This paper presents experimental results concerning the control of a distributed solar collector field, where the main objective concerns the regulation of the outlet oil temperature by suitably manipulating the oil flow rate. This is achieved by means of a constrained nonlinear adaptive model-based predictive control framework where the control action sequence is obtained by solving an open-loop optimization problem, subject to a set of constraints. The plant dynamics is approximated by an affine state-space neural network, whose complexity is specified in terms of the cardinality of dominant singular values associated with a subspace oblique projection of data-driven Hankel matrices. The neural network is first trained offline and subsequently improved through a recursive updating of its weights and biases, based on a dual unscented Kalman filter. The control scheme is implemented on the Acurex field of the Plataforma Solar de Almería, Spain. Results from these experiments demonstrate the feasibility of the proposed framework, and highlight the ability to cope with time-varying and unmodeled dynamics, under the form of disturbances, and its inherent capability for accommodating actuation faults.