A Discussion on Nonlinear Quadratic Control and Sontag's Formula
Abstract
The quadratic optimal state feedback (LQR) is one of the most popular designs for linear systems and succeeds via the solution of the algebraic Riccati equation. The situation is different in the case of nonlinear systems: the Riccati equation is then replaced by the Hamilton Jacobi Bellman equation (HJB), the solution of which is generally difficult. A compromise can be the socalled Inverse Optimal Control, a form of which is Sontag's formula [1]; here the minimized cost function follows from the feedback law chosen, not vice versa. Using Sontag's formula in the variant according to Freeman and Primbs [2, 9], the actually minimized cost function is given in the following sections, including cases when it reduces to the quadratic cost. Also some remarks and thoughts are presented for discussion.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.10594
 arXiv:
 arXiv:2301.10594
 Bibcode:
 2023arXiv230110594L
 Keywords:

 Mathematics  Optimization and Control;
 Electrical Engineering and Systems Science  Systems and Control
 EPrint:
 5 pages