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.

Payoff Sensitivity of Linear Quadratic Differential Games to Parameter Change

1981 ◽  
Vol 103 (1) ◽  
pp. 36-38
Author(s):  
C. T. Leondes ◽  
T. K. Sui
Keyword(s):  
Differential Games ◽  
Quadratic Differential ◽  
Optimal Strategy ◽  
Small Variation ◽  
Matrix Equations ◽  
Parameter Change ◽  
Linear Quadratic ◽  
System Parameters ◽  
Linear Quadratic Differential Games ◽  
Zero Sum

Both maximizing and minimizing players are concerned with the change in payoff due to small variation of system parameters. A technique is developed to derive linear algebraic matrix equations which can be used to determine the payoff sensitivity of all the parameters in linear zero- sum differential games with constant feedback. Above all, this technique is applicable for determining both the optimal strategy and payoff.

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