This study considers the finite time consensus tracking problems for second-order non-linear multi-agent system with the unknown dynamics. Firstly, the radial basis function neural networks are utilised to approximate the lumped unknown dynamic model. And then, to achieve the finite-time consensus tracking, a distributed non-singular fast terminal sliding mode control strategy is designed which can speed up the convergence of the multi-agent system. Moreover, the consistency under the proposed control strategy is theoretically analysed and the upper bound of setting time is explicitly obtained. Finally, two simulation examples are provided.

In this study, the stabilisation of quasi-one-sided Lipschitz non-linear systems is investigated. For the quasi-one-sided Lipschitz non-linear system, a condition for the existence of the observer is presented. For the weak quasi-one-sided Lipschitz non-linear system, a state feedback controller is proposed and a condition is derived for the existence of the state feedback controller. The separation principle is obtained for the observer-based controller of the quasi-one-sided Lipschitz non-linear systems. The main results in this study extend and improve those in the literature. Numerical examples are given to illustrate the main results.

Despite the importance of cyber-security for networked control systems, no suitable cryptosystem exists for networked control systems that guarantees stability and has low computational complexity. This study proposes a novel dynamic ElGamal cryptosystem for encrypted control systems. The proposed cryptosystem is a multiplicative homomorphic cryptosystem, and it updates key pairs and ciphertexts by simple updating rules with modulo operations at every sampling period. Furthermore, the authors modify the proposed cryptosystem by using a dynamic encoder and decoder so that the asymptotic stability of the encrypted control systems is guaranteed. Numerical simulations demonstrate that the encrypted controller with the proposed cryptosystem achieves asymptotic stability while randomly updating key pairs and ciphertexts. The feasibility of the proposed encrypted control system is evaluated through regulation control with a positioning table testbed. The processing time of the proposed encrypted control system is on the order of milliseconds, indicating that the system achieves real-time control.

This study tackles the problems of exponential stability analysis and model reduction for spatially interconnected discrete-time systems with time-varying delay. The well-posedness, exponential stability, and contractiveness of spatially interconnected discrete-time systems subject to time-varying delay are defined and a sufficient condition in terms of linear matrix inequality (LMI) is put forth to test these properties. By exploiting the above analysis result, a sufficient condition for guaranteeing the existence of a reduced-order system is derived. With the help of Finsler lemma, a reduced-order system is derived based on the LMI method. By taking advantage of the same method, a delay-free reduced-order system for a given spatially interconnected discrete time-varying delay system can also be attained. Finally, two examples have been carried out to show the feasibility and validity of the derived theories.

Resilient dynamic event-triggered control design problem is concerned for frequency stabilisation of multi-area power systems with renewable energy penetration under transmission delay and denial-of-service (DoS) attacks. The main works are presented as followings: (1) A novel state-space model is established to describe multi-area power systems with solar and wind generation disturbance under load frequency control and virtual inertia control (LFC-VIC). (2) The influence of DoS attacks is considered and first modelled by model-based average dwell time (MDADT). A criterion of preserving desired exponential performance is obtained about the required lower bound of average dwell time (ADT) of sleep intervals, namely and the tolerable upper bound of ADT of attack intervals, namely . (3) To reduce communication load, a dynamic event-triggered mechanism (DETM) is proposed and designed jointly with resilient LFC-VIC scheme by using piecewise Lyapunov–Krasovskii functional method and LMIs technique. (4) To defence DoS attacks actively, based on the resulting MDADT criterion, a dynamic prediction strategy is proposed to compensate the packet drops with unknown bound subjected to attack strategy. Finally, a numerical example for a two-area power system is carried out to verify the designed resilient LFC-VIC scheme and the DETM.

