Optimal boundary control of a distributed heterogeneous vibrating system with given states at intermediate times. (English) Zbl 1505.93105
Summary: The problem of optimal boundary control of a distributed heterogeneous vibrating system governed by the one-dimensional wave equation with piecewise constant characteristics is considered. It is assumed that each homogeneous segment is traveled by a wave over the same time. The control is performed via displacements of both ends. The cost functional is specified on the whole time interval. A constructive approach is proposed for finding an optimal control function that transfers the vibrations from an initial state through multipoint intermediate states to a terminal state over a given time interval. The results are illustrated by an example.
MSC:
| 93C20 | Control/observation systems governed by partial differential equations |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 35L05 | Wave equation |
Keywords:
optimal control of vibrations; optimal boundary control; heterogeneous vibration process; wave equation; piecewise constant characteristics; separation of variablesReferences:
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