Practical stabilization through real-time optimal control

Infinite-horizon, nonlinear, optimal, feedback control is one of the fundamental problems in control theory. In this paper we propose a solution for this problem based on recent progress in real-time optimal control. The basic idea is to perform feedback implementations through a domain transformation technique and a Radau based pseudospectral method. Two algorithms are considered: free sampling frequency and fixed sampling frequency. For both algorithms, a theoretical analysis for the stability of the closed-loop system is provided. Numerical simulations with random initial conditions demonstrate the techniques for a flexible robot arm and a benchmark inverted pendulum problem.