<p>This paper investigates a mathematical frictional contact model for electro-viscoelastic materials with long-memory effects on a semi-insulating foundation. The contact behavior is described using bilateral contact conditions combined with Tresca’s friction law. The study introduces a novel variational formulation that couples two time-dependent inclusions and sweeping processes, involving the strain, velocity, and electric fields as primary variables (unknowns). The paper establishes the existence and uniqueness of solutions and explores their continuous dependence on input data. Additionally, an optimal control problem associated with the model is formulated and solved, demonstrating the existence of optimal solutions and their convergence. The methodology relies on monotonicity principles, convexity arguments, and fixed-point theory. The analysis leverages monotonicity principles, convexity arguments, and fixed-point theory, contributing to the mathematical study of complex material behavior and control strategies.</p>