Том 28, № 4 (2017)

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 ye^y= x. The optimal control consists of three sections: the initial section that involves motion toward the singular ray L_sng = {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.

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.

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.

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.

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.