Power systems are a class of typical cyber-physical systems with switching-hybrid dynamics. With the innovation of power electronics technology and the implementation of power grid development strategy, the application of voltage source converter-based high voltage direct current (VSC-HVDC) transmission has been paid more and more attention. Firstly, the general small-signal model of the VSC-HVDC system is established, and its stability analysis is carried out by integrated modal analysis, participation factor analysis, and sensitivity analysis methods. It is clarified that the system controller parameters will have a significant impact on the stability of the VSC-HVDC system. Then, based on the switching system theory, the stabilising switching law of the bidirectional converter is derived, which makes the system energy attenuate fastest, and the stabilising switching controller is designed according to the switching law. Last, the effectiveness of the controller is verified by simulation, and the superiority of the stabilising switching control strategy is proved from the theoretical and simulation aspects by comparison with the traditional current vector control strategy.

This study focuses on the issue of asynchronous passive controller design for singular Markov jump systems with general transition rates under stochastic cyber-attacks. To maximise the utilisation of network resources by reducing unnecessary data transmissions, a dynamic event-triggered rule is properly presented. Assuming that the system might be attacked by two kinds of stochastic cyber-attacks, which are governed by two different functions. The asynchronous fact between the modes of the system and controller is described by the hidden Markov model. The criterion of stochastically admissible with a certain passive performance is established. In the light of a series of linear matrix inequalities, the asynchronous controller and dynamic event-triggered rule are designed simultaneously. A numerical instance under different event-triggered rules is offered to reveal the usefulness and effectiveness of the developed method.

This study investigates the intermittent semi-global containment of discrete-time high-order multi-agent systems with input saturation. The intermittent semi-global containment protocol is proposed based on discrete-time low-gain state feedback control. Some containment conditions are obtained, and the convergence analysis is given. It is turned out that all the followers beginning from a bounded initial set will asymptotically enter into the convex hull spanned by the leaders under the proposed protocol. Moveover, intermittent semi-global leader-following consensus with input saturation is considered as a special case, and the corresponding result is introduced. Finally, numerical simulations are presented to illustrate the theoretical findings.

An orthotopic-filtering-based hierarchical fault diagnosis algorithm is proposed for complex systems with multiple fault types. The given algorithm uses an orthotopic method to describe a feasible parameter set and detects whether a fault occurs by determining whether the feasible parameter set is empty. Then the hierarchical clustering method is applied to analyse the fault library. The clustering result is used as the prior knowledge for fault diagnosis analysis, and a discriminant analysis is conducted layer by layer. Finally, a model-matching method is applied to realise the fault identification. However, if the fault type is not included in the fault library, the fault type is then added to the fault library. Therefore, when the fault diagnosis is performed again, the fault library is re-hierarchically clustered. The analysis on the false alarm rate and the missing detection rate of the fault diagnosis algorithm are also studied. Finally, the fault diagnosis of a buck circuit is taken as an example to demonstrate the effectiveness and feasibility of the proposed method by analysing the fault diagnosis results.

This study deals with the problem of observer-based finite-time control for a class of one-sided Lipschitz (OSL) singular systems with uncertainties. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in both the state and output matrices but also in the non-linear function. With the help of some special derivations and transformation, the sufficient conditions ensuring robust finite-time boundedness of the closed-loop system and satisfying the performance index are given for OSL singular systems in terms of linear matrix inequalities (LMIs). Based on these, the observer and controller dynamics can be simultaneously involved in the design at one step. Two convex optimisation problems subject to LMIs are formulated to optimise the desired performance indices of interest to us. Finally, two examples are given to demonstrate the effectiveness of the proposed methods.

This study presents a novel fast non-linear model predictive control approach for a parallel double inverted pendulum. The approach uses dual-mode closed-loop predictions to obtain numerically robust optimal solutions. Moreover, it uses the real-time iteration (RTI) scheme to reduce the computational burden and achieve real-time performance. Furthermore, two main modifications are proposed which significantly improve the performance of the RTI scheme in the presence of large disturbances, namely; additional energy-based costs, and a hybrid switching scheme. Finally, the approach uses a non-standard discretised model combined with an online system identification scheme to address parameter uncertainty, and with an extended Kalman filter for state-estimation. The resulting performance is validated through both simulations and experimental results .

