Horseshoes, homoclinic connections and global chaos in current-mode controlled DC/DC converters

Chaos in a current-mode controlled boost converter is studied. First, the existence of chaos in this system is proven theoretically. The proof consists of showing that the dynamics of the system is semi-conjugate to that of a shift map, which implies positive entropy of the system and hence chaotic behavior. The essential tool is the horseshoe hypotheses theorem proposed by J. Kennedy and J.A. Yorke (see Trans. Amer. Math. Soc., vol.353, no.1, p.2513-30, 2001), which is reviewed prior to the discussion of the main finding. Then, the existence of chaos is illustrated in the light of homoclinic connection. Furthermore, global chaos resulting from homoclinic intersection of stable and unstable manifolds is illustrated numerically.