t maximizes Maximum Principle Moreover necessary conditions Note obtain optimal control problems optimal solution optimal value function p₁ p₁(t p₂(t partial derivatives piecewise continuous positive constants problem max prove quasi-concave replaced result satisfied Seierstad solution x(t solves the problem strictly increasing sufficient conditions Suppose t)dt t₁ T₂ terminal conditions theorem 11 transversality conditions type-B solution unique valid variational problem x(t₁ ди дн дх