Abstract
A linear regulator problem for mechanical vibrating systems is studied in the second-order formulation. We exploit the second-order form of the differential equations involved, and solve the problem without the traditional use of a Riccati equation. In its natural representation, the optimal control problem gives rise to minimisation of a functional depending on second derivatives. The Euler–Lagrange equations and the transversality conditions developed lead to a linear fourth-order differential equation that determines the optimal control. The results are demonstrated by examples.
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