A Control Parameterization Approach for Linear Quadratic Systems

This paper develops a control parameterization approach for determining the (near) optimal trajectories of linear time-invariant systems with quadratic performance indices. In solving the linear quadratic (LQ) problem for time-invariant systems each control variable is represented by a set of approximating functions with unknown coefficients. This converts the LQ problem into an unconstrained quadratic programming problem which can be solved for the (near) optimal control parameter values (i.e., the unknown coefficients) by solving a system of linear algebraic equations. As verified by simulation studies, the control parameterization approach is particularly efficient when applied to minimum energy problems and to problems with significantly fewer control variable than state variables.