Conditions for optimal control of random convex mappings in an infinite time interval

Cybernetics ◽  
1986 ◽  
Vol 21 (5) ◽  
pp. 670-677
Author(s):  
N. N. Bordunov
Keyword(s):  
Optimal Control ◽  
Time Interval ◽  
Infinite Time ◽  
Convex Mappings ◽  
Infinite Time Interval ◽  
Random Convex

scholarly journals Problems of Optimal Control for a Class of Linear and Nonlinear Systems of the Economic Model of a Cluster

2020 ◽  
Vol 07 (02) ◽  
pp. 109-127
Author(s):  
Zainelkhriet Murzabekov ◽  
Marek Milosz ◽  
Kamshat Tussupova ◽  
Gulbanu Mirzakhmedova
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Control Object ◽  
Quadratic Functional ◽  
Time Interval ◽  
Infinite Time ◽  
Optimal Stabilization ◽  
Infinite Time Interval ◽  
The Mathematical Model ◽  
Linear And Nonlinear Systems

For the mathematical model of a three-sector economic cluster, the problem of optimal control with fixed ends of trajectories is considered. An algorithm for solving the optimal control problem for a system with a quadratic functional is proposed. Control is defined on the basis of the principle of feedback. The problem is solved using the Lagrange multipliers of a special form, which makes it possible to find a synthesizing control. The problem of optimal stabilization for a class of nonlinear systems with coefficients that depend on the state of the control object is considered. The results obtained for nonlinear systems are used in the construction of control parameters for a three-sector economic cluster on an infinite time interval.

On the Interrelation of Two Linear NonStationary Problems with Multiple Evaders

2015 ◽  
Vol 17 (04) ◽  
pp. 1550013 ◽  
Author(s):  
N. N. Petrov ◽  
K. A. Shchelchkov
Keyword(s):  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Infinite Time ◽  
Pursuit Problem ◽  
Infinite Time Interval ◽  
Admissible Controls

A linear nonstationary pursuit problem in which a group of pursuers and a group of evaders are involved is considered under the condition that the group of pursuers includes participants whose admissible controls set coincides with that of the evaders and participants whose admissible controls sets belong to interior of admissible controls set of the evaders. The aim of the group of pursuers is to capture all the evaders. The aim of the group of evaders is to prevent the capture, that is, to allow at least one of the evaders to avoid the rendezvous. It is shown that, if in the game in which all the participants have equal capabilities at least one of the evaders avoids the rendezvous on an infinite time interval, then as a result of the addition of any number of pursuers with less capabilities, at least one of the evaders will avoid the rendezvous on any finite time interval.

On the Placement of Active Bars and Optimal Feedback Gain in Random Adaptive Structures for Vibration Suppression

2005 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
D. Younesian ◽  
E. Esmailzadeh
Keyword(s):  
Optimization Technique ◽  
Optimal Placement ◽  
Feedback Gain ◽  
Time Interval ◽  
Infinite Time ◽  
Random Load ◽  
Adaptive Structures ◽  
Optimal Velocity ◽  
Optimal Feedback ◽  
Infinite Time Interval

This paper addresses active vibration control of adaptive structures using piezoelectric active structural elements with built-in sensing and actuation function. Optimal placement and feedback gain of these active members are important issues, which are discussed in this study. An efficient optimal placement strategy has been developed using minimum control energy dissipating over infinite time interval. Optimal location of active members has been found through minimization of total control energy dissipating over infinite time interval using Simulated Annealing (SA) algorithm. Moreover, the effect of structural randomness and random load in optimal feedback gain has been investigated. To accomplish this, a mathematical model with reliability constraints on the stress and displacement is developed and the optimal velocity feedback gain of active members, using probabilistic optimization technique, is obtained. Illustrative examples are presented to demonstrate the effectiveness of this methodology. It is shown that deterministic approach can not provide reliable optimum design values.

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