No‐regret and low‐regret control for a weakly coupled abstract hyperbolic system

Abstract This paper explores an optimal control problem of weakly coupled abstract hyperbolic systems with missing initial data. Hyperbolic systems, known for their wave‐like phenomena and complexity, become even more challenging with weak coupling between subsystems. The study introduces no‐regret and low‐regret control strategies to handle missing information and achieve optimal performance. By deriving the Euler–Lagrange optimality system, it characterizes these control approaches in the context of weak coupling. Additionally, the paper establishes the existence and uniqueness of a no‐regret and low‐regret control, emphasizing the influence of uncertain coupling parameters. These findings are optimal control strategies for abstract weakly coupled hyperbolic systems under uncertainty. Finally, as highlighted in our conclusion, future research could explore integrating memory effects through fractional derivatives to improve the modeling of viscoelasticity, diffusion with memory, and wave damping.