Direct Integrability for State Feedback Optimal Control with Singular Solutions

  • Paolo Di GiamberardinoEmail author
  • Daniela Iacoviello
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 613)


The paper studies the problem of determining the optimal control when singular arcs are present in the solution. In the general classical approach, the expressions obtained depend on the state and the costate variables at the same time, so requiring a forward-backward integration for the computation of the control. In this paper, firstly sufficient conditions on the dynamics structure are discussed, in order to have both the control and the switching function depending on the state only, computable by a simple forward integration. Then, the possibility to extend this result by means of a preliminary dynamic extension is presented. The approach has been checked and validated making use of a classical SIR epidemic model.


Optimal control Singular control Costate independent singular surface SIR epidemic model 



This work was supported by Sapienza University of Rome, Grants No. 191/2016 and No. RP11715C82440B12.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computer, Control and Management Engineering Antonio RubertiSapienza University of RomeRomeItaly
  2. 2.Institute for Systems Analysis and Computer Science Antonio RubertiRomeItaly

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