Cloud computing is a new wave in computing that allows users to utilise dynamic, virtualised and scalable computing resources provided as services over a network such as the Internet. The key benefit of cloud computing is elasticity - the ability for users to add or remove resources on-demand through a self-serve interface. Users are only required to pay for the time the resources are in use. Elasticity coupled with the pay-as-you-go model has led to cloud computing becoming very popular in industry for hosting publicly-accessed applications and services. Elasticity enables users to avoid over-provisioning resources to handle potential peaks in demand, which may cause idle computing resources in periods of low- demand, and consequently increase the cost of infrastructure. On the other hand, cloud computing prevents users from under-provisioning that can lead to poor performance of services during periods of heavy workload. Therefore, computing resources are utilised more efficiently by meeting performance requirements as well as saving on expenses. Nevertheless, in order to achieve elasticity in cloud, we need to constantly monitor the performance of services and resource utilisation, and take appropriate re- source management actions to ensure that sufficient computing resources are employed so that the Service Level Agreements (SLA) for the services are met. Monitoring and reconfiguring a system requires detailed knowledge about the system behaviour, incoming workload, and also the type of actions that can maintain the performance of applications against the changes of workload. Therefore, many research efforts have been made in order to automated this process and minimise the role of human administration to reduce the management cost and also increase the efficiency of resource management systems. However, a study of the literature shows that most of these depend on accurately modelling service and system behaviours using historical data to achieve the best results. This thesis concentrates on model-free dynamic resource allocation in cloud. Model-free approach refers to resource management systems that are not required to have prior knowledge about a system. This is an advantage for a distributed and highly complex system where it is nearly impossible, as well as expensive and time consuming, to design accurate models that describe its behaviour under different workloads. Towards this objective, this thesis presents the design and implementation of a distributed and learning-based elastic controller in cloud to overcome this limitation. We have compared our controller with other similar resource provisioning through experiments that have been performed on Amazon EC2.