Pontryagin maximum principle for state constrained optimal sampled-data control problems on time scales

Abstract

In this paper we consider optimal sampled-data control problems on time scales with inequality state constraints. A Pontryagin maximum principle is established, extending to the state constrained case existing results in the time scale literature. The proof is based on the Ekeland variational principle and on the concept of implicit spike variations adapted to the time scale setting. The main result is then applied to continuous-time min-max optimal sampled-data control problems and a maximal velocity minimization problem for the harmonic oscillator with sampled-data control is numerically solved for illustration.

Loss control regions in optimal control problems

“…Remark 2.5. As explained in [9,10], the submersiveness hypothesis made in Theorem 2.1 can be removed.…”

“…For instance, in automatic, when the control is digital, the control value can be modified only in a discrete way in time, resulting into a piecewise constant control (also called sampled-data control ). A version of the PMP has been obtained for sampled-data controls, in which the Hamiltonian maximization condition is replaced by the so-called averaged Hamiltonian gradient condition (see [1,10,16,17,18]). In aerospace, the control is not permanent in the presence of an eclipse constraint (see [29,30]).…”

Maximum Principle for State-Constrained Optimal Control Problems of Volterra Integral Equations having Singular and Nonsingular Kernels

“…Note that Assumptions 1 and 2 are crucial for the well-posedness of the state equation in (2.1) by Lemma 2.1 (see also Appendix B) as well as the maximum principle of (P). Assumptions similar to Assumptions 1 and 2 have been used in various optimal control problems and their maximum principles; see [42,29,31,5,10,7,14,37,33,18,17,8,38,11,23] and the references therein.…”

Kelių transporto įmonių technologinės plėtros ir logistikos specialistų inžinerinių kompetencijų sąsajos tyrimas

“…Sąveikų procesai dažnai analizuojami technikos moksluose šilumos mainų charakteristikoms, lazerių veikimui pagrįsti, o transporto įmonės logistikos specialistų kompetencijų sąveikos aspektas nėra tirtas. Pontriagino sąveikos maksimumo principas taikytas nesudėtingoms techninėms sistemoms optimizuoti (Bettiol & Bourdin, 2021). Kai Pontriagino minimumo principas tenkinamas išilgai trajektorijos, jis tampa būtina optimalumo sąlyga.…”