Indefinite stochastic optimal LQR control with cross term under IQ constraints. (Q1880480)

The indefinite stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices to be indefinite. The dynamic system under consideration is an Ito stochastic differential equation which is linear in both the state and the control variable and the diffusion part depends on the control variable. Sufficient conditions for the problem to be well-posed are given. It is shown that the solvability for the corresponding stochastic Riccati equation is the very condition under which the LQR problem becomes a convex optimization problem. When the above-mentioned conditions are satisfied, through the dual theory, the optimal control can be obtained explicitly.