Underactuated systems are systems that have more degrees of freedom than number of actuators. The goal of this research is to extend existing control theory by designing innovative nonlinear controllers for underactuated systems and applying them to a three-link underactuated robot to evaluate the controller performance. This study will make available new control techniques for underactuated systems. Also, cost savings will be found in designing and manufacturing systems with fewer controllers, and systems with partial actuator failure may still be able to perform their function.

The designs of many future military aircraft will incorporate enhanced maneuver capabilities such as short takeoff and vertical landing as well as high angle of attack operation. Our objective is to effectively utilize recent advances in control theory to develop systematic, efficient, and high-performance design methods for integrated flight propulsion and high angle of attack control. The designs will be evaluated and tested in a full-scale nonlinear simulation. A set of design tools using standard software will be provided. To accomplish the objective, modern methods of linear robust and optimal control and nonlinear min-max design, such as nonlinear H _infin. , will be employed.

Multirate feedback systems, like single-rate ones, are sampled data control systems in which a continuous plant is controlled by a digital controller using sample and hold devices. Therefore, multirate systems are hybrid. To obtain a robust and high-performance controller for a multirate system, it is necessary to consider the hybrid nature of the problem. In this project a complete methodology of designing optimal H ^infin. or 1¹ controllers for the hybrid multirate sampled data problem is developed. Also, stability robustness and performance robustness nonconservative criteria are established. Furthermore, the asynchronous case (i.e., when not all the rates are related with rational ratios) is examined. These design techniques can be readily utilized in aerospace applications.

The problem of robust stabilization and optimal disturbance rejection is considered for systems that are nonlinear and nonautonomous. Special attention is given to periodically time-varying systems with nonlinearities. Generalized H ^infin. techniques are investigated in order to develop practical analysis and design methodologies. Furthermore, these methods can be tailored to specific applications of mechanical and aerospace systems.