Optimal control for third degree polynomial systems and its automotive application

Presents the optimal regulator for a nonlinear system state given by a polynomial equation of degree 3 with linear control input and quadratic cost criterion. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for a polynomial system state of degree 3 over linear observations. The obtained results are applied to solution of the optimal control problem for a nonlinear automotive system. Simulation results are compared for the optimal polynomial regulator given in the paper and the linear optimal regulator.