Convergence of efficient solutions for multiobjective optimal control problems and applications

This paper investigates the convergence of efficient solutions for multiobjective optimal control problems (MOCPs) with affine state equations under data perturbations. Unlike most existing studies that require convexity of the multiobjective function or strong regularity of problem data (e.g., norm convergence or G-convergence), our analysis is based solely on the pointwise convergence of the system coefficients, without assuming convexity of the objective. We begin by deriving fundamental properties of feasible solution sets and the corresponding objective maps, including compactness, continuity, and convergence of state trajectories. We then derive sufficient conditions for Hausdorff well-posedness and, building on this, prove upper and lower Painlevé–Kuratowski convergence of efficient solution sets. Additional hypotheses, such as the strong domination property or singleton level sets, allow us to relax regularity requirements on perturbed data while still ensuring convergence. A sufficient condition for these hypotheses is provided via the notion of a strictly natural convexlike integrand function. The theoretical results are applied to two practical (MOCPs): an irrigation management model capturing both soil moisture dynamics and water cost, and a production-inventory model balancing inventory deviation and production rate adjustment. These applications illustrate the broad applicability of our convergence framework to real-world control systems in agriculture and economics.