6533b83afe1ef96bd12a7083

RESEARCH PRODUCT

A Fokker–Planck control framework for multidimensional stochastic processes

Mario AnnunziatoAlfio Borzì

subject

Stochastic controlMathematical optimizationContinuous-time stochastic processOptimization problemoptimal control stochastic processesStochastic processApplied MathematicsOptimal controlComputational MathematicsModel predictive controlMultidimensional stochastic processOptimal control theoryLimit cycleProbability density functionFokker–Planck equationFokker–Planck equationModel predictive controlMathematics

description

AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The resulting optimality system is discretized by the Chang–Cooper scheme that guarantees positivity of the forward solution. The effectiveness of the proposed computational framework is validated with a stochastic Lotka–Volterra model and a noised limit cycle model.

yearjournalcountryeditionlanguage
2013-01-01Journal of Computational and Applied Mathematics
https://doi.org/10.1016/j.cam.2012.06.019