Constrained unidirectionally connected FASs: part I. Models

In addition to the single-order and multi-order fully actuated systems (FASs) or sub-FASs, in this paper, a more general class of complex systems termed as unidirectionally connected FASs (UC-FASs) is proposed, which represents an extra tremendously big class of systems, possibly subject to state and control constraints. Although a UC-FAS may not be converted into a single FAS or a sub-FAS, similar to a FAS, it can also be well sub-stabilised, as shown in Duan (Constrained unidirectionally connected FASs: Part II. Sub-stabilization. International Journal of Systems Science, 2025a. https://doi.org/10.1080/00207721.2025.2467223), in the sense that a sub-stabilising controller can be designed such that, on the feasible set, the closed-loop system is composed of a set of linear systems with desired eigenstructures. The approach is successfully applied in Duan (Constrained unidirectionally connected FASs: Part III. Applications. International Journal of Systems Science, 2025b, 1–15. https://doi.org/10.1080/00207721.2025.2467221) to the control of a class of manoeuvred moving objects, including the well-known PVTOL system. This, together with several complicated examples, sufficiently demonstrates the effect and the power of the proposed approach.