2018/05/23 by Jochen Bröcker, Bröcker, Jochen
Mathematics · #49K35 #60G35 #93E99 #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Analysis #Optimization and Control (math.OC) #Primary 49J55 #Probability (math.PR) #Secondary 86A10
paper · pdf · doi:10.48550/arxiv.1805.09269
openalex publication_date 2018/05/23 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
A variant of the optimal control problem is considered which is nonstandard\nin that the performance index contains "stochastic" integrals, that is,\nintegrals against very irregular functions. The motivation for considering such\nperformance indices comes from dynamical estimation problems where observed\ntime series need to be "fitted" with trajectories of dynamical models. The\nobservations may be contaminated with white noise, which gives rise to the\nnonstandard performance indices. Problems of this kind appear in engineering,\nphysics, and the geosciences where this is referred to as data assimilation.\nPathwise existence of minimisers is obtained, along with a maximum principle as\nwell as preliminary results in dynamic programming. The results extend previous\nresults on the maximum aposteriori estimator of trajectories of diffusion\nprocesses. To obtain these results, classical concepts from optimal control\nneed to be substantially modified due to the nonstandard nature of the\nperformance index, as well the fact that typical models in the geosciences do\nnot satisfy linear growth nor monotonicity conditions.\n