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

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Singular Nonlinear ${\mathcal{H}}_{\infty }$-Control and ${\mathcal{H}}_{\infty }$-Control for Singularly-Perturbed Nonlinear Systems

In this chapter, we discuss the singular nonlinear ${\mathcal{H}}_{\infty }$-control problem. This problem arises when the full control signal is not available in the penalty variable due to some rankdeficiency of the gain matrix, and hence the problem is not well posed. The problem also arises when studying certain robustness issues in parametric or multiplicative uncertain systems.

Two approaches for solving the above problem are: (i) using the regular nonlinear ${\mathcal{H}}_{\infty }$-control techniques discussed in Chapters 5 and 6; and (ii) using high-gain feedback and/or converting the problem to the problem of “almost-disturbance-decoupling” discussed also in Chapter 5. We shall discuss ...