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UID:submissions.pasc-conference.org_PASC24_sess153_msa270@linklings.com
SUMMARY:Hermite Kernel Surrogates for the Value Function of  High-Dimensio
 nal  Nonlinear Optimal Control Problems
DESCRIPTION:Minisymposium\n\nTobias Ehring (University of Stuttgart)\n\nNu
 merical methods for the optimal feedback control of high-dimensional dynam
 ical systems typically suffer from the curse of dimensionality. We devise 
 a mesh-free data-based approximation method for the value-function for hig
 h dimensional optimal control problems, which partially mitigates the dime
 nsionality problem. The data comes from open-loop control systems, which a
 re solved via the first-order necessary conditions of the problem, called 
 the  Pontryagin’s maximum principle. In this, the most informative initial
  states for the open-loop process are chosen using a greedy selection stra
 tegy. Furthermore, the approximation method is based on a greedy Hermite-i
 nterpolation scheme, and incorporates context-knowledge by its structure. 
 Especially, the value function surrogate is elegantly enforced to be 0 in 
 the target state, non-negative and constructed as a correction of a linear
 ized model. The algorithm is proposed in a matrix-free way, which avoids a
 ssembling a large system representing the interpolation conditions. For fi
 nite time horizons, convergence of the corresponding scheme can be proven 
 for both the value-function and the surrogate as well as for the optimal v
 s. the surrogate controlled dynamical system. Experiments support the effe
 ctiveness of the scheme, using among others a new academic toy model with 
 an explicit given value function, that may be useful for the community.\n\
 nDomain: Climate, Weather, and Earth Sciences, Engineering, Life Sciences,
  Computational Methods and Applied Mathematics\n\nSession Chair: Robert Ba
 raldi (Sandia National Laboratories)
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