Hamilton-Jacobi Inequalities

In the previous chapters we have encountered at various places Hamilton-Jacobi equations, or, more generally, Hamilton-Jacobi inequalities. In this chapter we take a closer look at conditions for solvability of Hamilton-Jacobi inequalities and the structure of their solution set using invariant manifold techniques for the corresponding Hamiltonian vectorfield (Section 8.1), and apply this to the nonlinear optimal control problem in Section 8.2. An important theme will be the relation between Hamilton-Jacobi inequalities and the corresponding Riccati inequalities, in particular for dissipativity (Section 8.3) and nonlinear H_∞ control (Section 8.4).