Irregular LQG optimal control problem involving multiplicative noise?

In this paper, the stochastic irregular linear quadratic Gaussian (LQG) optimal control problem simultaneously with multiplicative noise is investigated. Notably, the problem of irregular LQG is not solvable under the standard quadratic performance indicator due to the existence of additive noise in some cases. In order to ensure the solvability of the irregular LQG control problem, the quadratic term of the mathematical expectation of the state terminal is included in the performance index. The main contribution of this paper is to derive the solvable conditions and obtain the explicit solution of the irregular LQG problem. The key technique is to give the analytical solution of the forward and backward stochastic differential equations obtained from the maximum principle.(c) 2023 Elsevier B.V. All rights reserved.