Optimal control theory with applications to resource and environmental economics michael hoel university of oslo july 15, 2016 abstract this note gives a brief, nonrigorous sketch of basic optimal con trol theory, which is a useful tool in several simple economic problems, such as those in resource and environmental economics. This note gives a brief, nonrigorous sketch of basic optimal control theory, which is a useful tool in several simple economic problems, such as those in resource and environmental economics. Chapter 2 optimal control optimal control is the standard method for solving dynamic optimization problems. Optimal control all of these examples have a common structure. Optimal control theory with applications in economics. Optimal control theory with applications in economics by.
Arrow and kurz 1970, hadley and kemp 1971, takayama. In many economic problems the variable xt will be constrained to be non negative. This fully revised 3rd edition offers an introduction to optimal control theory and its diverse applications in management and economics. There h been many applications of control theory, particularly in physics. T0 in the capital problem is known as a trans versality condition. Presented at the session new applications of mathematics to the behavioral scien. An economic interpretation of optimal control theory this section is based on dorfmans 1969 excellent article of the same title.
Optimal control theory with applications in economics pdf free. A second application of optimal control theory to economics is science. Optimal control theory with applications in economics on jstor. Notes on optimal control theory with economic models and exercises. Applications of optimal control theory in economics. Evans department of mathematics university of california, berkeley chapter 1. Each turn on by the state variable along its path is associated with a discrete jump by the control variable. While the mathematical analysis in the note is selfcontained. The basic theory is given in section 2, and the subsequent sections are applications to several problems in resource and environmental economics. The purpose of the article was to derive the technique for solving optimal control problems by thinking through the economics of a particular problem.
This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one. Introduction to optimal control one of the real problems that inspired and motivated the study of optimal control problems is the next and so called \moonlanding problem. Weber find, read and cite all the research you need. Optimal control theory with applications to resource and environmental economics pdf logo. In general, we must piece together the results from case 1 and case 2. The optimal path for the state variable must be piecewise di erentiable, so that it cannot have discrete jumps, although it can have sharp turning points which are not di erentiable.
Consider the problem of a spacecraft attempting to make a soft landing on the moon using a minimum amount of fuel. Applications of optimal control theory in economics jstor. In addition, this new edition features materials on stochastic nash and stackelberg differential games and an adverse selection model in the principalagent framework. Optimal control theory with applications in economics optimal control theory with applications in economicsthomas a. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume.
Introduction to stochastic control theory appendix. In addition, this new edition features materials on stochastic nash and stackelberg differential games and an adverse selection model in the principalagent. References from our text books are chapter 10 of dixit 1990, chapter 20 chiang and wainwright 2005, and chapter 12. Although more advanced than what these notes cover, luenberger 1969 is the classic. Optimal control theory 6 3 the intuition behind optimal control theory since the proof, unlike the calculus of variations, is rather di cult, we will deal with the intuition behind optimal control theory instead. Optimal control theory with applications in economics by thomas a. An economic interpretation of optimal control theory. In many economic problems the variable xt will be constrained to be nonnegative. Notes on optimal control theory with economic models. Batabyal and others published optimal control theory with applications in economics by thomas a.
An introduction to mathematical optimal control theory. The book exploits optimal control theory to the functional areas of management including finance, production and marketing and to economics of growth and of natural resources. Other readily available useful refer ences invclude dorfman 1969 who derives the maximum principle in a model of capital accumulation and. Application of optimal control theory in finance and economy. The curve of minimal length and the isoperimetric problem suppose we are interested to nd the curve of minimal length joining two distinct points in the plane. Technically rigorous and largely selfcontained, it provides an introduction to the use of optimal control theory for deterministic continuoustime systems in economics.