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This paper is concerned with the cross-layer control of wireless multihop networks, in particular with joint network layer queueing control and physical layer resource allocation. For this, we bring a recently developed cost-function based queueing network control framework called μ-MaxWeight into the wireless network context. Thereby we combine the advantages of μ- MaxWeight, which provides universal stability while staying close to an inherent cost-metric, with an advanced wireless physical layer resource allocation policy for interference mitigation based on power control. To circumvent the difficult non-convex nature of the latter problem, we use a powerful successive convex approximation technique. Apart from interference mitigation, the proposed cost-based cross-layer control framework allows to easily incorporate application-dependent constraints and inherently handles the routing and scheduling issues in wireless multihop and relaying networks. Using numerical simulations, insight into the operation of the cost-based control and the convex-approximation power control is given. Moreover, the performance of this cross-layer approach is evaluated by comparing to state-of-the-art backpressure based wireless cross-layer optimization algorithms.