Stochastic impulse control of non-smooth dynamics with partial observation and execution delay: application to an environmental restoration problem

摘要: Non-smooth dynamics driven by stochastic disturbance arise in a wide variety of engineering problems. Impulsive interventions are often employed to control systems; however, the modeling and analysis subject execution delay have been less explored. In addition, continuously receiving information is not always possible. this paper, with an application environmental restoration problem, continuous-time impulse problem under discrete random observations newly formulated analyzed. The non-smooth coefficient modulated Markov chain, eventually attain undesirable state like depletion due non-smoothness. goal find most cost-efficient policy that can prevent from attaining state. We demonstrate finding optimal reduces solving non-standard system degenerate elliptic equations, optimality equation, which rigorously analytically verified simplified case. associated Fokker-Planck equation for controlled derived solved explicitly as well. model finally applied numerical computation recent river problem. equations successfully computed, probability density functions numerically obtained. impacts discussed deeper analyze model.