Optimization of a boundary control by a displacement at one end of a string based on minimization of the integral of the modulus of the derivative of the displacement raised to an arbitrary power \(p \geq 1\)

Optimality conditions for problems involving partial differential equations (49K20) Control, switches and devices (``smart materials) in solid mechanics (74M05) Control/observation systems governed by partial differential equations (93C20) Control of mechanical systems (70Q05) Strings (74K05)

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Optimization of a boundary control of an elastic force at one end of a string based on minimization of the integral of the modulus of the elastic force raised to an arbitrary power \(p \geq 1\) ⋮ The independence of optimal boundary controls of string oscillations from the choice of a point of compatibility of the initial and final conditions ⋮ Uniqueness theorems for generalized solutions to four mixed problems for the wave equation with nonlocal boundary conditions ⋮ An analytic form of an optimal boundary control by displacement at one end of a string under a model nonlocal boundary condition of one of four types ⋮ Optimization of a boundary control by a displacement at one end of a string with second end free during an arbitrary sufficiently large time interval ⋮ Optimization of boundary controls by displacements at two ends of a string during an arbitrary sufficiently large time interval ⋮ Optimization of a control by an elastic boundary force during an arbitrary sufficiently large time interval \(T\) at one end of a string with second end free ⋮ Optimization of boundary controls by elastic boundary forces at two ends of a string during an arbitrary sufficiently large time interval \(T\) ⋮ A heat exchange control problem

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