Mean-variance receding horizon control for discrete time linear stochastic systems

A control strategy based on a mean-variance objective and expected value constraints is proposed for systems with additive and multiplicative stochastic uncertainty. Subject to a mean square stabilizability condition, the receding horizon objective can be obtained by solving a system of Lyapunov equations. An algorithm is proposed for computing the unconstrained optimal control law, which is the solution of a pair of coupled algebraic Riccati equations, and conditions are given for its convergence. A receding horizon controller based on quasi-closed loop predictions is defined. The control law is shown to provide a form of stochastic convergence of the state, and to ensure that the time average of the state variance converges to known bounds.