HJB equation for optimal control system with random impulses
Yu Guo, Xiao‐Bao Shu, Fei Xu, Cheng Yang
Abstract
This paper studies the optimal control problem of random impulsive differential equations. Based on the influence of random impulse generation, we define a more reasonable performance index by setting the random function and obtain the HJB equation of random impulse. Using the basic analysis method and stochastic process theory, we prove that the value function satisfies the random impulse HJB equation, and the value function is the viscosity solution of the random impulse HJB. As an application, we present an example of optimal feedback control.
Topics & Concepts
Hamilton–Jacobi–Bellman equationMathematicsImpulse controlImpulse (physics)Random functionBellman equationStochastic processApplied mathematicsStochastic controlViscosity solutionStochastic differential equationOptimal controlMathematical optimizationRandom variableStatisticsPsychotherapistPhysicsQuantum mechanicsPsychologyStability and Controllability of Differential EquationsStochastic processes and financial applicationsNonlinear Differential Equations Analysis