Economic Control Problem Research Articles

Modern methods for solving the optimal control problem in economics

The modern formulation of the optimal control problem is given, following which a survey of the methods currently applied in solving the optimal control problem in economics is conducted, with a focus given to numerical methods. The most important problems in the application of numerical methods in solving the optimal control problem are given and explained. The article then lists and explains the most common computational methods of solving the optimal control problem that are being applied in todays economic sphere, how far these methods go in terms of achieving their objectives and providing solutions, the difficulties in implementing these methods, and the associated limitations. The latest developments in software and programs that are beginning to be used by mainly economists in solving some of the most common optimal control problems are listed, and their advantages and limitations are explained. Lastly, a general analysis of some of the next-generation methods and the future of the optimal control problem in general is made.

Applications of Markov chain approximation methods to optimal control problems in economics

In this paper we explore some benefits of using the finite-state Markov chain approximation (MCA) method of Kushner and Dupuis (2001) to solve continuous-time optimal control problems in economics. We first show that the implicit finite-difference scheme of Achdou et al. (2022) amounts to a limiting form of the MCA method for a certain choice of approximating chains and policy function iteration for the resulting system of equations. We then illustrate that relative to the implicit finite-difference approach, using variations of modified policy function iteration to solve income fluctuation problems both with and without discrete choices can lead to an increase in the speed of convergence of more than an order of magnitude. Finally, we provide several consistent chain constructions for stationary portfolio problems with correlated state variables, and illustrate the flexibility of the MCA approach by using it to construct and compare two simple solution methods for a general equilibrium model with financial frictions.

Control over costs and resource savings in the process of logistics activities of construction enterprises: methods, organization

Introduction. In the process of managing the logistics activities of these enterprises, an important role is given to control over costs and resource savings. These components of management allow to constantly monitor the pace of housing construction and identify problems that arise there in order to eliminate objective obstacles, ensure compliance with construction schedules at the stages of the construction process, delivery of finished housing to individual customers in the agreed time and with declared, in contractual obligations, its quality.Purpose. The purpose of the article is to critically analyze publications on the problems of economic control of costs and resource savings, logistics activities in enterprises, including construction, and to develop their own position and proposals of the authors to solve these problems.Method (methodology). In the process of researching this topic, the following methods were used: monographic – in order to study the literature on economic control over costs and resource savings in the process of logistics activities of construction companies; regulatory and legal support – in order to identify violations of Ukrainian legislation in the field of construction and logistics; tabular – to build a table on the methodology of audit control of logistics costs and their resource savings in the process of logistics activities of construction companies, etc.Results. Control over logistics costs (state and domestic) and savings (overspending) of resources in construction enterprises should be carried out in the form of monitoring, verification, aimed at their rational use of resources (building materials and structures, electricity, fuel, lubricants, water, etc.), that is, to save money during the design of the construction object, preparation of the construction site for the beginning of capital construction, the implementation of direct construction and installation work, delivery- acceptance of the constructed object into operation.Bankruptcy of the construction company «Elita-Center», Bank «Arcade», serious violations in the activities of «Ukrbud», unsuccessful reform of DABI, explosion of a residential building in Poznyaki revealed an acute problem in the renewal of the Ukrainian housing stock. There is a relevant practice in the world aimed at protecting the interests of people who invest in housing (in the UK, Israel, Poland). It must be taken into account in Ukraine.Outsourcing specialists can be involved in work in construction organizations (enterprises) on a contractual basis, which will allow these organizations (enterprises) to save time and save costs for logistics operations.The audit of logistics costs (external and internal) and resource savings in the process of logistics activities in construction makes it possible to establish the reasons for deviations from such costs and certain officials who are involved in these deviations in construction companies. It should be noted here that deviations can be manifested not only in the overspending of logistics costs and resources, but also in their savings (in this case, the official must be encouraged in some way). Perspectives. Promising are the studies aimed at the general improvement of the system of economic control over the activities of construction companies and each of their logistics in the development of the digital economy and overcoming the consequences of the fight against СOVID-19.

Nonlinear model predictive control of organic Rankine cycles for automotive waste heat recovery: Is it worth the effort?

Using organic Rankine cycles (ORC) for waste heat recovery in vehicles promises significant reductions in fuel consumption. Controlling the organic Rankine cycle, however, is difficult due to the highly transient exhaust gas conditions. To tackle this issue, nonlinear model predictive control (NMPC) has been proposed and approximate NMPC solutions have been investigated to reduce computational demand. Herein, we compare (i) an idealized economic NMPC (eNMPC) scheme as a benchmark to (ii) a NMPC enforcing minimal superheat and (iii) a PI controller with dynamic feed-forward term (PI-ff) in a control case study with highly transient disturbances. We show that, for an ORC system with supersonic turbine, the economic control problem can be reduced to a single-input single-output superheat tracking problem combined with a decoupled steady-state real-time optimization (RTO) of turbine operation, assuming an idealized condenser. Our results indicate that the NMPC enforcing minimal superheat provides good control performance with negligible losses in average power compared to the full solution of the economic NMPC problem and that even PI-ff only results in marginal losses in average power compared to the model-based controllers.

