This paper studies a linear regulatory quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We establish the existence of a unique viscosity and a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and, hence, derive an optimal control from the optimality conditions in the HJB equation.
Stochastic differential equation, Hamilton-Jacobi-Bellman equation, Linear-Quadratic problem, Viscosity solutions, Applications to control theory
BATEN, MD. AZIZUL (2006) "Existence of Linear-Quadratic Regulator for Degenerate Diffusions," Turkish Journal of Mathematics: Vol. 30: No. 3, Article 7. Available at: https://journals.tubitak.gov.tr/math/vol30/iss3/7