Multi-objective optimal control for eigen-frequencies of a longitudinal bar using Pontryagin's maximum principle

Lê Hải Bùi, Thúy Minh Trần

Abstract


In this paper, the problem of multi-objective optimal control for eigen-frequencies of a longitudinal bar using Pontryagin's maximum principle (PMP) is presented. Maximizing system’s eigen frequencies and minimizing system’s weight are simultaneously solved by using Maier objective functional in order to control the final state of the objective functional. By considering eigen frequencies as state variables, the analogy coefficient k in the necessary optimality condition is explicitly determined. The Pareto front is constructed for the objectives, system’s eigen frequencies and weight, to estimate of the trade-off levels between objectives.

Keywords


Eigen frequencies; Multi-objective optimal control; Longitudinal bar; Pontryagin’s maximum principle

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