Optimal control of perturbed Hamiltonian systems in R-2 is studied. Systems are considered with a control term scaling with the size of a small perturbing noise. The dynamics are shown to converge in a certain sense to a diffusion on a graph. Using the approach developed in [M. I. Freidlin and A. D. Wentzell, Mem. Amer. Math. Soc., 109 (1994), pp. 1-82] and [M. I. Freidlin and A. D. Wentzell, Ann. Probab., 21 (1993), pp. 2215-2245] for random perturbations of Hamiltonian systems, a convergence theorem is discussed. An optimal control theorem is then developed to maximize the expected exit time from a domain. This control is asymptotically robust for small noise. Several examples are provided. [References: 15]
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机译：研究了R-2中摄动哈密顿系统的最优控制。系统被认为是控制项随小扰动噪声的大小而缩放。动力学显示在某种意义上收敛到图上的扩散。使用[M. I. Freidlin和A. D. Wentzell，Mem。阿米尔。数学。 Soc。，109（1994），第1-82页]和[M. I. Freidlin和A. D. Wentzell，Ann。 Probab。，21（1993），pp。2215-2245]针对哈密顿系统的随机扰动，讨论了一个收敛定理。然后开发最佳控制定理，以使从域的预期退出时间最大化。该控制对于小噪声渐近鲁棒。提供了几个示例。 [参考：15]
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