Direct Integrability for State Feedback Optimal Control with Singular Solutions
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.
KeywordsOptimal 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.
- 4.Bryson AE, Ho YC (1969) Applied optimal control: optimization, estimation, and controlGoogle Scholar
- 10.Di Giamberardino P, Compagnucci L, De Giorgi C, Iacoviello D (2018) Modeling the effects of prevention and early diagnosis on HIV/AIDS infection diffusion. IEEE Trans Syst Man Cybern SystGoogle Scholar
- 12.Ledzewicz U, Aghaee M, Schattler H (2016) Optimal control for a sir epidemiological model with time-varying population. In: 2016 IEEE conference on control applicationsGoogle Scholar
- 13.Di Giamberardino P, Iacoviello D (2018) State feedback optimal control with singular solution for a class of nonlinear dynamics. In: Proceedings of the 15th international conference on informatics in control, automation and robotics (ICINCO 2018), vol 1Google Scholar