Nonlinear H ∞ -Filtering

This chapter discusses the nonlinear H∞ sub-optimal filtering problem. This problem arises when the states of the system are not available for direct measurement, and so have to be estimated in some way, which in this case is to satisfy an H∞-norm requirement. The states information may be required for feedback or other purposes, and the estimator is basically an observer that uses information on the measured output of the system and sometimes the input, to estimate the states. It would be seen that the underlying structure of H∞- nonlinear filter is that of Kalman-filter, but differs from it in the fact that the plant is nonlinear; basic assumptions on the nature of the noise signal; and the cost function to optimize. The chapter examines the continuous-time problem and the discrete-time problem. It also examines the continuous-time robust nonlinear H∞--filtering problem in the presence of structured uncertainties in the system. The linear H∞- filtering problem has been considered by many authors.