Resource allocation problems in communication and control systems

Resource allocation in control and communication systems constitutes the distribution of (finite) system resources in a way that achieves maximum system functionality and or cost effectivesness. Specific resource allocation problems in subband coding, Discrete Multi-tone modulation based systems and autonomous multi-agent control are addressed in this thesis. In subband coding, the number of bits used (out of a target bit budget) to code a subband signal are allocated in a way that minimizes the coding distortion. In Discrete Multi-tone modulation based systems, high bit rate streams are split into several parallel lower rate streams. These individual data streams are transmitted over different subchannels. Given a target bit rate, the goal of resource allocation is to distribute the bits among the different subchannels such that the total transmitted power is minimized. The last problem is achieving stable control of a fleet of autonomous agents by utilizing the available communication resources (such as transmitted Power and bandwidth) as effectively as possible. We present an efficient bit loading algorithm that applies to both subband coding and single-user multicarrier communication system. The goal is to effect an optimal distribution of B bits among N subchannels (subbands) to achieve a minimum transmitted power (distortion error variance) for multicarrier (subband coding) systems. All the algorithms in literature, except a few (which provides a suboptimal solution), have run times that increase with B. By contrast, we provide an algorithm that solves the aforementioned problems exactly and with a complexity (given by O(N log(N)),) which is dependent only on N. Bit loading in multiuser multicarrier systems not only involves the distribution of bit rates across the subchannels but also the assignment of these subchannels to different users. The motivation for studying suboptimal bit allocation is under-2 scored by implicit and explicit claims made in some of the papers which present suboptimal bit loading algorithms, without a formal proof, that the underlying problem is NP-hard. Consequently, for no other reason than the sake of completeness , we present a proof for NP-hardness of the multiuser multicarrier bit loading problem, thereby formally justifying the search for suboptimal solutions. There has been a growing interest in the area of cooperative control of networks of mobile autonomous agents. Applications for such a set up include organization of large sensor networks, air traffic control, achieving and maintaining formations of unmanned vehicles operating underwater, air traffic control etc. As in Abel et al, our …