On the Speed-in-Action Problem for the Class of Linear Non-stationary Infinite-Dimensional Discrete-Time Systems with Bounded Control and Degenerate Operator
“…We consider the system described by the equation đ 2 u đt 2 â Îu + |u|u + đu = f (x, t) and Q = đș Ă (0, T), (1) with initial u(x, 0) = u 0 (x), đu(x, 0) đt = u 1 (x), x â đș, (2) and the boundary condition…”
Section: Problem Statementmentioning
confidence: 99%
“…As is known, the speed-in-action problem is one of the first problems of mathematical theory of the optimal control. 1,2 As a generalization of a number of practical problems of designing optimal control systems, it has become one of the intensively studied problems. In the theory of optimal control for the processes described by ordinary differential equations, the speed-in-action problems are studied rather well.…”
Section: Introductionmentioning
confidence: 99%
“…As is known, the speedâinâaction problem is one of the first problems of mathematical theory of the optimal control 1,2 . As a generalization of a number of practical problems of designing optimal control systems, it has become one of the intensively studied problems.…”
In the paper the speedâinâaction problem is investigated for the secondâorder nonlinear hyperbolic equation. The main feature of the paper is that for the first time the problem is considered with a nonlocal condition in differ from many works devoted the similar problems. A theorem on the existence of the optimal control is proved. Freshet differentiability of the corresponding functional is shown. The necessary optimality conditions are derived in the form of variational inequalities.
“…We consider the system described by the equation đ 2 u đt 2 â Îu + |u|u + đu = f (x, t) and Q = đș Ă (0, T), (1) with initial u(x, 0) = u 0 (x), đu(x, 0) đt = u 1 (x), x â đș, (2) and the boundary condition…”
Section: Problem Statementmentioning
confidence: 99%
“…As is known, the speed-in-action problem is one of the first problems of mathematical theory of the optimal control. 1,2 As a generalization of a number of practical problems of designing optimal control systems, it has become one of the intensively studied problems. In the theory of optimal control for the processes described by ordinary differential equations, the speed-in-action problems are studied rather well.…”
Section: Introductionmentioning
confidence: 99%
“…As is known, the speedâinâaction problem is one of the first problems of mathematical theory of the optimal control 1,2 . As a generalization of a number of practical problems of designing optimal control systems, it has become one of the intensively studied problems.…”
In the paper the speedâinâaction problem is investigated for the secondâorder nonlinear hyperbolic equation. The main feature of the paper is that for the first time the problem is considered with a nonlocal condition in differ from many works devoted the similar problems. A theorem on the existence of the optimal control is proved. Freshet differentiability of the corresponding functional is shown. The necessary optimality conditions are derived in the form of variational inequalities.
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