Direct computation of optimal control of forced linear system

It is known that the optimal control of a forced linear system may be reduced to that of tracking the system without forces. The solution of the tracking problem is available via the costate variables method. This procedure is computationally expensive for large order systems. It requires solution of matrix Riccati equation and two final value problems. An alternate approach is outlined for the direct computation of the optimal control. Instead of Riccati equation, a matrix Volterra integral must be solved. For this purpose two computational schemes are described, and an illustrative example is given. The results compare favorably with the classical solution. This alternative approach may be especially useful for the control of large space structure where large order models are required.