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

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Introduction

During the years 1834 to 1845, Hamilton found a system of ordinary differential equations which is now called the Hamiltonian canonical system, equivalent to the Euler-Lagrange equation (1744). He also derived the Hamilton-Jacobi equation (HJE), which was improved/modified by Jacobi in 1838 [114, 130]. Later, in 1952, Bellman developed the discrete-time equivalent of the HJE which is called the dynamic programming principle [64], and the name Hamilton-Jacobi-Bellman equation (HJBE) was coined (see [287] for a historical perspective). For a century now, the works of these three great mathematicians have remained the cornerstone of analytical mechanics and modern optimal control theory.

In mechanics, Hamilton-Jacobi-theory (HJT) ...