On linear-quadratic optimal regulator for continuous-time descriptor system

An approach to dealing with the linear-quadratic optimal control problems for the continuous-time descriptor systems is proposed. A Riccati equation with a new form is established through the use of the necessary conditions for the optimal control. Unlike the existing approaches, transformation to the Riccati equation is made directly to find its solution. The sufficient conditions for the existence of the unique solution of the Riccati equation are found. The solution of the Riccati equation is then used in the construction of the optimal control strategies. It is believed that the full-order Riccati equation derived here may have some relation to the dynamic programming theory for the descriptor system