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Matlab implementation of direct and indirect shooting methods to solve an optimal control problem with state constraints

Karbowski Andrzej

Journal of Automation Mobile Robotics and Intelligent Systems

2021

Vol. 15, No. 1

43--50

The paper presents a general procedure to solve nume‐ rically optimal control problems with state constraints. It is used in the case, when the simple time discretization of the state equations and expressing the optimal cont‐ rol problem as a nonlinear mathematical programming problem is too coarse. It is based on using in turn two multiple shooting BVP approaches: direct and indirect. The paper is supplementary to the earlier author’s paper on direct and indirect shooting methods, presenting the theory underlying both approaches. The same example is considered here and brought to an end, that is two full listings of two MATLAB codes are shown.

A Shortened Time Horizon Approach for Optimization with Differential-Algebraic Constraints

Drąg Paweł

Annals of Computer Science and Information Systems

2021

Vol. 25

211--215

In this work a new numerical optimization scheme based on a shortened time horizon approach was designed. The shortened time horizon strategy has never been presented or tested numerically. The new methodology was applied for a single objective optimization task subject to a system of nonlinear differential-algebraic constraints, which can take a form of differential-algebraic equations (DAEs). Moreover, it was assumed, that an application of a cooperated multiple shooting with direct solution method, like direct shooting approach, does not enable us to solve the DAE system, even on relatively small subintervals. Therefore, the new solution procedure is based on two main parts: i) designing of an alternative differentialalgebraic constraints, ii) parametrization of a new constraints system by the multiple shooting approach and further simulation of the alternative system independently on small subintervals. Then, the simulation interval can be modified by the shortened time horizon approach. The presented algorithm was used to solve a highly nonlinear optimization task of a fed-batch reactor operation.