Abstract
This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion coefficient. This control problem is difficult to solve with the classical method of spike variation. The authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control problem. Sufficient optimality conditions are also investigated.
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This research was supported by the National Natural Science Foundation of China under Grant Nos. 11201268 and 61105077, and the Natural Science Foundation of Shandong Province under Grant Nos. ZR2011AQ018 and ZR2012AQ013.
This paper was recommended for publication by Editor ZHANG Jifeng.
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Zhang, F. Stochastic maximum principle for mixed regular-singular control problems of forward-backward systems. J Syst Sci Complex 26, 886–901 (2013). https://doi.org/10.1007/s11424-013-0287-6
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DOI: https://doi.org/10.1007/s11424-013-0287-6