Fully actuated system theory and applications: new developments in 2023

In the field of systems and control, a Fully Actuated System (FAS) approach was proposed to deal with the control design for nonlinear systems. Compared to the state-space model, the FAS model offers a unique advantage in handling complex nonlinear terms in a control system. Through its full-actuation structure, the FAS model facilitates the straightforward elimination of the nonlinear term, regardless of its complexity, as long as the nonlinear term is measurable. Eventually, a constant linear closed-loop system with an arbitrarily assignable eigenstructure is obtained. Due to its distinct advantages, the investigation of the FAS approach has garnered significant and enduring interest from control theorists and mathematicians as well as control engineers. In recent years, a large number of results on the FAS approach have been developed.

For the above-mentioned reasons, the Guest Editors have proposed this ‘Special Issue on Fully Actuated System Theory and Applications: New Developments in 2023’, which is aimed at presenting the latest new and significant results on FAS theory and its applications in 2023 to the readers of the International Journal of Systems Science (IJSS). The goal is to highlight recent advances and developments in many facets, both analytical and numerical, of FAS theory with their applications in control systems analysis and design.

On the FAS approach, there has been an annual conference organised, that is, Conference on Fully-Actuated System Theory and Applications (FASTA). FASTA 2022 was held in Harbin, China, with more than 150 participants, and FASTA 2023 was held in Qingdao, China, with more than 430 participants. Since FASTA 2023, the conference proceeding has been indexed by EI. As an officially affiliated journal of the FASTA conference starting in 2023, IJSS will publish a special issue on the FAS approach each year by selecting some solid papers from that year’s FASTA conference. Finally, there are 12 papers accepted in this special issue, which can be divided into 4 categories:

1. Nonlinear FAS Control (4 papers).

2. Linear FAS Control (3 papers).

3. FASs with actuator saturation and faults (2 papers).

4. Aerospace vehicle control via the FAS approach (3 papers).

In the first category, the first paper ‘Stabilization of four types of underactuated systems: a FAS approach’, by G.-R. Duan, proposes four general types of time-varying underactuated systems treated by the FAS approach. The second paper ‘Adaptive prescribed performance control for uncertain nonlinear HOFA systems with time delay’, by Y.-Z. Zhao, D. Ma, focuses on the adaptive prescribed performance control problem for high-order FAS with state time delay. The third paper ‘High-order fully actuated system models for discrete-time strict-feedback systems with increasing dimensions’, by X. Xu, proposes a high-order FAS model for discrete-time strict-feedback systems with nonuniform dimensions. The final paper ‘Robust adaptive dynamic surface control of high-order strict feedback systems based on fully actuated system approach’ by G.-B. Cai, Y.-Q. Xiao, H. Wei, T. Wu and M.-Z. Hou proposes a robust adaptive dynamic surface control method by using the FAS approach for high-order strict-feedback systems with parameter uncertainty and disturbance.

In the second category, the first paper ‘Stabilization of multi-agent systems over finite fields based on high-order fully actuated system approaches’, by Y.-S. Yang, J.-E. Feng, and L. Jia, studies the controllability of multi-agent systems over finite fields based on the high-order FAS approaches. The second paper ‘Controllability and control for discrete periodic systems based on fully actuated system approach’ by L.-L. Lv, Z.-K. Li, R. Chang and X.-Y. Liu, proposes a controllability criterion and periodic state-feedback control laws for discrete periodic systems based on the FAS approach. The third paper ‘Fully actuated system approach for high-order linear systems with high-order input derivatives’, by L.-X. Zhang, Z. Zhang and H.-Y. Jiang, presents a frequency-domain method for transforming a class of high-order linear systems with high-order derivatives of input into the corresponding FAS models.

In the third category, the first paper ‘Robust fault-tolerant stabilization of uncertain high-order fully actuated systems with actuator faults’ by M.-T. Gong, L. Sheng and D.-H. Zhou, presents a novel fault tolerance strategy for a class of uncertain high-order FAS with actuator faults. The second paper ‘Tracking control for nonlinear high-order fully actuated system with state constraints: An explicit reference governor approach’, by L. Yang and Y.-L. Li, studies tracking control problem of nonlinear high-order FAS subject to state constraints.

In the last category, the first paper ‘Prescribed-time fault-tolerant control for the formation of quadrotors based on fully-actuated system approaches’, by M.-S. Li, K. Zhang, Y.-H. Ma and B. Jiang, investigates the problem of prescribed-time fault-tolerant control for the formation of quadrotors by utilising the FAS approach. The second paper ‘A high-order fully actuated predictive control approach for spacecraft flying-around’ by D.-W. Zhang and G.-P. Liu, establishes a HOFA predictive control approach to solve the spacecraft flying-around problem under the framework of HOFA system theory. The third paper ‘Appointed-time safety-guaranteed control for spacecraft flying around non-cooperative target based on fully actuated system theory’, by, Y.-P Xing, Z.-Y. Yin and C.-S. Wei, proposes an appointed-time safety-guaranteed control method based on the FAS theory considering the effects of external disturbances and undesired orbital manoeuvres of the non-cooperative target, oriented to the control problem of the spacecraft flying around the non-cooperative target.

The guest editors would like to take this opportunity to thank all the authors of the Special Issue for their great contributions and express their sincere gratitude to all the reviewers for their time and efforts spent in providing valuable suggestions and comments to the authors. They are also very grateful to the Editors-in-Chief, Prof. Zidong Wang, of the International Journal of Systems Science for providing them with the opportunity of organising this Special Issue.