Time-variant Hamiltonian control systems: a covariant approach
Sprache des Vortragstitels:
GAMM Annual Meeting 2007
Sprache des Tagungstitel:
In this contribution we present an intrinsic description of time variant Hamiltonian control systems. This formulation based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invariant with respect to time variant coordinate transformations. The analysis of the change of the Hamiltonian along solutions of the system leads to some newe perspectives in the time variant setting, which can be analyzed using geometric methods. This is important from the control theoretic point of view, since this is linked closely to the stability analysis. The trajectory tracking problem for time invariant Hamiltonian control systems can be formulated using the developed theory, since the use of displacement or error coordinates fits perfectly into this covariant setting. Furthermore, if the nontrivial state bundle connection can be absorbed in a modified Hamiltonian, the control task to stabilize the tracking error can be handled by standard methods.