Combustion instability is characterized by large-amplitude pressure fluctuations in combustion chambers, and it presents a major challenge for the designer of high-performance, low-emission energy systems such as gas turbines. The instability arises due to complex interactions among acoustics, heat release and transport, and hydrodynamics, which occur over a huge span of time/length scales. In the past, various aspects of the interaction were modelled in isolation, and often on an empirical basis. Advanced mathematical techniques, matched asymptotic expansion technique and multiple-scale methods, provide a means to tackle this multi-physical phenomenon in a self-consistent and systematical manner. By using this approach, a first-principle flame-acoustic interaction theory, valid in the so-called corrugated flamelet regime, has been derived recently. The reduced system in the theory ratains the key mechanisms of combustions instability but is much more tractable computationally. In the present proposed project, the flame-acoustic interaction theory will be extended first to account for the influence of a general externally imposed perturbation. A more general asymptotic theory will be formulated in the so-called thin-reaction-zone regime. Numerical algorithms to solve the asymptotically reduced systems will be developed. The asymptotic theories and numerical methods provide, in principle, an efficient tool for predicting the onset of combustion instability. The fidelity of this approach will be assessed by accurate direct numerical simulations (DNS). It will be applied to the situations pertaining to important experiments in order to predict a number of remarkable phenomena, such as self-sustained oscillations, flame stabilization by pressure oscillations, parametric instability induced by pressure and/or enthalpy fluctuations and onset of chaotic flames. The theoretical models will be employed to develop effective active control of combustion instability by modulating fuel rate, and the effectiveness and robustness of the controllers designed will be tested by simulations using the asymptotic models as well as the fundamental equations for reacting flows.