Abstract

This thesis includes two main parts. In the first part, the main contribution is to develop nonsingular rigid-body attitude control laws using a convex formulation, and
implement them in an experimental set up. The attitude recovery problem is first parameterized in terms of quaternions, and then two polynomial controllers using an SoS Lyapunov function and an SoS density function are developed. A quaternion-based polynomial controller using backstepping is also designed to make the closed-loop system
asymptotically stable. Moreover, the proposed quaternion-based controllers are implemented in a Quanser helicopter, and compared to the polynomial controllers and a PID
controller experimentally.
The main contribution of the second part of this thesis is to analytically solve the Hamilton-Jacobi-Bellman equation for a class of third order nonlinear optimal control
problems for which the dynamics are affine and the cost is quadratic in the input. One special advantage of this work is that the solution is directly obtained for the control input without the computation of a value function first. The value function can however also be obtained based on the control input. Furthermore, a Lyapunov function can be constructed for a subclass of optimal control problems, yielding a proof certificate for stability. Using
the proposed methodology, experimental results of a path following problem implemented in a Wheeled Mobile Robot (WMR) are then presented to verify the effectiveness of the
proposed methodology.