Linear Quadratic Control Problem on a Finite-Horizon for a Class of Differential-Algebraic Equations

We study the linear-quadratic (LQ) control problem on a finite-horizon for linear differential-algebraic equations (DAEs) of arbitrary index. By means of a projection, we derive a differential Riccati equation whose solution yields the optimal control. No index reduction is performed. Numerical simulations are given to illustrate the theoretical findings.