Optimal Control and Estimation Theory
THE optimal estimation foundations and applications of Chapters 2 through 7are rooted in probability theory. Although the optimal algorithms derived in these chapters can be implemented solely for estimation and filtering applications, they are oftentimes used in control applications as well. For example, the Kalman filter is typically used to provide optimal estimates of state variables that are implemented in a control algorithm to guide a dynamic system along a desired trajectory. A practical scenario of this concept involves using the α-β filter to provide optimal position and rate estimates from position measurements only, which are required for a proportional-derivative controller. If the rate estimates are adequate then a rate hardware sensor may not be needed, which may produce significant cost savings.