Active control techniques play a key role in today's aircraft developments to reduce structural loads during gust encounter and thereby enable highly fuel-efficient aircraft designs. The performance of such gust load alleviation (GLA) systems, however, is often limited by physical limitations in the actuation system. In this paper, a novel GLA control approach is presented which exploits actuator redundancies to avoid performance degradations when individual actuators are driven to their limits or become faulty. To that end, a baseline controller for damping loads-dominating aeroelastic modes is extended with a dynamic control allocation system for handling constrained actuators. Thereby, virtual control inputs, generated for a targeted aeroelastic mode control, are distributed to the actual control inputs in an optimal way. To do so, a convex optimization problem is formulated which is solved in real time with the goal to minimize performance degradations due to actuator constraints. The effectivity of the presented GLA controller is experimentally validated on a highly flexible wing in a wind tunnel considering different actuator constraints and gust excitations at multiple airspeeds.