Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations

8

Nonlinear ${\mathcal{H}}_{\infty }$-Filtering

In this chapter, we discuss the nonlinear ${\mathcal{H}}_{\infty }$ 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 ${\mathcal{H}}_{\infty }$-norm requirement. The states information may be required for feedback or other purposes, and the estimator is basically an observer [35] that uses the 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 the ${\mathcal{H}}_{\infty }$ nonlinear filter is that of the Kalman-filter [35, 48, 119], but differs from it in the fact that (i) the plant is nonlinear; (ii) basic assumptions on the nature of the ...