scholarly journals Disturbance attenuation problem using a differential game approach for feedback linear quadratic descriptor systems

2015 ◽  
Vol 25 (4) ◽  
pp. 445-462 ◽  
Author(s):  
Muhammad Wakhid Musthofa
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Information Structure ◽  
Disturbance Attenuation ◽  
Descriptor Systems ◽  
Linear Quadratic ◽  
Feedback Information ◽  
Zero Sum

Abstract This paper studies the H∞ disturbance attenuation problem for index one descriptor systems using the theory of differential games. To solve this disturbance attenuation problem the problem is converted into a reduced ordinary zero-sum game. Within a linear quadratic setting the problem is solved for feedback information structure.

State-Feedback Zero-Sum Dynamic Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Discrete Time ◽  
Information Structure ◽  
Dynamic Games ◽  
State Feedback ◽  
Linear Quadratic ◽  
Feedback Information ◽  
Time Dynamic ◽  
Finite State ◽  
Solution Methods ◽  
Zero Sum

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum discrete time dynamic game in a state-feedback policy. It begins by considering solution methods for two-player zero sum dynamic games in discrete time, assuming a finite horizon stage-additive cost that Player 1 wants to minimize and Player 2 wants to maximize, and taking into account a state feedback information structure. The discussion then turns to discrete time dynamic programming, the use of MATLAB to solve zero-sum games with finite state spaces and finite action spaces, and discrete time linear quadratic dynamic games. The chapter concludes with a practice exercise that requires computing the cost-to-go for each state of the tic-tac-toe game, and the corresponding solution.

scholarly journals An Analytic and Numerical Investigation of a Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 66
Author(s):  
Aviv Gibali ◽  
Oleg Kelis
Keyword(s):  
Differential Game ◽  
Equation Approach ◽  
Linear Quadratic ◽  
Control Cost ◽  
Dual Representation ◽  
Cost Functional ◽  
Variational Derivatives ◽  
Zero Sum ◽  
The Cost ◽  
Derivatives Of

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

scholarly journals Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 132
Author(s):  
Valery Y. Glizer
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Cheap Control ◽  
Optimal Values ◽  
Definition Of ◽  
Zero Sum ◽  
Equilibrium Sequence

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

DETERMINISTIC DIFFERENTIAL GAMES UNDER PROBABILITY KNOWLEDGE OF INITIAL CONDITION

2008 ◽  
Vol 10 (01) ◽  
pp. 1-16 ◽  
Author(s):  
P. CARDALIAGUET ◽  
M. QUINCAMPOIX
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Random Distribution ◽  
Uniqueness Result ◽  
Initial Condition ◽  
Initial State ◽  
Lack Of Information ◽  
In The Beginning ◽  
Zero Sum ◽  
Future Work

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝn. This result is the first step for future work on differential games with lack of information.

One-Player Differential Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Dynamical System ◽  
Differential Games ◽  
Continuous Time ◽  
Information Structure ◽  
Dynamic Games ◽  
State Feedback ◽  
Open Loop ◽  
Linear Quadratic ◽  
Time Dynamic ◽  
Termination Time

This chapter focuses on one-player continuous time dynamic games, that is, the optimal control of a continuous time dynamical system. It begins by considering a one-player continuous time differential game in which the (only) player wants to minimize either using an open-loop policy or a state-feedback policy. It then discusses continuous time cost-to-go, with the following conclusion: regardless of the information structure considered (open loop, state feedback, or other), it is not possible to obtain a cost lower than cost-to-go. It also explores continuous time dynamic programming, linear quadratic dynamic games, and differential games with variable termination time before concluding with a practice exercise and the corresponding solution.

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.

Sign in / Sign up

Export Citation Format

Share Document