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

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$Mixed{\mathscr{H}}_2/{\mathscr{H}}_{\infty }$ Nonlinear Filtering

The ${\mathcal{H}}_{\mathrm{\infty }}$ nonlinear filter has been discussed in Chapter 8, and its advantages over the Kalman-filter have been mentioned. In this chapter, we discuss the mixed ${\mathcal{H}}_2$/${\mathcal{H}}_{\mathrm{\infty }}$-criterion approach for estimating the states of an affine nonlinear system in the spirit of Reference [179]. Many authors have considered mixed ${\mathcal{H}}_2$/${\mathcal{H}}_{\mathrm{\infty }}$-filtering techniques for linear systems [162, 257], [269]-[282], which enjoy the advantages of both Kalman-filtering and ${\mathcal{H}}_{\mathrm{\infty }}$-filtering. In particular, the paper [257] considers a differential game approach to the problem, which is attractive and transparent. In this chapter, we present counterpart results for nonlinear systems using a combination of the differential game approach with a dissipative ...