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.

Mixed Control Problem for the Linearized Quasi-Stationary Phase Field System of Equations

2016 ◽  
Vol 845 ◽  
pp. 170-173 ◽  
Author(s):  
Marina Plekhanova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Phase Field ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Operator Differential Equation ◽  
Field Equations ◽  
Mixed Control ◽  
Phase Field Equations

Conditions are obtained for unique solution existence of a mixed control problem without taking in account control expenses for a system that described by an initial-boundary value problem for the linearized quasi-stationary system of phase field equations. The problem is reduced to an optimal control problem for operator differential equation of first order in abstract space with degenerate operator at derivative using start and distributed controls simultaneously. The theorem on the unique solvability of this problem is applied to studying of optimal control problem for the phase field equations system.

scholarly journals Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Kin Wei Ng ◽  
Ahmad Rohanin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conjugate Gradient ◽  
Optimization Problem ◽  
Numerical Solutions ◽  
Gradient Methods ◽  
Parabolic Partial Differential Equation ◽  
Conjugate Gradient Methods ◽  
Monodomain Model

We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY) method and the Liu-Storey-Conjugate-Descent (LS-CD) method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.

Optimal control of a phase field model for solidification

1992 ◽  
Vol 13 (1-2) ◽  
pp. 11-27 ◽  
Author(s):  
Karl-Heinz Hoffman ◽  
Lishang Jiang
Keyword(s):  
Optimal Control ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model
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