High-order fully actuated system approaches: part VII. Controllability, stabilisability and parametric designs

Abstract

In this paper, high-order fully actuated (HOFA) models with multiple orders for general dynamical control systems are firstly proposed, for which controllers can be easily designed such that the closed-loop systems are constant linear ones with completely assignable eigenstructures. Based on this special feature of the type of HOFA models, controllability of general dynamical control systems is proposed. It is revealed that a general dynamical control system can be represented by a controllable subsystem described by a HOFA model, and an extra uncontrollable one or supplementary one. While a general dynamical control system is called stabilisable if its uncontrollable (autonomous) subsystem does not exist, or is stable in a certain sense. Finally, two parametric design approaches for control of the type of general HOFA models are proposed, which provide all the design degrees of freedom. Several examples, including ones of sub-fully actuated systems, are treated, which demonstrate the effect of the proposed theories.

High-order fully actuated system approaches: Part VIII. Optimal control with application in spacecraft attitude stabilisation

“…As argued in Duan (2020a), Duan (2020b), Duan (2020d) and Duan (2020j), high-order fully actuated (HOFA) models also serve as a general model for dynamical control systems, and are especially convenient and effective in dealing with control problems. The demonstration of this with robust control, adaptive control and disturbance rejection control has been given in Duan (2020f), Duan (2020g), Duan (2020h) and Duan (2020i).…”

“…Another contribution of the paper is the treatment of the sub-fully actuated system case. Sub-fully actuated systems are defined in Duan (2020a) and Duan (2020j), and are relatively more difficult to handle due to a problem of feasibility. Using a feature of linear quadratic optimal control, a feasibility condition is established for the optimal control of sub-fully actuated systems.…”

“…The system (1) satisfying the above Assumption A1 is called a (globally) fully actuated system (Duan, 2020j).…”

“…Remark 2.1: The above HOFA model ( 3) might be easily mistaken to represent a very small portion of systems due to the full-actuation Assumption A1. While as discussed in Duan (2020a), Duan (2020d) and Duan (2020j), it serves as a general model for dynamical control systems. Many systems which are in state-space forms can be converted into HOFA systems (see Duan (2020a), Duan (2020b), Duan (2020d) and Duan (2020e)), and practical systems can also be modelled as HOFA systems.…”

“…When such physical laws are used in modelling, a series of second-order subsystems are originally obtained (Duan, 2020a). From this stage we can further get a state-space model by variable extension, and on the other side, we can get a HOFA model by variable elimination if the system is controllable (Duan, 2020j). It should be noted that many physically fully actuated systems exist, which are already in the form of second-order HOFA systems at the modelling stage.…”