Robust Control Design for an Uncertain Macroeconomic Dynamical System with Unknown Characteristics and Inequality Control Constraint

The stabilization problem of a macroeconomic dynamical system is considered in this paper. The main features of this system are that the system uncertainties may be unknown functions of state and time but with known bounds. Furthermore, the control inputs are subject to constraints, which is a salient feature in an economic control problem. To ensure that the controls are within the specified boundaries, in our control design procedure, a creative diffeomorphism, which converts bounded controls into unbounded corresponding signals by choosing an appropriate transformation function, is proposed. For the uncertain system, a deterministic robust control is designed to render the practical stability: uniform boundedness and uniform ultimate boundedness. The range of the input bounds is related to the uncertainties and can be designed according to the actual situation. Numerical simulations are performed to verify the effectiveness of the stabilization policy.

Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics

Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics

An estimate of a smooth approximation of the production function for integrating Hamiltonian systems

In many applied control problems in economics, ecology, demography, and other areas, the relationship between dependent and independent main variables is determined statistically, which does not guarantee the smoothness of the model functional dependence. Particularly, in economic growth models, the production function describing the dependence of the output on the production factors is commonly supposed to be everywhere smooth; however, because of this constraint, qualitative parameters affecting the output cannot be included in the model. We propose an approach overcoming the requirement for the production function to be everywhere differentiable. The method is based on a smooth approximation of the production function, which is constructed in parallel with the integration of the Hamiltonian system. A differentiable approximation of the production function is derived by constructing an asymptotic observer of the state of an auxiliary system. It should be noted that the standard approach to the approximation of nonsmooth components of the model on a finite time interval may not work here, which implies the necessity to stabilize the Hamiltonian system on an infinite time interval. The theoretical results are supported by numerical experiments for the one-sector economic growth model.

Another view of the maximum principle for infinite-horizon optimal control problems in economics

The authors present their recently developed complete version of the Pontryagin maximum principle for a class of infinite-horizon optimal control problems arising in economics. The main distinguishing feature of the result is that the adjoint variable is explicitly specified by a formula analogous to the Cauchy formula for solutions of linear differential systems. In certain situations this formula implies the ‘standard’ transversality conditions at infinity. Moreover, it can serve as an alternative to them. Examples demonstrate the advantages of the proposed version of the maximum principle. In particular, its applications are considered to Halkin’s example, to Ramsey’s optimal economic growth model, and to a basic model for optimal extraction of a non-renewable resource. Also presented is an economic interpretation of the characterization obtained for the adjoint variable. Bibliography: 62 titles.

Another view of the maximum principle for infinite-horizon optimal control problems in economics

В статье представлен недавно полученный авторами полный вариант принципа максимума Понтрягина для класса задач оптимального управления с бесконечным горизонтом, возникающих в экономике. Главной отличительной чертой данного результата является определение сопряженной переменной посредством явной формулы, аналогичной формуле Коши для решений линейных дифференциальных систем. В некоторых случаях эта формула влечет выполнение "стандартных" условий трансверсальности на бесконечности. Более того, она может использоваться в качестве их альтернативы. Приведены примеры, иллюстрирующие преимущества предлагаемого варианта принципа максимума. В частности, рассмотрено его применение к примеру Халкина, к модели оптимального экономического роста Рамсея, а также к базовой модели оптимальной эксплуатации невозобновляемого ресурса. Кроме того, дана экономическая интерпретация полученной характеризации сопряженной переменной. Библиография: 62 названия.

Numerical solution of a parabolic optimal control problem in economics

In this paper, we construct and study finite difference approximations of optimal control problems arising in the mathematical modeling of certain management and financial problems. For the definiteness we consider two-dimensional in space variables problems, although all the theoretical results remain valid for any dimension. The numerical calculation results are presented for 1D and 2D problems. To approximate the state equations we use implicit (backward Euler) and fractional steps (operator splitting) methods. The solutions of the constructed mesh state equations are strictly positive and keep an analogue of the mass balance condition. We provide the existence results and first order optimality conditions for the corresponding mesh optimal control problems. We use several iterative methods to implement the constructed nonlinear optimization problems and compare their effectiveness.

