The problem of turbulent premixed flames is considered within the framework of the field equations describing flames as level surfaces for scalar fields and stochastic control theory for Markov diffusion processes. It is shown that all field equations can be interpreted as a dynamic programming partial differential equation of second order (Hamilton - Jacobi - Bellman PDE) and the corresponding scalar fields can be regarded as the value functions. The explicit formulae for the scalar fields as a minimum/maximum of a functional integral have been derived and the most interesting result is that the running cost function is the same as a Lagrangian function for a relativistic particle moving in an external field and the particle velocity plays the role of a control function.