This thesis considers the design of nonlinear and adaptive control systems for the control of submersibles as well as aircraft. In the first part of the thesis, control of submersibles using bow and stern hydroplanes is considered, and (i) a robust output feedback nonlinear control law using modeling error compensation, (ii) a nonlinear adaptive state feedback law using SDU decomposition; and (iii) an output feedback linear adaptive law for the dive-plane maneuvering are derived. The robust nonlinear controller with high-gain observer is designed for depth and pitch angle tracking along constant trajectories in the presence of parametric uncertainties and disturbances due to the sea waves. Next, the adaptive backstopping controller is developed to accomplish depth and pitch angle tracKing SDU decomposition of the high-frequency gain matrix is done to prevent singularity in the control law. For this design, one needs to know the sign of the two minors of the input matrix, but no other knowledge of the submarine parameters is required. Finally, a Model Reference Adaptive Control (MRAC) law using output feedback is derived for the linear model of the submersible; In the second part of the thesis (i) an adaptive Variable Structure flight Control (VSC) system and (ii) an adaptive flight control system for the roll-coupled maneuvers of aircraft using the aileron, rudder and elevator inputs are derived. Again, the SDU decomposition of the high frequency gain matrix is used for the derivation of singularity free control laws. Simulations performed for the underwater and the air vehicles using Matlab and Simulink show that in the closed-loop system, desired trajectory tracking is accomplished using each of the control systems
