Optimal Control Problem with Regular Mixed Constraints via Penalty Functions

Maria do Rosário Pinho (), Maria Margarida A. Ferreira () and Georgi Smirnov ()
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Maria do Rosário Pinho: Universidade do Porto
Maria Margarida A. Ferreira: Universidade do Porto
Georgi Smirnov: Universidade do Minho

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 2, No 19, 1564-1586

Abstract: Abstract Below we derive necessary conditions of optimality for problems with mixed constraints (see Dmitruk in Control Cybern 38(4A):923–957, 2009) using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., De Pinho et al. in Optimization 71(11):3363–3381, 2022) and, more recently, to solve optimal control problems with pure state constraints (see De Pinho et al. in Syst Control Lett 188:105816, 2024). We intentionally consider a smooth case and the simplest boundary conditions; we consider global minimum and assume that the set of trajectories of the control system is compact. Based on our penalty functions approach we develop a numerical method admitting estimates for its parameters needed to achieve a given precision.

Keywords: Optimal control; Mixed constraints; Maximum principle; Approximations (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02510-6

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