Information and communication technologies (ICT) are playing an important role in the development of software platforms for Smart Cities to improve city services, sustainability, and citizen quality of life. Smart City software platforms have a significant role to transform a city into a smart city by providing support for the development and integration of intelligent services. However, these large-scale data-intensive smart city services have been facing several engineering issues related to extensibility, integrability, scalability, and context-aware configuration. In order to handle these problems, big data analytics and self adaptation are key enabling approaches to support the development of effective smart city software architectures and intelligent services. In this Ph.D. research, in collaboration with the Smart Cities and Communities Lab. of the Italian national agency ENEA, we focus on the design and development of a software platform for smart city based on self-adaptation, as realized in the IBM MAPE-K (Monitor, Analyze, Plan, and Execute over a shared Knowledge) control loop architecture model, and on machine intelligence, as provided by a big data analytics framework. This last is introduced in between the analysis and planning modules of the MAPE-K control loop model. We will evaluate the effectiveness of the proposed approach with a real showcase in the public lighting domain.