The variational formulation of a pseudo feedback control algorithm

Abstract

An on-line, suboptimal feedback control algorithm is proposed and demonstrated. The procedure is developed using a variational formulation of the optimal control problem. A convex index of performance is presumed. The Finite Element Method is used in conjunction with a variable mesh gridation scheme to produce accurate local approximations of the weak functional forms that result from the variational formulation. These local results provide a basis for the continual updating of the suboptimal control strategy.

The extension of the algorithm to the control of nonlinear dynamical systems is also investigated. The Euler Necessary Conditions that describe the analytical solution of the Optimal Control Problem for the nonlinear plant are linearized using two different approaches, Quasilinearization, and Linearization at a Point. The simulated response of both a linear and a nonlinear dynamical system to the input of the suboptimal control generated using the proposed algorithm is offered in plot form. The closure of the disseration includes a suggested list of recommendations for further research.