{"title":"Conservativeness of Probabilistic Constrained Optimal Control Method for Unknown Probability Distribution","authors":"Tomoaki Hashimoto","volume":105,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":534,"pagesEnd":539,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10002375","abstract":"In recent decades, probabilistic constrained optimal\r\ncontrol problems have attracted much attention in many research\r\nfields. Although probabilistic constraints are generally intractable\r\nin an optimization problem, several tractable methods haven been\r\nproposed to handle probabilistic constraints. In most methods,\r\nprobabilistic constraints are reduced to deterministic constraints\r\nthat are tractable in an optimization problem. However, there is a\r\ngap between the transformed deterministic constraints in case of\r\nknown and unknown probability distribution. This paper examines\r\nthe conservativeness of probabilistic constrained optimization method\r\nfor unknown probability distribution. The objective of this paper is\r\nto provide a quantitative assessment of the conservatism for tractable\r\nconstraints in probabilistic constrained optimization with unknown\r\nprobability distribution.","references":"[1] D. Q. Mayne, J. B. Rawlings, C. V. Rao and P. O. M. Scokaert,\r\nConstrained Model Predictive Control: Stability and Optimality,\r\nAutomatica, Vol. 36, 2000, pp.789-814.\r\n[2] T. Hashimoto, Y. Yoshioka, T. Ohtsuka, Receding Horizon Control with\r\nNumerical Solution for Thermal Fluid Systems, Proceedings of SICE\r\nAnnual Conference, 2012, pp.1298-1303.\r\n[3] T. Hashimoto, Y. Yoshioka, T. Ohtsuka, Receding Horizon Control with\r\nNumerical Solution for Spatiotemporal Dynamic Systems, Proceedings\r\nof IEEE Conference on Decision and Control, 2013, pp.2920-2925.\r\n[4] T. Hashimoto, Y. Yoshioka and T. 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