Fully actuated system approach to robust control of uncertain multi-order sub-fully actuated systems

Motivated by the fully actuated system (FAS) approach, this paper proposes a direct robust control method for a type of uncertain multi-order sub-fully actuated systems (MOSFASs). Unlike numerous previous results, this paper broadens to a more general multi-order model and the more challenging sub-fully actuated case with the presence of singular problems. Firstly, a general uncertain MOSFAS model is presented, where the uncertainty merely needs to satisfy a common assumption. Secondly, a direct robust control method is proposed, giving a robust controller which only needs to satisfy very loose and basic requirements to ensure that the states ultimately converge into an arbitrarily small region. Simultaneously, by constraining the initial values of the states, it is perfectly guaranteed that the states always remain in a “safe” zone free of singular points, thus preserving the realizability of the controller. Finally, under certain conditions, a less conservative robust control scheme is introduced, which can relax the constraint of initial values easily. A simulation for a coarse-fine angle system demonstrates the validity and value of the proposed robust control method.