One key feature of software-defined networking (SDN) is a centralized control plane. However, having a central controller has some disadvantages, e.g., scalability and reliability, especially for multihop wireless networks (MWNs). Different models with multiple controllers have been proposed, each controller managing a smaller domain and collaborating with others. In an SDN architecture, solving the controller placement problem (CPP) in a multi-controller environment plays an important role on network performance in terms of delay, reliability, control overhead, etc. In this thesis, control overhead, referred to as the network cost, consists of controller-device communications to discover the network topology, exchange configurations and set up flow tables as well as inter-controller communications, if needed, to synchronize different network views and achieve the global view of the network. In software-defined multihop wireless networking (SDMWN), because of the capacity limitation and the effect of interference on wireless links, and an in-band architecture in some types of networks to exchange both data and control traffic, it is important to solve the CPP while minimizing the control overhead to reduce energy consumption, have lower packet losses and improve reliability. Therefore, the objective of the thesis is to solve the CPP in SDMWN while minimizing the number of required control packets to be exchanged in the control plane. The novelty of this work is proposing two different nonlinear optimization models while considering the characteristics of SDMWN and the capacity of wireless links to solve the CPP and select routes among network devices and controllers in the network. The results demonstrate the impact of different factors such as the number of controllers, the capacity of wireless links and the arrival rate of new flows in devices on control overhead, the average number of controller-device hops and the average number of inter-controller hops in SDMWN.