Analysis of Finite Difference Approximations of an Optimal Control Problem in Economics

Analysis of Finite Difference Approximations of an Optimal Control Problem in Economics

Optimal Control Problems with State Specific Jumps in the State Equation

An important class of control problems in economics are those in which the state equation switches (jumps) whenever the state variable crosses a threshold. An example is a life-cycle problem in which a household faces higher rates on borrowing than on lending, and therefore the interest rate on the household's asset balance switches discretely each time the asset balance switches signs [6]. The existing method for solving such a problem is notoriously difficult to compute because the first-order conditions include a continuum of complementary slackness conditions. In this paper we provide an easy solution method that utilizes the standard Maximum Principle for unconstrained optimization problems. No inequality constraints (and therefore no complementary slackness conditions) are required.

Local Memory Search Bat Algorithm for Grey Economic Dynamic System

Control system is a pattern for describing microeconomic performance, so it can provide theory basis for policy-making to make economic performance well and continuously by analyzing and solving the model of economic control system. After analyzing the characteristics of Bat Algorithm (BA), the method to adjust each step of BA is proposed. In the method, each bat took advantage of the optimal location that it had found to guide the direction of search. The result of the case study showed that the proposed algorithm was efficient, then the proposed algorithm was used to solve the grey economic dynamic system, and the results further showed that the method was valid for solving economic control problems. DOI: http://dx.doi.org/10.11591/telkomnika.v11i9.3149

Model Reference Control for an Economic Growth Cycle Model

A useful method in intelligent engineering, called model reference control (MRC), is applied in an economic control problem. The authors review the main framework of MRC and Goodwin growth cycle (GGC) model between two countries and drive the employment rate to be approximate stable in a high level by controlling the workers′ share in the national income automatically. It is very helpful to constitute economic policies for a country or an economic union.

The development of the fuzzy-statistical method modeling and control problems in Economics

The mathematical models and methods for adaptive fuzzy control are offered. The methods also take into account the statistical information and risk conditions at the control implementation.

Isoperimetric Problems on Time Scales with Nabla Derivatives

We prove a necessary optimality condition for isoperimetric problems under nabla-differentiable curves. As a consequence, the recent results of Caputo (2008), that put together seemingly dissimilar optimal control problems in economics and physics, are extended to a generic time scale. We end with an illustrative example of the application of our main result to a dynamic optimization problem from economics.

On a class of optimal control problems arising in mathematical economics

This paper is devoted to the study of the properties of the adjoint variable in the relations of the Pontryagin maximum principle for a class of optimal control problems that arise in mathematical economics. This class is characterized by an infinite time interval on which a control process is considered and by a special goal functional defined by an improper integral with a discounting factor. Under a dominating discount condition, we discuss a variant of the Pontryagin maximum principle that was obtained recently by the authors and contains a description of the adjoint variable by a formula analogous to the well-known Cauchy formula for the solutions of linear differential equations. In a number of important cases, this description of the adjoint variable leads to standard transversality conditions at infinity that are usually applied when solving optimal control problems in economics. As an illustration, we analyze a conventionalized model of optimal investment policy of an enterprise.

A unified view of ostensibly disparate isoperimetric variational problems

A class of isoperimetric variational calculus problems is solved. It is shown that the said class ties together seemingly dissimilar optimal control problems in economics and physics, to wit, the classical nonrenewable resource extracting model of the firm, the model of the patient worker, and the principle of maximum entropy. In particular, it is shown that a certain family of wealth maximizing nonrenewable resource extracting firms extract at the rate that maximizes the entropy of extraction, and that patient intertemporal utility maximizing individuals do not procrastinate and maximize the entropy of leisure.

MULTIDIMENSIONAL TRANSITIONAL DYNAMICS: A SIMPLE NUMERICAL PROCEDURE

We propose the relaxation algorithm as a simple and powerful method for determining the transition process in growth models numerically. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including stiff differential equations and systems giving rise to a continuum of stationary equilibria. (2) The application of the procedure is fairly user-friendly. The only input required consists of the dynamic system. (3) The variant of the relaxation algorithm we propose exploits in a natural manner the infinite time horizon, which usually underlies optimal control problems in economics. As an illustrative application, we compute the transition process of the models of Jones [Jones, C.I. (1995) R&D-based models of economic growth. Journal of Political Economy 103 (3), 759–784] and Lucas [Lucas, R.E., Jr. (1988) On the mechanics of economic development. Journal of Monetary Economics 22, 3–42].

Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure

We propose the relaxation algorithm as a simple and powerful method for simulating the transition process in growth models. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including stiff differential equations and systems giving rise to a continuum of stationary equilibria. (2) The application of the procedure is fairly user friendly. The only input required consists of the dynamic system. (3) The variant of the relaxation algorithm we propose exploits in a natural manner the infinite time horizon, which usually underlies optimal control problems in economics. As an illustrative application, we simulate the transition process of the Jones (1995) and the Lucas (1988) model.