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Optimal control of stochastic hybrid system with jumps: A numerical approximation

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
259
Identifiers
DOI: 10.1016/j.cam.2013.10.021
Keywords
  • Stochastic Hybrid Systems
  • Jump Diffusions
  • Markov Processes
  • Switching Approximation
  • Optimal Control
Disciplines
  • Mathematics

Abstract

Abstract The generalized class of stochastic hybrid systems consists of models with regime changes including the occurrence of impulsive behavior. In this paper, the stochastic hybrid processes with jumps are approximated by locally consistent Markov decision processes that preserve local mean and covariance. We further apply a randomized switching policy for approximating the dynamics on the switching boundaries. To investigate the validity of the approximation, we study a stochastic optimal control problem. On the basis of the discrete approximation, we solve the optimal control problem and show that the solution obtained from the discretized problem converges to the solution of the original optimal control problem.

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