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It is a challenge to design optimal, distributed traffic control mechanisms in a network where the link capacities and Class of Service (CoS) requirements may vary with time, such as a virtual network, an overlay network, or a wireless network. In this paper, we develop a family of optimization-based distributed traffic control laws to meet this challenge. This family of control laws enables Quality of Service (QoS), Traffic Engineering (TE), and Failure Recovery (FR) features simultaneously in a network where the link capacities and CoS requirement may vary with time. The approach taken relies on the concept of Sliding Modes to solve the resulting time-varying optimization problem. Running at the edge of a network, a set of control laws selected from this family enables class-of-service-based multi-path load balancing and/or rate adaptation to respond to network congestion, CoS requirement variation and link failures. The only nonlocal information needed as input to the control laws is the number of congested links along a forwarding path. This family of control laws is particularly viable to be implemented in a software-defined network (SDN) where the available underlying resources may not be accurately predictable and vary with time, due to, e.g., network virtualization. [ABSTRACT FROM AUTHOR]