


Vol 28, No 4 (2017)
- Year: 2017
- Articles: 8
- URL: https://journals.rcsi.science/1046-283X/issue/view/15437
I. Investigating Control Problems
Optimal Control in the Resource Allocation Problem for a Two-Sector Economy with a CES Production Function
Abstract
We consider the resource allocation problem in a two-sector economy with a Constant Elasticity of Substitution (CES) production function on a given sufficiently long finite planning horizon. The performance criterion being optimized is one of the phase coordinates at the terminal time. The scalar control u satisfies the geometrical constraint u ∈ [0, 1]. The optimal control contains a singular section. Analyzing the Pontryagin maximum principle boundary-value problem we find the extremal triple and prove its optimality using a special representation of the functional increment (the theorem of sufficient conditions of optimality in terms of maximum-principle constructs). The solution is constructed with the aid of a Lambert special function y = W(x), that solves the equation yey= x. The optimal control consists of three sections: the initial section that involves motion toward the singular ray Lsng = {x1 = x2 > 0} , the singular section that involves motion along the singular ray, and terminal section that involves motion under zero control. When the initial state is on the singular ray, the optimal control consists of two sections — singular and terminal. The article is related to a number of the authors’ publications using other production function.



Article
A Nonlinear Two-Dimensional Time-Optimal Control Problem
Abstract
A two-dimensional time-optimal problem with nonlinear gravity is investigated. The Pontryagin maximum principle is applied to solve the problem. The controllability set is investigated, the extremal control and the extremal time function are determined, optimality is proved by regular synthesis.



The Problem of Package Guidance with Incomplete Information for a Linear Control System with a Delay
Abstract
The control-package method is applied to solve the problem of constructing guaranteed positional guidance for a linear control dynamical system with a delay under incomplete information about the initial state. The problem is solved for the case when the initial state is contained in a compact functional set. A solvability criterion and a method for the construction of a guidance program package are proposed. The proposed procedure is applied to a particular linear control system of delayed differential equations.



Hyperchaotic Analysis and Adaptive Projective Synchronization of Nonlinear Dynamical System
Abstract
In this paper, a new nonlinear dynamical system has been studied which is obtained from the 3D chaotic system. The hyperchaotic analysis of the new system is checked in terms of dissipation, equilibrium points and their stability, Lyapunov exponent, time series, phase portraits, Poincaré section and bifurcation diagram. Furthermore, the adaptive projective synchronization technique is used to synchronize the novel hyperchaotic system. A brief theoretical analysis and simulation results are presented to prove the behavior of the novel hyperchaotic system.



Modeling of Environmental-Economic Indicators of Regional Development
Abstract
One of the current topical problems is the prediction of climate change and mitigation of its consequences. All-sided analysis of ecological, economic, and social aspects of climate issues relies on interdisciplinary assessment models. This article adapts the MERGE optimization model to the current state of the world economy and introduces into the model a new component that implements a simplified procedure of “green” GDP calculation (“green” GDP, or GGDP, provides information about the efficiency of use of environmental resources). The objective of our numerical simulations is to tests the consequences of Russia’s hypothetical participation in the program for reducing greenhouse gas (GHG) emissions and to analyze the environmental indicators of Russia’s GDP. The input data are mainly provided by the project of scenario conditions and main macroeconomic parameters for the forecasting of socio-economic development in Russia in the near future implemented by the Ministry of Economic Development of the Russian Federation. The calculations reveal the existence of reserves for Russia’s “painless” participation in environment-preserving initiatives that call for not exceeding the 1990 emission level in 2020–2025. At the same time, increasing the environmental efficiency of Russia’s GDP is a relevant task that requires immediate attention.



Numerical Analysis of the Maximum Principle Boundary-Value Problem for the Influenza Virus Spread Model
Abstract
We consider the optimal control problem for a model of the spread of the influenza virus ignoring natural births and deaths. The problem is investigated by the Pontryagin maximum principle. A maximum principle boundary-value problem is constructed and it is analyzed numerically by the parameter continuation method. The best control is obtained in the class of piecewise-constant controls with one switching point, which is of definite interest in applications. The functional value under this control is worse by approximately 12.8% than the functional value under extremal control.



Reachable Set of a Control Model for Two-Step Wastewater Biotreatment
Abstract
We consider a mathematical model describing a two-step process of wastewater biotreatment. This is a four-dimensional nonlinear system of differential equations with a scalar constraint on the control. The Pontryagin maximum principle is applied to investigate the boundary of the reachable set in this system. Among the possible parameter values and initial conditions of the model, we identify those for which piecewise-constant controls corresponding to boundary points of the reachable set have at most one, two, and three switching points.



II. Mathematical Control Models
Quadcopter Terminal Control in the Presence of Disturbances
Abstract
We construct a mathematical model of quadcopter flight and design a positional control that solves the terminal control problem in the presence of a disturbance parameter. The study relies on the results of [6–9] and provides sufficient existence conditions for a positional control that solves the control problem for a class of boundary conditions.


