Congestion associated with freeway work zones can adversely affect mobility, safety, and sustainability. Variable speed limits (VSL) control has been widely studied to mitigate the congestion caused by lane closures at work zones. However, most VSL controllers are designed without consideration of traffic sensor faults, especially recurrent sensor faults (RSFs) that commonly exist in freeway transportation systems. Therefore, this study proposes an interacting multiple model approach with a pseudo-model set (IMMP) to achieve VSL control with fault tolerance to different types of RSFs. With the design of a traffic flow model, an adaptive model set is developed using likelihood estimation to reduce the associated computational complexity. To ensure reliable RSF diagnosis, state covariance adaption is proposed to compensate for potential discrepancies caused by improper model parameters. A pseudo-mode set is designed to provide accurate traffic state estimations for VSL control without the prerequisite of a good match between the model parameters and the extent of corresponding sensor failures. The proposed system is evaluated under a realistic work zone environment using the traffic simulator SUMO. The results demonstrate that the system can achieve reliable RSF diagnosis and consistent improvements in mobility, safety, and sustainability near a freeway work zone area despite RSFs.