Guest Editorial: Learning, optimisation and control of cyber-physical systems

Cyber-physical systems (CPS) are engineered systems with built-in seamless integration of physical and cyber components. Fundamental developments in sensing, communication, control, and computing technologies endow CPS with flexibility, adaptability, scalability, and robustness. The availability and size of input-output data generated along with the control of CPS bring a unique opportunity for machine learning techniques to advance the theory of dynamical control systems, by learning control rules directly from data. Integration of input-output data into adaptive, robust, predictive, and distributed control policies holds the key to exploiting the potential of learning and optimisation in the CPS designs. There are several challenges related to sampling, transmission, synchronization, as well as associated cyber security when merging contemporary data-based and traditional model-based control techniques for CPS.

The overarching goal of this special issue is to bring together innovative developments on the interface between learning, control, and optimisation targeting cyber-physical opportunities emerging from power, transportation, and manufacturing systems. Through a rigorous peer review process, three articles have been accepted, which are summarised below.

In the study, “Learning-based distributed adaptive control of heterogeneous multi-agent systems with unknown leader dynamics”, the authors develop a distributed adaptive tracking control method for heterogeneous multi-agent systems with unknown leader dynamics in a directed graph. In contrast to the reported leader-following consensus studies, the prior knowledge of the leader is supposed to be cognised by some or all of the followers, the situation that the leader's dynamics are totally unrecognised but can be learned for each individual follower is considered. A data-driven learning algorithm using the system’s data is developed to reconstruct the unknown systems matrix. Then, an adaptive distributed dynamic compensator is exploited to provide the leader's state estimation in a directed graph. Afterwards, a dynamic output feedback control law for each agent is projected. Theoretical analysis shows that the proposed algorithms not only ensure that all followers can identify the unknown system matrix but also guarantee that the distributed output leader-following consensus control with heterogeneous dynamics is achieved without any global information.

In the study, “Sampled-data synchronisation of singular Markovian jump system (SMJS): application to a DC motor model”, the authors consider the sampled-data synchronisation problem for SMJSs subject to aperiodic sampled-data control. Firstly, by constructing mode-dependent one-sided loop-based Lyapunov functional (LBLF) and two-sided LBLF, two different stochastically admissible conditions are suggested for error SMJSs with aperiodic sampled-data. It is guaranteed that the slave system is stochastically synchronised to the master system on the basis of the proposed stochastically admissible conditions. Secondly, two corresponding mode-dependent aperiodic sampled-data controller design approaches are provided for error SMJSs based on two different conditions, respectively. Finally, the validity of these approaches is demonstrated by a DC motor model. It also demonstrated that the two-sided LBLF method possesses a larger upper bound of the sampling period than the one-sided LBLF method.

In the study, “Predefined-time distributed event-triggered algorithms for resource allocation”, the authors propose a predefined-time distributed algorithm and analyse its convergence by using the Lyapunov stability theory in which the local constraint is ensured by a differential projection operator. Thus, a predefined time is obtained using a time-varying time-based generator. In addition, to reduce the communication consumption between agents, the authors develop a static as well as a dynamic-based event-triggered control scheme, where the information broadcast only occurs at some discrete time instants. Moreover, the three proposed algorithms converge precisely to the global optimal solution. Besides, the Zeno behaviour is excluded in the above static and dynamic event-triggered mechanisms.

The guest editors would like to thank the Editor-in-Chief of the IET Cyber-Physical Systems: Theory & Applications, Prof. Shiyan Hu, and the Editorial Office for their great support of our special issue. In addition, we thank all the authors who submitted their quality papers to this special issue, and special thanks go to all anonymous reviewers for their great efforts and time to accomplish their review tasks.