The problem of controlling the chaotic dynamics of an inverted pendulum is addressed. Starting from the optimal excitation obtained in previous works, which gives satisfactory results but only on one side of the phase space, two different implementations have been developed in order to improve the controlled feature of the system.

The implementations consist in a shrewd alternation of one-side optimal and of harmonic excitation, and in an alternation of right and left optimal excitations. They are aimed at reducing the scattered nature of the response, which has been synthetized by the number of jumps between the two potential wells.

Some numerical simulations have been performed, showing the effectiveness of the proposed procedure. Furthermore, the comparison between the two cases has been discussed on both a local and a global basis.

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