The Linear Quadratic Tracking Problem

In this chapter we will study a very important problem in the field of optimal control theory. In general, control theory is concerned with using the measurements in a dynamical system to “control” the state vector x. The precise meaning of the word control will be made clear as we proceed. The word “quadratic” in the title of this chapter refers to a particular class of control problems that use a quadratic form to measure the performance of a system. The reason we choose this particular performance index is that in the stochastic case it leads to a tractable solution. For reasons that will be clear later, we begin with the deterministic problem.