QUADRATIC REGULATOR THEORY AND LINEAR-FILTERING UNDER SYSTEM CONSTRAINTS

In this paper, we present some recent results on the theory of linear quadratic regulators and linear filtering problems subject to constraints on control matrices and system structure. The approach is based on direct optimization in the space of operators, thereby allowing constraints on the operator types and norms. Furthermore the systems may be subject to general martingale inputs and not restricted to Wiener martingales as in the classical theory. It is also shown that lifting the constraints leads to the classical results. The approach is general and yet simple and instructive.