Stabilization of Nonlinear Systems via Trajectory Following

Kiss B., J. Levine and P. Mullhaupt. Control of a Reduced Size Model of US Navy Crane Using Only Motor Position Sensors. Springer, London, 259 Volume 2, 1- 12

Mullhaupt P., B. Srinivasan and D. Bonvin. On the Nonminimum-phase Characteristics of Two-link Underactuated Mechanical Systems. 37th Conference on Decision and Control, Tampa, Florida, USA (December 1998), 4579-4583 MUELLHAUPT Philippe, BONVIN Dominique

The aim of this project is to provide a new paradigm for solving difficult nonlinear control problems such as those arising in nonholonomic systems. It is well known that such systems are not smooth stabilizable (cannot be stabilized using a smooth feedback), though they are controllable (there exists an input that can steer the system to the desired state).

The proposed paradigm exploits this subtle difference between the concepts of controllability and stabilizability. The classical control paradigm is linked to stabilizability as it searches for a map between the state and inputs of the system, so that the state converges to the desired equilibrium point. On the other hand, the new paradigm uses the fact that, due to controllability, there exists a trajectory following which the system can be steered to the desired point.

The use of trajectory following to achieve stabilization around an equilibrium point is studied. Such an objective has two steps: (i) generation of the reference trajectory that ends up at the equilibirium point and (ii) design of a local controller that ensures trajectory following. To handle large disturbances, the trajectory generation should be repeated from time to time. Stabilization at the equilibrium point then follows from both the convergence of each trajectory to the equilibrium point and the local stability around the trajectories.