scholarly journals An evasion differential game problem on the plane

2019 ◽  
Vol 11 (2) ◽  
pp. 229
Author(s):  
A.J. Badakaya ◽  
M.A. Umar
Keyword(s):  
Differential Game ◽  
Game Problem

scholarly journals On pursuit-evasion differential game problem in a Hilbert space

2020 ◽  
Vol 5 (6) ◽  
pp. 7467-7479
Author(s):  
Jamilu Adamu ◽  
◽  
Kanikar Muangchoo ◽  
Abbas Ja’afaru Badakaya ◽  
Jewaidu Rilwan ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Game Problem ◽  
Pursuit Evasion

Solving the Problem of UAV Air Combat Game Based on Differential Variational Inequality and D-Gap Function

2014 ◽  
Vol 1042 ◽  
pp. 172-177
Author(s):  
Guang Yan Xu ◽  
Ping Li ◽  
Biao Zhou
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Differential Game ◽  
Numerical Solutions ◽  
Game Problem ◽  
Gap Function ◽  
Differential Variational Inequality ◽  
Air Combat

The strategy of unmanned aerial vehicle air combat can be described as a differential game problem. The analytical solutions for the general differential game problem are usually difficult to obtain. In most cases, we can only get its numerical solutions. In this paper, a Nash differential game problem is converted to the corresponding differential variational inequality problem, and then converted into optimal control problem via D-gap function. The nonlinear continuous optimal control problem is obtained, which is easy to get numerical solutions. Compared with other conversion methods, the specific solving process of this method is more simple, so it has certain validity and feasibility.

scholarly journals Stochastic Recursive Zero-Sum Differential Game and Mixed Zero-Sum Differential Game Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Lifeng Wei ◽  
Zhen Wu
Keyword(s):  
Saddle Point ◽  
Differential Game ◽  
Stopping Time ◽  
Optimal Solution ◽  
Game Problem ◽  
Existence Results ◽  
Double Barrier ◽  
Zero Sum ◽  
Reflected Bsdes ◽  
Theoretical Results

Under the notable Issacs's condition on the Hamiltonian, the existence results of a saddle point are obtained for the stochastic recursive zero-sum differential game and mixed differential game problem, that is, the agents can also decide the optimal stopping time. The main tools are backward stochastic differential equations (BSDEs) and double-barrier reflected BSDEs. As the motivation and application background, when loan interest rate is higher than the deposit one, the American game option pricing problem can be formulated to stochastic recursive mixed zero-sum differential game problem. One example with explicit optimal solution of the saddle point is also given to illustrate the theoretical results.

scholarly journals One Game Problem for Oscillatory Systems

2021 ◽  
pp. 5-15
Author(s):  
Greta Chikrii
Keyword(s):  
Differential Game ◽  
Direct Method ◽  
Game Problem ◽  
Oscillatory Systems ◽  
Terminal Set ◽  
Damped Oscillations ◽  
Pontryagin’S Condition ◽  
Linear Differential ◽  
Second Order Systems ◽  
Time Stretching

The paper concerns the linear differential game of approaching a cylindrical terminal set. We study the case when classic Pontryagin’s condition does not hold. Instead, the modified considerably weaker condition, dealing with the function of time stretching, is used. The latter allows expanding the range of problems susceptible to analytical solution by the way of passing to the game with delayed information. Investigation is carried out in the frames of Pontryagin’s First Direct method that provides hitting the terminal set by a trajectory of the conflict-controlled process at finite instant of time. In so doing, the pursuer’s control, realizing the game goal, is constructed on the basis of the Filippov-Castaing theorem on measurable choice. The outlined scheme is applied to solving the problem of pursuit for two different second-order systems, describing damped oscillations. For this game, we constructed the function of time stretching and deduced conditions on the game parameters, ensuring termination of the game at a finite instant of time, starting from arbitrary initial states and under all admissible controls of the evader. Keywords: differential game, time-variable information delay, Pontryagin’s condition, Aumann’s integral, principle of time stretching, Minkowski’ difference, damped oscillations.

scholarly journals A Purusit Differential Game Problem on a Closed Convex Subset of a Hilbert Space

2020 ◽  
pp. 115-119
Author(s):  
Abbas Ja'afaru Badakaya ◽  
Bilyaminu Muhammad
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Finite Number ◽  
Differential Game ◽  
Convex Subset ◽  
Game Problem ◽  
Nonempty Closed Convex Subset ◽  
First Order ◽  
Control Functions ◽  
And Control

We study a pursuit differential game problem with finite number of pursuers and one evader on a nonempty closed convex subset of the Hilbert space l2. Players move according to certain first order ordinary differential equations and control functions of the pursuers and evader are subject to integral constraints. Pursuers win the game if the geometric positions of a pursuer and the evader coincide. We formulated and prove theorems that are concern with conditions that ensure win for the pursuers. Consequently, wining strategies of the pursuers are constructed. Furthermore, illustrative example is given to demonstrate the result.

scholarly journals Partial Information Stochastic Differential Games for Backward Stochastic Systems Driven by Lévy Processes

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Fu Zhang ◽  
QingXin Meng ◽  
MaoNing Tang
Keyword(s):  
Differential Game ◽  
Stochastic Systems ◽  
Partial Information ◽  
Backward Stochastic Differential Equation ◽  
Game Problem ◽  
Stochastic Differential Game ◽  
Linear Quadratic ◽  
Independent Brownian Motion ◽  
Teugels Martingales ◽  
Zero Sum

In this paper, we consider a partial information two-person zero-sum stochastic differential game problem, where the system is governed by a backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. A sufficient condition and a necessary one for the existence of the saddle point for the game are proved. As an application, a linear quadratic stochastic differential game problem is discussed.

Single-Axis Gyroscopic Motion With Uncertain Angular Velocity About Spin Axis

1977 ◽  
Vol 99 (4) ◽  
pp. 259-267 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Angular Velocity ◽  
Differential Game ◽  
Game Problem ◽  
Spin Axis ◽  
Theoretic Approach ◽  
Control Moment ◽  
Target Manifold ◽  
Game Theoretic ◽  
Gyroscopic Motion ◽  
Control Moment Gyro

A differential game approach is presented for studying the response of a gyro by treating the controlled angular velocity about the input axis as the evader, and the bounded but uncertain angular velocity about the spin axis as the pursuer. When the uncertain angular velocity about the spin axis desires to force the gyro to saturation a differential game problem with two terminal surfaces results, whereas when the evader desires to attain the equilibrium state the usual game with single terminal manifold arises. A barrier, delineating the capture zone (CZ) in which the gyro can attain saturation and the escape zone (EZ) in which the evader avoids saturation, is obtained. The CZ is further delineated into two subregions such that the states in each subregion can be forced on a definite target manifold. The application of the game theoretic approach to Control Moment Gyro is briefly discussed.

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