A non-linear optimal control system is developed for attenuating thermos-acoustic pressure oscillations in a combustion chamber where the unsteady flow field associated with the internal instability is modelled in terms of a finite set of assumed modes of the non-linear in-homogeneously driven pressure wave field. A distributed set of auxiliary fuel injectors are used to control the thermo-acoustic pressure field with pressure measurements at independent locations. The mathematical model of the thermo-acoustic pressure field with multiple fuel injectors is developed. The flame dynamics is also modelled and its states are included in the design of the controller. Extensive simulations are performed to reveal the features of the thermo-acoustic pressure field within the combustion chamber and qualitatively compared with published data. The controller is synthesized on the basis of a non-linear quadratic Gaussian approach as well as a non-linear H controller approach. The performances of the two controllers are compared. The influence of the flame dynamics is assessed by comparing the closed-loop performance by including the lag effects of a simplified flame transfer function. In particular it is shown that the non-linear H controller approach is well-suited for the control of the combustion chamber pressure field as it has the structure of comb or multiple-notch filter and can attenuate acoustic tones associated with the combustion instabilities.