Multiple Capture in a Group Pursuit Problem with Fractional Derivatives and Phase Restrictions

The problem of conflict interaction between a group of pursuers and an evader in a finite-dimensional Euclidean space is considered. All participants have equal opportunities. The dynamics of all players are described by a system of differential equations with fractional derivatives in the form D(α)zi=azi+ui−v,ui,v∈V, where D(α)f is a Caputo derivative of order α of the function f. Additionally, it is assumed that in the process of the game the evader does not move out of a convex polyhedral cone. The set of admissible controls V is a strictly convex compact and a is a real number. The goal of the group of pursuers is to capture of the evader by no less than m different pursuers (the instants of capture may or may not coincide). The target sets are the origin. For such a conflict-controlled process, we derive conditions on its parameters and initial state, which are sufficient for the trajectories of the players to meet at a certain instant of time for any counteractions of the evader. The method of resolving functions is used to solve the problem, which is used in differential games of pursuit by a group of pursuers of one evader.

Controllability of Semilinear Systems with Multiple Variable Delays in Control

In the paper semilinear, finite-dimensional, control systems with multiple time variable point delays in admissible controls are considered. Using Rothe’s fixed-point theorem, sufficient controllability conditions are formulated. The results of the paper are generalization to many time variable delays in control, of the results published recently.

Capture of two coordinated evaders in a problem with fractional derivatives, phase restrictions and a simple matrix

In the finite-dimensional Euclidean space, a task of pursuing two evaders by a group of pursuers is considered, described by a system of the form D(α)zij=azij+ui−v, where D(α)f is the Caputo fractional derivative of order α∈(0,1) of the function f, and a is a real number. It is assumed that all evaders use the same control and that the evaders do not leave a convex cone with vertex at the origin. The aim of the group of pursuers is to capture two evaders. The pursuers use program counterstrategies based on information about the initial positions and the control history of the evaders. The set of admissible controls is a unit ball centered at zero, the target sets are the origins. In terms of initial positions and game parameters, sufficient conditions for the capture are obtained. Using the method of resolving functions as a basic research tool, we derive sufficient conditions for the solvability of the approach problem in some guaranteed time

OPTIMAL CONTROL FOR A CONTROLLED ILL-POSED WAVE EQUATION WITHOUT REQUIRING THE SLATER HYPOTHESIS

In this paper, we investigate the problem of optimal control for an ill-posed wave equation without using the extra hypothesis of Slater i.e. the set of admissible controls has a non-empty interior. Firstly, by a controllability approach, we make the ill-posed wave equation a well-posed equation with some incomplete data initial condition. The missing data requires us to use the no-regret control notion introduced by Lions to control distributed systems with ncomplete data. After approximating the no-regret control by a low-regret control sequence, we characterize the optimal control by a singular optimality system.

METHODS FOR PROBLEMS OF VECTOR GENERALIZED OPTIMAL CONTROL OF SYSTEMS WITH DISTRIBUTED PARAMETERS

The paper develops the theory of existence and necessary optimality conditions for optimal control problems with a vector quality criterion for systems with distributed parameters and generalized impacts. The concept of $(K, e, \epsilon)$-approximate efficiency is investigated. Necessary conditions for $(K, e, \epsilon)$-approximate efficiency of admissible controls in the form of variational inclusions are proved. Methods for solving problems of vector optimization of linear distributed systems with generalized control are proposed. Convergence of algorithms with errors is proved.

Optimal Control of the Separation Process with Flow Restrictions

Here we formulate the problem of optimal process control with distributed parameters, taking into account the constraints on the control and associated flows. The necessary optimality conditions are obtained. The analysis of the stationarity conditions is carried out and the method for constructing the domain of admissible controls is proposed. The developed optimization method is applied in the automation of industrial distillation plants for the sulfuric acid alkylation of isobutane with butylenes, ortho-xylene production, etc.