Exact boundary controllability of an integrodifferential equation
Copyright policy )Exact boundary controllability of an integrodifferential equation
An integro-differential equation of Volterra type, describing the deflection of a plate of viscoelastic material, having a long memory for its deformation history, is considered. A boundary value problem with inhomogeneous boundary conditions of class \(L^ 2\) on a part of the boundary is investigated. It is shown that the problem has a unique weak solution whose representation is derived. Using that representation, it is proved, by harmonic analysis arguments, that the boundary control problem is exactly controllable for any fixed time of control \(T>0\).
Controllability, boundary control, Integro-partial differential equations, integro-differential equation of Volterra type, Attainable sets, reachability, Volterra integral equations, boundary value problem, Optimization problems in solid mechanics, Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems), weak solution, Existence theories in calculus of variations and optimal control
Controllability, boundary control, Integro-partial differential equations, integro-differential equation of Volterra type, Attainable sets, reachability, Volterra integral equations, boundary value problem, Optimization problems in solid mechanics, Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems), weak solution, Existence theories in calculus of variations and optimal control
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