Optimal regulator for third degree polynomial systems

Abstract

This paper presents the optimal regulator for a nonliiear 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 regulator for third degree polynomial systems given in this paper and the best regulator existing for the linearized model.

Optimal Risk-Sensitive Filtering for System Stochastic of Second and Third Degree

“…The system formed by the equations (20) and (21), is simulated using Simulink in MatLab7. The performance of the designed equations is compared versus the equations of the polynomial filtering [1] and the equations of the extended Kalman-Bucy filtering [16], applied to the system (20), that is optimal with respect to the conventional exponential mean-square cost criterion.…”

“…The corresponding equations for the polynomial filter [1] are given by: Table 4 presents comparison between the exponential mean square cost criterion J for the two types of filtering equations; it can be saw, that the R S J  values are the smallest for all values of the intensity parameter  .…”

“…The system Equations (24), (25) and (26) is simulated using Simulink in MatLab7. The performance of the designed equations is compared versus the equations of the polynomial filter [1], with respect to the exponential mean-square exponential criterion J.…”

“…Since the linear optimal filter was obtained by Kalman and Bucy (60's), numerous works are based on it, see for example [1][2][3][4][5], of the variety of all those. The deterministic filter model introduced by Mortensen [6] provides an alternative to stochastic filtering theory.…”