Computation of optimal control in partially controlled linear systems

In many optimal control problems the performance criterion depends in part on the behavior of a system that is not subject to control. Since the control affects only a subset of the system state variables, such systems are said to be partially controlled. This paper considers continuous-time systems with linear system equations and quadratic performance criterion. The major result of this correspondence is that the computation of the optimal control for partially controlled systems can be split into the following parts: first, the optimal control for the controlled system is computed using a Riccati equation; next, a linear equation is solved to obtain a term for the control that accounts for the behavior of the uncontrolled system. Hence, the problem of computing the optimal control for an (
n_{1} + n_{2}
)-dimensional system, where n
1
is the dimension of the controlled system and n
2
is the dimension of the uncontrolled system, is essentially reduced to computing the optimal control for the n
1
-dimensional controlled system. This results in a significant reduction in the computational requirements.