scholarly journals Feedback saddle point equilibria for soft-constrained zero-sum linear quadratic descriptor differential game

2013 ◽  
Vol 23 (4) ◽  
pp. 473-493
Author(s):  
Muhammad Wakhid Musthofa ◽  
Jacob C. Engwerda ◽  
Ari Suparwanto ◽  
Keyword(s):  
Saddle Point ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Descriptor Systems ◽  
Linear Quadratic ◽  
Linear Quadratic Differential Games ◽  
Zero Sum ◽  
Necessary And Sufficient ◽  
Saddle Point Equilibrium ◽  
Infinite Planning Horizon

Abstract In this paper the feedback saddle point equilibria of soft-constrained zero-sum linear quadratic differential games for descriptor systems that have index one will be studied for a finite and infinite planning horizon. Both necessary and sufficient conditions for the existence of a feedback saddle point equilibrium are considered

Titik Setimbang Nash pada Permainan Linear Kuadratik Non-kooperatif dengan Asumsi Keseluruhan Pemain dapat Menstabilkan Sistem

2017 ◽  
Vol 1 (2) ◽  
pp. 211-224
Author(s):  
Ezhari Asfa’ani
Keyword(s):  
Quadratic Differential ◽  
Information Structure ◽  
Nash Equilibria ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Open Loop ◽  
Linear Quadratic ◽  
Linear Quadratic Differential Games ◽  
Necessary And Sufficient ◽  
Infinite Planning Horizon

We discuss about Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable.      Keywords: linear quadratic differential games, open-loop information structure

SOLVABILITY OF LINEAR-QUADRATIC DIFFERENTIAL GAMES ASSOCIATED WITH PURSUIT-EVASION PROBLEMS

2008 ◽  
Vol 10 (04) ◽  
pp. 481-515 ◽  
Author(s):  
JOSEF SHINAR ◽  
VLADIMIR TURETSKY ◽  
VALERY Y. GLIZER ◽  
EDUARD IANOVSKY
Keyword(s):  
Quadratic Differential ◽  
Sufficient Conditions ◽  
Lebesgue Integral ◽  
Linear Quadratic ◽  
Pursuit Evasion ◽  
Linear Quadratic Differential Games ◽  
Matrix Differential ◽  
Zero Sum ◽  
Generalized Cost ◽  
Riccati Matrix

A finite horizon zero-sum linear-quadratic differential game with a generalized cost functional, involving a Lebesgue integral with a measure that has both discrete and distributed parts, is considered. Sufficient conditions for the solvability of such a game are established in terms of the eigenvalues of an integral operator in Hilbert space. The game solution is based on solving an impulsive Riccati matrix differential equation. These results are applied for two games associated with pursuit-evasion problems. Illustrative examples are presented.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

scholarly journals On an infinite dimensional linear-quadratic problem with fixed endpoints: The continuity question

2014 ◽  
Vol 24 (4) ◽  
pp. 723-733
Author(s):  
K.Maciej Przyłuski
Keyword(s):  
Minimum Energy ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Minimum Norm Solution ◽  
Quadratic Problem ◽  
Infinite Dimensional ◽  
Necessary And Sufficient ◽  
Quadratic Control Problems

Abstract In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

Mixed Policies

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Probability Distribution ◽  
Saddle Point ◽  
Security Policy ◽  
General Type ◽  
Zero Sum Games ◽  
Security Levels ◽  
Mixed Action ◽  
Zero Sum ◽  
Saddle Point Equilibrium ◽  
Action Spaces

This chapter explores the concept of mixed policies and how the notions for pure policies can be adapted to this more general type of policies. A pure policy consists of choices of particular actions (perhaps based on some observation), whereas a mixed policy involves choosing a probability distribution to select actions (perhaps as a function of observations). The idea behind mixed policies is that the players select their actions randomly according to a previously selected probability distribution. The chapter first considers the rock-paper-scissors game as an example of mixed policy before discussing mixed action spaces, mixed security policy and saddle-point equilibrium, mixed saddle-point equilibrium vs. average security levels, and general zero-sum games. It concludes with practice exercises with corresponding solutions and an additional exercise.

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