The disturbance decoupling problem (DDP) whereby the system outputs become insensitive to exogenous signals or disturbances plays a vital role in systems engineering and biological systems. Notably, many biological signalling systems with multiple outputs are usually susceptible to external environmental changes. The authors investigate the DDP for Boolean control networks (BCNs) and present a novel technique based on Boolean algebra to solve the DDP. In particular, the results on the DDP solvability are derived by transforming the system dynamics to a simplified form called output-friendly form. Furthermore, a constructive procedure based on the Karnaugh map to design all possible feedback controllers such that the states affecting the outputs are free from disturbances is proposed. Moreover, the presented results are extended to switched BCNs, and design all possible mode-independent feedback controllers. Finally, some examples including a Boolean model of Escherichia coli are provided to validate the main findings.

This study proposes a bounded controller for flexible-joint robot manipulators that only requires state measurements of joint motors. Firstly, the singular perturbation theory is used to decouple the dynamics model of the flexible-joint robot manipulator into slow and fast subsystems. Then, a saturated adaptive scheme combining backstepping control and radial basis function neural network approximator is applied to make the controller bounded and simplify the control law for the slow subsystem, and a new filtering operator is used in the fast subsystem to enhance the overall performance. Furthermore, the extended Kalman filter is involved to eliminate the states measurements of links in the closed-loop tracking control. Finally, the stability of the whole system is analysed and the effectiveness of the proposed approach is verified.

The main focus of this study is to develop a finite-time super-twisting sliding mode control strategy for the quadrotor based on a higher-order sliding mode observer (HOSMO). 12 state variables are required to describe the motion of the quadrotor, of which six state variables, namely the position, altitude, and orientation, are assumed to be obtained from the sensors. The remaining state variables, i.e. the linear and angular velocities, are determined using the HOSMO. Besides, the HOSMO aids in determining the unknown bounded lumped disturbances acting on the quadrotor. The output of the HOSMO is utilised for implementing the finite-time super-twisting sliding mode controller (FTSTSMC). The proposed FTSTSMC ensures finite-time convergence of tracking error with chattering attenuation. The chattering analysis for a super-twisting algorithm is presented in this work. Moreover, the overall system stability is investigated using the Lyapunov theory, and an expression for the time of convergence of the tracking and estimation error is presented. The effectiveness of the proposed methodology is established using numerical simulations and its performance is compared to a finite-time sliding mode observer coupled with a combination of proportional–integral–derivative and continuous sliding-mode controller. This is then validated in real-time using the DJI Matrice 100.

The aim of this study is to design a robust output-based control to regulate the output for a class of linear systems with input saturation and affected by parameter uncertainties and external disturbances. The proposed robust control approach is composed of a homogeneous observer and a linear control law. The design and convergence analysis of the homogeneous observer is based on the implicit Lyapunov function theorem guaranteeing the finite-time convergence of the state estimation error to a neighbourhood of the origin. The linear control law, that uses the estimated states and takes into account the saturated input constraint, is designed based on the attractive ellipsoid method and a barrier Lyapunov function approach. The synthesis of the robust-output based control is given in terms of linear matrix inequalities. Simulation results are presented to illustrate the feasibility of the proposed robust control approach.

This study deals with fixed-time consensus problems of second-order multi-agent systems with uncertain bounded disturbances. Instead of the time-triggered control algorithm, a distributed event-triggered control algorithm is developed in the presence of uncertain disturbance. By designing a novel threshold, a triggering function is proposed, which is fully distributed and does not require continuous communication. To tackle the chattering problem, a saturation function is defined to improve the control algorithm. Several conditions are derived and the rigorous proof is given by using Lyapunov stability theory and fixed-time stability theory. Then, to reduce the disturbance effect, an event-triggered control algorithm is proposed by using a disturbance observer. Finally, two simulation examples are given to verify the efficiency of the proposed control method.

In the control field, the adaptive model predictive control (AMPC) has the capability of taking effective control actions on unknown-but-bounded time-independent or slowly time-varying systems coupling with constraints. In essence, AMPC estimates the uncertain parameters or uncertainty set online by utilising historian data to extract model information. The model estimation procedure imposes some specific conditions on data and these extra conditions have restricted its practical use. To overcome these problems, a new data-driven control methodology is presented that integrates the data-driven concept into robust model predictive control (RMPC) architecture for unknown-but-bounded time-independent or slowly time-varying plant. The key novelty is to employ historian data to derive control policy and make a prediction in replacement with the complicated procedure of utilising data to estimate model parameters. A data-driven RMPC algorithm is developed within the robust model predictive control framework with the fulfilment of recursive feasibility and stability. The authors display the highlights of the data-driven model predictive control controller through two simulation examples. The resulting controller is verified to reduce conservativeness and increase the closed-loop performance of the system.

