Optimal Control Models & Applications
16:711:613, Index # 06641, 3 credits
Fall 1996
General information
This is a reading course, intended for self-study
and independent research.
- Class website: http://rutcor.rutgers.edu:80/~bisrael/oc.html
- First Meeting: Tuesday, Sep 3, 12:00 noon, RUTCOR, Room 139
- Instructor: Adi Ben-Israel
- E-mail:
bisrael@rutcor.rutgers.edu
- Office: 113 RUTCOR Bldg, Busch Campus
- Telephone: 445-5631
- Text: M.I. Kamien and N.L. Schwartz,
Dynamic Optimization: The Calculus of Variations and Optimal Control
in Economics & Management (2nd Edition),
North-Holland, 1981
- Description: This course is an introduction to deterministic optimal control
and its applications. The exposition is elementary and self contained, using
the Bellman optimality principle (the dynamic programming prerequisites are
reviewed at the beginning of the course). Applications are given to well known models of
economics, management and finance.
- Intended for:
Graduate students in operations research, economics
and finance, as well as for students of mathematics and engineering
who are interested in applications of optimal control.
- Prerequisites: Advanced Calculus. Ordinary Differential Equations.
Probability. Linear Programming. Knowledge of Dynamic Programming is desirable.
Syllabus
- Review of Dynamic Programming (DP), Bellman's Optimality Principle
and recursive computation.
- Selected applications of DP: Equipment replacement.
Resource allocation. Shortest path problems.
- Discrete time optimal control problems.
Problems with linear dynamics and quadratic criteria.
- Review of stochastic DP.
- Calculus of variations. The Euler-Lagrange necessary conditions.
``Derivation'' using DP. The Legendre, Weiestrass and Erdmann conditions.
The Hamilton-Jacobi-Bellman equation.
- Optimal control. The Pontryagin Maximum Principle.
``Derivation'' using DP. The Hamilton-Jacobi-Bellman equation. The adjoint.
Economic interpretations.
- Applications to economic models of optimal growth: The Ramsey model.
The turnpike theorem.
- Applications to finance: The cash balance problem, with
overdraft and short-selling. An optimal financing model.
-
Applications to production and inventory.
-
Applications to marketing: The Nerlove-Arrow and Vidal-Wolfe advertising
models.
-
Applications to non-renewable natural resources.
The Hotteling optimal extraction rate.
-
Applications to renewable natural resources. Fishery and
forestry models, optimal harvesting.
-
Applications to maintenance and replacement.
Course Work
Each student is required to write LaTeX notes of one or more
topics, to present a lecture on one of the topics 7-13 above,
and to write a paper on some aspect or application of DP/Optimal Control.
References
-
K.J. Arrow and M. Kurz, Public Investment, the Rate of Return
and Optimal Fiscal Policy, J. Hopkins, 1970
-
A. Bensoussan, E.G. Hurst, Jr. and B. Näslund, Management
Applications of Modern Control Theory, Elsevier, 1974
-
D.P. Bertsekas, Dynamic Programming: Deterministic and Stochastic Models,
Prentice-Hall, 1989
-
C.W. Clark, Mathematical Bioeconomics, 2nd Edition, J. Wiley, 1990
-
E.V. Denardo, Dynamic Programming: Models and Applications,
-
W.H. Fleming and R.W. Rishel,
Deterministic and Stochastic Optimal Control, Springer-Verlag, 1975
-
M. Intrilligator, Mathematical Optimization and Economic Theory,
Prentice-Hall, 1971
-
S.M. Ross, Introduction to Stochastic Dynamic Programming,
Academic Press, 1983
-
S.P. Sethi and G.L. Thompson, Optimal Control Theory:
Applications to Management Science, M. Nijhoff, 1981
-
C.S. Tapiero, Managerial Planning: An Optimum and Stochastic Control Approach,
Gordon Breach, 1977
-
H.Y. Wan, Economic Growth, Harcourt, Brace & Jovanovich, 1971