The suppression of thermoacoustic combustion instabilities represents one of the main goals in the design of reliable high-performances combustion chambers. Unstable dynamics arise when a non-linear coupling is established between the acoustic field and the flame front generating high-amplitude and low-frequency pressure and heat release oscillations, associated with the excitation of the combustor's natural modes. Temperature and pressure peaks due to these phenomena are particularly harmful for the structural damage they can cause as well as for performance degradations and increase of pollutant emissions. Due to the non-linear nature of the phenomenon, relevant problems arise when it is necessary to define model-based control-systems. The aim of this study is to define a control strategy, based on the application of recent results in the field of neural control of non-linear systems. The proposed strategy is an application of an innovative neural-network-based technique, namely Neural Dynamic Optimization, which is able to exploit the potential of optimal control strategies in dealing with complex non-linear systems and the flexibility and the generalisation properties of neural networks. Reported simulations show the satisfactory performance of the proposed controller in suppressing undesired thermoacoustic combustion instabilities.