Nonlinear optimal trade-off control for LQG problem

For discrete-time Linear Quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index, is considered. The utility function is viewed as an overall objective of system. The nonlinear utility function is first converted into an auxiliary parameters optimization problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimization problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this paper.