In this dissertation, we focus on development of algorithms for estimating the severity of air leakage and for predicting the out-of-adjustment of pushrod in an air brake system of heavy commercial vehicles. The leakage of air from the brake system causes a reduction in the steady-state pressure in the brake chamber and an increase in the lag of the braking pressure response thereby increasing the stopping distance of the vehicle. Currently a presence of leak in the system is detected for the severities of leak that cause the reservoir pressure to drop below a threshold, such as, the leakage of compressed air due to rupture of the reservoir or of the hoses carrying the compressed air. The leakage of air is also possible due to several other reasons such as, cracks in the hoses, loose couplings between the hoses etc. The severities of leak, corresponding to such situations, do not lead to the reservoir pressure drop below the threshold; therefore, their presence remains undetected. For the detection and estimation of such severities of leak, a diagnostic scheme has been given and is based on a model developed for the mass ow rate of the leakage of air from the air brake system. Out-of-adjustment of the pushrod is the extension of pushrod beyond a prede- ned value and for safety concerns, an extension beyond this value is not desired. Currently no warning system is available for monitoring the out-of-adjustment of pushrod, except, during the safety inspection. Inspection of the pushrod for outof- adjustment is the most labor-intensive and time consuming task during a typical safety inspection procedure. For efficient and continuous monitoring of the pushrod for out-of-adjustment, a diagnostic algorithm for estimating the steady-state pushrod stroke has been developed. The scheme is expected to expedite the inspection process for the out-of-adjustment of pushrod. Experimental data from the air brake test setup at Texas A and M University has been used for corroborating both the models. Also, the problem of parameter estimation of sequential hybrid systems such as the air brake system, has been addressed. The \hybrid" nature of the air brake system stems from the system being in di erent modes corresponding to di erent values of the displacement of the pushrod and is a result of di erent spring compliances associated with the pushrod in di erent ranges of its displacement. The air brake system is \sequential" in the sense that as the pressure increases, the displacement of the pushrod increases and there is a distinct sequence of modes that the system will transition through and upon a reduction in pressure, the sequence of modes is revisited in the reverse order. The mode to mode transition of the air brake system is governed by the parameters, such as, the clearance between the brake pad and the brake drum. The problem of estimation, that has been addressed, is as follows: Suppose the pressure in the air brake system were to be measured and that the motion of the pushrod is not measured. Is it possible to estimate the nal displacement of the pushrod without knowing the parameters, such as the clearance, that govern the system to transition from one mode to another?