4 - State Estimation

Abstract

This chapter deals with the explanation of state estimation. The state of a system is the minimal set of information required to completely summarize the status of the system at an initial time. Because the state is a complete summary of the status of the system, it is immaterial how the system managed to get to its state at initial time. The goal of the control system designer is to specify the inputs to a dynamic system to force the system to perform some useful purpose. This task can be interpreted as forcing the system from its state at initial time to a desired state at a future time. For dynamic systems described by a finite number of ordinary differential equations, the state of the dynamic system can be represented as a vector x(t) in continuous-time. For dynamic systems described by a finite number of ordinary difference equations, the state of the dynamic system can be represented as a vector x(k) in discrete-time. State estimation is desired for two reasons. First, when the measurement matrix H ≠ 1, then the state is not directly measured. Second, even if H = 1, it may be beneficial to filter the measurements to decrease the effects of the measurement noise. Filtering can be considered as a state estimation process. State estimation and control processes are often implemented via a computer. Two categories of state estimator design approaches are commonly discussed: Luenberger observers and Kalman filters.