Covariance constrained LQ control and applications

Variance control is one of the main themes in the stochastic control theory. The optimal LQ control with generalized covariance constraints (LQGCC) for the continuous linear time-invariant systems is studied in this paper. This problem consists of two aspects: (1) the feasibility of the generalized covariance constrained control problem, which is to make the covariances of different controlled variables satisfy certain pre-specified covariance constraints; (2) the optimization of LQ performance over the feasible controller set. It is shown that the feasibility of the GCC problem is equivalent to the feasibility of several linear matrix inequalities (LMIs). Furthermore, if the LMIs are feasible, the controller set can be parameterized by the solutions of the LMIs. If the GCC is feasible, then the minimization of the LQ performance is equivalent to solving a semi-definite programming problem and our approach ensures the global optimality.