The method of controlled lagrangians (CL) is the way of designing control laws which stabilize mechanical systems. The CL method, by which the stability of systems is analyzed and synthesized from the viewpoint of energy, utilizes and preserves the structural characteristics of the underlying mechanical systems during the designing of the control laws. This makes the method be known for its larger stabilizing convergence region and better robustness. This project, based on the CL method, will study a class of mechanical systems with the lagrangians of kinetic energy minus potential energy, and investigate the control problems beyond the stabilization. This class of mechanical systems covering satellite, various ground vehicles, surface/undersurface crafts, and unmanned aircraft etc, is of wide range of engineering applications background. This study will include the following three aspects.
1. The tracking of the underactuated mechanical systems, investigates how to construct the CL in order to realize the tracking in a manner of stabilizing. For the mechanical systems with symmetry, the various steady motions are achieved in a manner of tracking, i.e., the switching between relative equilibria.
2. The control of the networks of mechanical systems which is formed through communicating connection, solves the problems of stabilizing coordinate motion which keeps the relative positions and/or orientations to be fixed, and generalizes the stabilizing method for a single system to that of multiple systems.
3. The applicability of the CL method will be analyzed when considering the control and communication being constrained; the improved designing method will be investigated.