LTI Learning Control via Parameter Estimation

In the previous chapter we were interested in a qualitative assessment of the nature of a linear time-invariant (LTI) learning scheme. Because we wanted to get some idea of the best possible performance, we assumed the system dynamics were known. In this chapter we partially relax this assumption. We now consider the learning control problem when the plant has a known structure, but unknown parameters. Our approach to this problem will be based on parameter estimation techniques. Previously we found that, if the plant is known, then iteration is not necessary. However, if the plant is not known, then it seems reasonable to expect that learning would be useful in improving the system response. Below we describe a learning control scheme for this situation. We begin with a description of the scheme. Then we present our main result, followed by some comments on the implications of the result.