Necessary Conditions for Optimal Strategies in a Class of Noncooperative N-Person Differential Games

1969 ◽  
Vol 7 (4) ◽  
pp. 637-644 ◽  
Author(s):  
I. G. Sarma ◽  
R. K. Ragade ◽  
U. R. Prasad
Keyword(s):  
Differential Games ◽  
Necessary Conditions ◽  
Optimal Strategies

Parameter Optimization for Linear Quadratic Differential Games

1977 ◽  
Vol 99 (1) ◽  
pp. 58-62
Author(s):  
C. T. Leondes ◽  
T. K. Siu
Keyword(s):  
Differential Games ◽  
Parameter Optimization ◽  
Quadratic Differential ◽  
Necessary Conditions ◽  
Optimal Parameter ◽  
Small Region ◽  
Optimal Parameters ◽  
Numerical Techniques ◽  
Linear Quadratic ◽  
Linear Quadratic Differential Games

How should the minimizing player choose the values of certain parameters, if he wants to further optimize his payoff at the maximizing player’s expense? Hence what would be the greatest lower bound for the maximizing player’s payoff? To answer these questions, necessary conditions for parameter optimization for linear quadratic differential games will be derived. Iterative numerical techniques for determining optimal parameters will be developed. Search techniques which will locate a “small” region of uncertainty in which the optimal parameter must lie will also be discussed.

scholarly journals THE MAIN HAMILTON FUNCTION AND THE NECESSARY CONDITIONS FOR THE EXISTENCE OF A SITUATION IN THE FORM OF THE HAMILTON-JACOBI EQUATIONS

2021 ◽  
Vol 73 (1) ◽  
pp. 32-41
Author(s):  
Sh.D. Makhmudova ◽  
◽  
A.N. Urazgalieva ◽  
Keyword(s):  
Learning Outcomes ◽  
Differential Games ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Analytical Mechanics ◽  
Equilibrium Conditions ◽  
Holistic Understanding ◽  
Theory Of Optimal Control ◽  
Necessary And Sufficient ◽  
Jacobi Equations

Interdisciplinary application of learning outcomes is essential to the field of mathematics, attainable at intersection of math with other subjects – which includes applied tasks When studying a number of technical disciplines, as well as solving applied problems, it is possible to use certain aspects of the theory of optimal control - which is an example of interdisciplinary link. Analytical mechanics, among other disciplines, enables leverage of certain aspects of the theory of differential games, namely, equilibrium conditions in non-coalitional differential games of several players. This article provides studies of the necessary and sufficient conditions for the existence of equilibrium situations, using some concepts of analytical mechanics. In line with Hamilton’s definition, necessary conditions were obtained in the form of Hamilton-Jacobi equations. This form of necessary conditions in differential games of N persons is of interest to students of natural and technical fields. The main goal of the article is to demonstrate interdisciplinary link, an important component of the process of training future engineers for various sectors of the economy. It is necessary for the holistic understanding of the material, so that students of technical specialties of various fields can use it. Proposed work can aid in study of this area of analytical mechanics by university students and young scientists alike.

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