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

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Mixed $\mathscr{H}$₂/$\mathscr{H}$_∞Nonlinear Control

In this chapter, we discuss the mixed $\mathscr{H}$₂/$\mathscr{H}$_∞-control problem for nonlinear systems. This problem arises when a higher-degree of performance for the system is desired, and two criteria are minimized to derive the controller that enjoys both the properties of an $\mathscr{H}$₂ (or LQG [174]) and $\mathscr{H}$_∞-controller. A stronger motivation for this problem though is that, because the solution to the $\mathscr{H}$_∞-control problem is nonunique (if it is not optimal, it can hardly be unique) and only the suboptimal problem could be solved easily, then is it possible to formulate another problem that could be solved optimally and obtain a unique solution?

The problem for linear systems was first considered by Bernstein and Haddad [67], where a solution ...