Structured Linear Quadratic Regulator Design
In this paper, we study linear quadratic regulator (LQR) design subject to linear equality constraints in the controller parameters. Necessary solvability conditions are provided, and a method for choosing the weighting matrices in the quadratic objective function minimized by the constrained LQR is presented. To this end, the problem at hand is transformed into a set of polynomial inequalities that can be solved using Bernstein polynomials. We explicitly show how the requirement of input-output decoupling can be transformed into a set of linear equations in the controller parameters. All control structures that can be transformed into a set of linear equality constraints, e.g. output feedback control, decentralized control, or combinations thereof, can be determined with our method. We demonstrate the proposed method by designing structured optimal controllers for a three-tank system.