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

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 constrained case existing results in scale literature. The proof based Ekeland variational and concept of implicit spike variations adapted setting. main result then applied continuous-time min-max problems, a maximal velocity minimization problem for harmonic oscillator numerically solved illustration.