Development of Integrated Health Management systems (IHMS) and, in particular, on-board failure diagnostics and prognostics (FD&P) systems for the Solid Rocket Boosters (SRBs) is a NASA requirement for the next-generation Crew Exploration and Heavy-Lift Launch Vehicles. Typical design of an SRB is shown in Fig. 1, left. The difficulties in the development of on-board FD&P systems for SRBs are: (i) internal hydrodynamics of SRBs are highly nonlinear, (ii) a number of failure modes may lead to abrupt changes of SRB parameters, (iii) the number and types of available sensors are severely limited, and (iv) the recovery time is typically a few seconds. Such systems should accommodate the abrupt changes of the model parameters in various nonlinear dynamical off-nominal regimes. These difficulties dictate the model based approach to the FD&P of SRBs that minimizes the number of misses and false alarms by utilizing deep understanding of the physical processes underlying the nominal and off-nominal regimes of SRBs.