A LINEAR-QUADRATIC OPTIMAL-CONTROL PROBLEM WITH DISTURBANCES - AN ALGEBRAIC RICCATI EQUATION AND DIFFERENTIAL-GAMES APPROACH

A linear quadratic optimal control problem with coexisting initial and persistent disturbances is studied. Upper and lower values and relevant algebraic Riccati equations (ARE for short) are introduced. Various relations among these values are presented. The solvability of the resulting AREs is shown to be closely related to the solvability of the original optimal control problem. A formula is obtained for the solution of one of the AREs, which is of nonstandard form. Several unexpected features of the original problem are revealed from the standpoint of differential games. Some known results on the so-called H(infinity) optimal control problem are recovered.