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Solution of Optimal Control Problems

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Book cover Optimal Operation of Batch Membrane Processes

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

In this chapter we derive necessary conditions for optimality (NCO) that can identify candidates for a solution of an OCP. We introduce analytical methods of solving the OCPs. Next, we discuss how gradients to optimisation criterion w.r.t. optimisation variables can be gathered. These represent a key issue in solving the OCP numerically. We present a few most popular numerical methods used to solve the problem of optimal control. We also discuss closed-loop implementation, handling of disturbances and nonlinear state-feedback control.

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Notes

  1. 1.

    For further explanation see [16].

  2. 2.

    In this case, an \(\ell _1\) norm is used in the objective and the controls are restricted to not change a sign.

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Authors and Affiliations

  1. Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, Dortmund, Germany

    Radoslav Paulen

  2. Institute of Information Engineering, Automation and Mechanics, Slovak University of Technology in Bratislava, Bratislava, Slovakia

    Miroslav Fikar

Authors
  1. Radoslav Paulen
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  2. Miroslav Fikar
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Correspondence to Radoslav Paulen .

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Paulen, R., Fikar, M. (2016). Solution of Optimal Control Problems. In: Optimal Operation of Batch Membrane Processes. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-20475-8_3

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  • DOI: https://doi.org/10.1007/978-3-319-20475-8_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20474-1

  • Online ISBN: 978-3-319-20475-8

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