A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Abstract

Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.

Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach

“…The result would be compared to the result which is obtained by using the Gauss-Newton method [18] [19]. Hence, the calculation procedure in the IOCPE could be simplified.…”

“…For more detail, see [14] [18] [19] [33] for the proof of the derivation on this feedback optimal control law.…”

“…In addition, the optimal output solution obtained from the IOCPE algorithm has been improved by using the weighted output residual [16], which is introduced into the model cost function, and the output matching scheme [17], where the adjusted parameter is introduced into the model output. Moreover, the application of the approaches on the least-square and the Gauss-Newton with the principle of model-reality differences, which omits from using the adjusted parameters, enhance the practical usage of the IOCPE algorithm for delivering the optimal solution of the original optimal control problem [18] [19].…”

Application of Conjugate Gradient Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

“…Notice that the parameter estimation problem is defined by Equation (7) andthe computation of multipliers is given by Equation (8). Indeed, the necessary conditions, which are defined by Equations (6a) to (6d), are the optimality for the modified model-based optimal control problem.…”