This work provides first and second-order expressions to approximate neighboring solutions to the m-point boundary value problem. Multi-point problems arise in optimal control because of interior constraints or switching dynamics. Many problems have this form, and so this work fills a void in the study of extremal fields and neighboring optimal control of constrained systems. Only first and second-order terms are written down, but the approach is systematic and higher order expressions can be found similarly. The constraints and their parameters define an extremal field because any solution to the problem must satisfy the constraints. The approach is to build a Taylor series using constraint differentials, state differentials, and state variations. The differential is key to these developments, and it is a unifying element in the optimization of points, optimal control, and neighboring optimal control. The method is demonstrated on several types of problems including lunar descent, which has nonlinear dynamics, bounded thrust, and free final time. The control structure is bang-off-bang, and the method successfully approximates the unknown initial conditions, switch times, and final time. Compared to indirect shooting, computation time decreases by about three orders of magnitude.

This thesis addresses flight control of the perch landing maneuver for micro-aerial vehicles. A longitudinal flight model is constructed for a pigeon-sized aircraft. In addition to a standard elevator control surface, wing-rotation also considered as a non-standard actuator for increasing low-speed aerodynamic braking. Optimal state and control trajectories for the perch landing maneuver are computed using commercial software. A neighboring optimal control law is then developed and implemented in a set of flight simulations. Simulations are run with both a quasisteady and an unsteady aerodynamic model. The effectiveness of wing rotation and of the neighboring optimal control law is discussed, as is the importance of unsteady aerodynamics during the maneuver. Wing rotation was found to be minimally effective in this case, but it showed potential to be more effective in further research. The unsteady aerodynamic model has significant influence over the success or failure of the maneuver.