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

7

Discrete-Time Nonlinear ${\mathcal{H}}_{\infty }$-Control

In this chapter, we discuss the nonlinear ${\mathcal{H}}_{\infty }$ sub-optimal control problem for discrete-time affine nonlinear systems using both state and output measurement-feedbacks. As most control schemes are implemented using a digital controller, studying the discrete-time problem leads to a better understanding of how the control strategy can be implemented on the digital computer, and what potential problems can arise. The study of the discrete-time problem is also important in its own right from a system-theoretic point of view, and delineates many different distinctions from the continuous-time case.

We begin with the derivation of the solution to the full-information problem first, and then specialize it to the ...