In this dissertation, we employ recent theoretical advances in differential geometric formulation of nonlinear control theory and adaptive control to develop a practical adaptive nonlinear control strategy.

We first present a new scheme for tracking and decoupling of multi-input/multi-output nonlinear systems with parametric uncertainty in their dynamics. We obtain an adaptive right-inverse that can be used as a decoupling prefilter for the original system and to generate the input necessary such that the outputs track a desired path. The procedures are systematic and have been implemented into a computer code. an integrated symbolic-numerical software system, written a Mathematica and C, has been developed that includes capabilities for automatic generation of model equations, for design of nonlinear tracking, regulation, stabilization, and adaptive control laws, and for generation of simulation codes (in C) for performance evaluations. This system is then used to design a nonlinear adaptive control algorithm for active suspensions for vehicles with the objective to effectively isolate the sprung body dynamics from the road disturbances. We also consider the design of a magnetic levitation control system.

For systems that do not satisfy the restrictive regularity assumptions of the current adaptive nonlinear control methodologies, commonly based on exact feedback linearization technique, we develop a technique of adaptive approximate tracking and regulation. This technique achieves reasonable stable tracking performance under parameter uncertainty in nonlinear dynamics for a large class of nonlinear systems with guaranteed bounds on the tracking error and parameter estimates. While the controller structure is designed using the approximate system, the adaptive loop is constructed around the true system in order to avoid any parameter drift typically caused by dynamic uncertainty in the system. Furthermore, for adaptive regulation, our scheme removes the linear parameter dependence assumption on the location of the unknown parameters. It also replaces the involutivity condition for exact feedback linearization with an order n involutivity assumption for approximate feedback linearization. For nonlinear systems that are linearly controllable, we give a simple systematic design procedure using a dynamic state feedback that achieves adaptive quadratic linearization.

We then investigate the use of this technique in the design of flight control systems using a simplified planar VTOL aircraft model. While due to the non-minimum phase property of the VTOL system the previous results in adaptive nonlinear control theory are not applicable, a comparison between the performance of our adaptive controller to the non-adaptive case reveals that the adaptive controller performs about 90% better in signal tracking.