Parameter identification of nonlinear systems using indirect solution of optimal control problem

This paper describes a novel offline approach to estimate the parameters of a nonlinear system using the optimal control theory. In the conventional methods, only the output is considered in the identification process and the problem is stated as a nonlinear optimization problem. Nevertheless, the proposed method here is based on the least square error of both output and input. To do this, the problem is first stated as a tracking problem with some unknown parameters. The necessary and sufficiency conditions of optimality conditions are derived using the fundamental theorem of variational calculus. The problem is deployed as an effort optimal control problem which finally leads to a two point boundary value problem. To solve the resultant equations, a secondary optimal control problem is deployed to be solved using the homotopy algorithm. So the parameters are gradually converged to the real values. The proposed algorithm is analyzed for a one-link manipulator with the full measurements. Thereafter, the proposed method is applied on a real one-link manipulator and nonlinear model of permanent magnet dc motor. Application of the method for the identification of a few test beds at the AUT proves the validity and efficiency of the proposed approach.