Optimal boundary control of vibrations at one endpoint of a string when the second endpoint is free
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The generalized solution u(x, t) of the wave equation u tt (x, t) − u xx (x, t) = 0 admitting the existence of finite energy at every time instant t is used to find among all W 2 1 [0,T]-functions with a long time interval T the optimal boundary control for a string with a free endpoint that takes the vibration process from a given arbitrary state to a given final state.
KeywordsWave Equation Generalize Solution Boundary Control Boundary Energy Arbitrary State
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