Sufficient conditions for reachability and controllability of discrete systems with phase constraints

Optimization ◽  
1998 ◽  
Vol 43 (4) ◽  
pp. 303-321 ◽  
Author(s):  
P.H. Sach
Keyword(s):  
Sufficient Conditions ◽  
Discrete Systems ◽  
Phase Constraints

scholarly journals Linear Discrete Pursuit Game with Phase Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Asqar Raxmanov ◽  
Gafurjan Ibragimov
Keyword(s):  
Sufficient Conditions ◽  
Discrete Systems ◽  
Geometric Constraints ◽  
Time Interval ◽  
Finite Time Interval ◽  
Pursuit Game ◽  
Terminal Set ◽  
Phase Constraints ◽  
The Right ◽  
Linear Discrete Systems

We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Position of the evader satisfies phase constraints:y∈G, whereGis a subset ofRn. We considered two cases: (1) controls of the players satisfy geometric constraints, and (2) controls of the players satisfy total constraints. Terminal setMis a subset ofRnand it is assumed to have a nonempty interior. Game is said to be completed ifyk-x(k)∈Mat some stepk; thus, the evader has not the right to leave setG. To construct the control of the pursuer, at each stepi, we use the value of the control parameter of the evader at the stepi. We obtain sufficient conditions of completion of pursuit from certain initial positions of the players in finite time interval and construct a control for the pursuer in explicit form.

Stability and Stabilization for Discrete System With Probabilistic Nonlinearities

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Xia Zhao ◽  
Engang Tian
Keyword(s):  
Sufficient Conditions ◽  
Discrete Systems ◽  
System Model ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Mean Square Stability ◽  
New Type ◽  
Stability And Stabilization ◽  
The Mean ◽  
Varying Delay

This paper investigates stability and stabilization of discrete systems with probabilistic nonlinearities and time-varying delay. New characters of the nonlinearities, the probability of the nonlinearities happening between different bounds, are used to build new type of system model, which can help us make a full use of the inner variation information of the nonlinearities. With the help of the new characters, new system model is proposed. Then, sufficient conditions for the mean square stability of the system can be obtained by using the Lyapunov functional approach and linear matrix inequalities technique. An example is proposed to illustrate the efficiency of the proposed method.

PHASE CONSTRAINTS IN MATERIAL MEANS SEPARATION MODELS IN MICROECONOMICS

2021 ◽  
Vol 1 (195) ◽  
pp. 88-94
Author(s):  
A.P. Chernyaev ◽  
◽  
I.V. Sukhorukova ◽  
G.P. Fomin ◽  
A.Yu. Meerson ◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Production Capacity ◽  
Phase Constraint ◽  
Household Economy ◽  
Time Points ◽  
Material Resources ◽  
Discounted Utility ◽  
Phase Coordinates ◽  
Phase Constraints ◽  
Crisis Conditions

One of the important and urgent tasks of microeconomics is the problems of research of the economic system, in which there are restrictions associated with the planned volume of output or the size of the enterprise production capacity. These constraints are set by the requirement that the analyzed trajectories do not leave some given region of the control existence space. Most often, such restrictions for all time points are set in the form of inequalities, and certain requirements are imposed on the function of the phase coordinates of the object, their value at a given time. This problem is classified as an optimal control problem with mixed and phase constraints. In general, this area is of scientific interest and requires consideration. In this case, we study the microeconomic model of the household economy as the most stable object in the conditions of crises. The accumulated savings are subject to a natural phase constraint of non-negativity. This led to the study of the features of the microeconomic formulation of the problem of finding a method for the optimal division of material resources into consumed and accumulated parts, since the imposition of a natural phase restriction on the non-negativity of accumulated savings makes everything much more complicated. Just as in macroeconomics, consumption is optimized, but not in its pure form, but the integral discounted utility of consumption is maximized. The relation equation in this paper differs from a similar macroeconomic equation, since the household exists and survives in crisis conditions in a different way than do social organisms and large enterprises. That is why the article formulates and proves sufficient conditions for solving the problem with a phase constraint.

scholarly journals An Approach for Solving Discrete Game Problems with Total Constraints on Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Asqar Raxmonov ◽  
Gafurjan I. Ibragimov
Keyword(s):  
Explicit Form ◽  
Control Parameter ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Nonempty Interior ◽  
Pursuit Game ◽  
Terminal Set ◽  
Control Forces ◽  
Linear Discrete Systems ◽  
Discrete Game

We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Controls of the players satisfy total constraints. Terminal setMis a subset ofℝnand it is assumed to have nonempty interior. Game is said to be completed ifyk-xk∈Mat some stepk. To construct the control of the pursuer, at each stepi, we use positions of the players from step 1 to stepiand the value of the control parameter of the evader at the stepi. We give sufficient conditions of completion of pursuit and construct the control for the pursuer in explicit form. This control forces the evader to expend some amount of his resources on a period consisting of finite steps. As a result, after several such periods the evader exhausted his energy and then pursuit will be completed.

scholarly journals Ketercapaian dan Keterkontrolan Sistem Deskriptor Diskrit Linier Positif

2017 ◽  
Vol 3 (2) ◽  
pp. 65-73
Author(s):  
Yulia Retno Sari
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Algebraic Method ◽  
Discrete Systems ◽  
Descriptor System ◽  
Linear Algebraic Method

A positive discrete descriptor system has been widely used in modeling economics, engineering, chemistry and others. In this research, we studied the necessary conditions and sufficient conditions for a positive discrete descriptors system is achieved positive and controlled postively. In addition, it is also studied on sufficient terms and conditions which ensure that discrete systems are null controlled. By using linear algebraic method and Inverse Drazin, this research has proved several theorems for discrete descriptors system achieved positive, controlled positively and controlled null. In addition, examples are given as illustrations to reinforce the validity of the proven theorems.

scholarly journals Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Kexue Zhang ◽  
Xinzhi Liu
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Impulsive Systems ◽  
Uniform Asymptotic Stability ◽  
Stability And Instability ◽  
Special Cases ◽  
Two Measures

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results.

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