Optimal control for non-polynomial systems

This paper shows that a large class of nonlinear systems can be recasted into polynomial ones via state variable embedding an idea used by Carleman many decades ago. Then, by representing the original nonlinear system as a polynomial system, one could apply powerful control techniques. In particular, in this work, an infinite-time state-feedback optimal regulator has been synthesized by solving the Hamilton-Jacobi-Bellman equation for the recasted polynomial system, achieving asymptotic stability and minimizing a cost functional.The prowess of the proposal is validated via simulations in the recasting and optimal control of two applications: a pendulum and a synchronous generator connected to an infinite bus.