In particular, two different, but related, constrained control areas are investigated. The first is the problem of Linear Time Invariant systems subject to nonlinear actuators. That is, actuators that have symmetric or asymmetric position constraints and possibly rate constraints. The second problem is the detection and resolution of aircraft conflicts. Both problems are very pressing in their own distinct ways.

For the first problem a nonlinear state feedback methodology is developed that has guaranteed constraint satisfaction and global asymptotic stability. This is brought about by scheduling the gain to avoid saturation at all times, and is accomplished through a set of nested invariant ellipsoids that for each gain approximate the maximal invariant set. A comparison to sub-controllable sets and an application to the F/A-18 are given.

The second problem is approached through a two phase method. Firstly, aircraft conflicts are detected by performing a worst case analysis of the situation through Linear Matrix Inequality feasibility problems. Once this is completed the resolution problem is approached by formulation as a convex optimization problem. The resulting strategy is highly combinatorial in its complexity. A possible solution to this problem is attempted by formulation of a lower bound obtained by convex optimization techniques. The figure below is taken from an example of a spring mass system.

High performance bounded control of systems subject to input and input rate constraints (Accepted to the 1997 AIAA GNC)

Linear Matrix Inequalities for Free Flight Conflict Problems (Accepted to the 1997 CDC)

Constrained Control using Convex Optimization (S.M. Thesis, August 1997)