This study is concerned with the design of an event-triggered fault estimation and fault tolerant model predictive control scheme for linear systems subject to disturbances and actuator faults by using the method of delta operator. First, an observer is established to estimate the state and the fault simultaneously. An model predictive controller with fault compensation signals is then proposed through solving a constrained optimisation problem. An event-triggered scheme is employed to conserve the network bandwidth. The new design techniques are shown to be effective via simulation results.

This study presents the design and analysis of a novel funnel function-based sliding mode reaching law for uncertain discrete-time systems. The presented reaching law is featured by the funnel function, which is established on the basis of the switching function, and the perturbation estimation technique. As compared with previous researches, the developed method is capable of regulating both transient and steady-state performance. The system trajectory can be maintained within a predefined boundary, i.e. the desired limit of the trajectory evolution, described by the funnel function in the presence of disturbances. Theoretical analyses confirm the convergence and boundedness of the controlled system. A practical verification example is given to demonstrate the validity of the presented method.

This manuscript proposes an adaptive backstepping synchronous control method with full state constraints by drawing into the time-varying barrier Lyapunov functions (T-BLFs) for a kind of uncertain switched complex networks. Generally, a complex dynamic network in practical terms either possesses a switched topology or its nodes are with switched parameters. In this context, the synchronisation problem of the switched complex network is tackled by utilising adaptive backstepping method after converting switched complex network into the non-autonomous strict feedback form. Meanwhile, most of the system states are supposed to be constrained during the switch over the procedure. Thus, the constraint-handling method based on T-BLFs is developed in the backstepping process to guarantee the full state restriction boundaries are not violated, and then to realise the asymptotic stability of the nodes states of the switched complex networks. Four simulation examples are presented to verify the feasibility and effectiveness of the proposed control approach.

In this article, we investigate a new way of dealing with fault detection and isolation (FDI) for a class of delayed non-linear systems with an event-triggered mechanism (ETM). This article is based on 1) To estimate the dynamics of the nonlinear plant, Sliding Mode Observers (SMO's) is manipulated with Luenberger. 2) Under the ETM, sampled data is released only when the plant's measurement (sampled) violate the specific threshold of the event condition. 3) First, transform into two subsystems. In subsystem-A contains uncertainties without sensor fault and vice-versa in subsystem-B. To handle the uncertainties that appeared in subsystem-A, a new SMO's implemented while traditional Luenberger is employed to detect the sensor fault. Then, by using a new Lyapunov-Krasovskii function approach performance index is proposed. Based on stability criteria, sufficient conditions are provided in the account of Linear Matrix Inequalities (LMIs). The simulation example is given to demonstrate the effectiveness of our design method.

This study investigates the problem of mean-square asymptotic stability analysis of stochastic genetic regulatory networks with mixed time-varying delays. The innovation of this study lies in that several stochastic integral inequalities are improved based on auxiliary function integral inequalities. Thereby, less conservative mean-square asymptotic stability criteria are derived by constructing Lyapunov–Krasovskii functional with multiple integral terms and employing the proposed stochastic integral inequalities and the (reciprocal) convex combination technique. The obtained stability criteria are described in terms of linear matrix inequalities, which can be easily verified by using standard software tools. Finally, three numerical examples are provided to test and verify the effectiveness and less conservativeness of the proposed stability criteria.

The robustness of continuous non-smooth Lyapunov control for two-level quantum systems with uncertainties in the Hamiltonians is analysed in this study. The authors first transform a perturbed two-level system into a real-variable system by expressing the quantum state in terms of its complex exponential and then present two theorems to describe the behaviour of solutions of the perturbed system after a certain finite time by combining the Lyapunov and converse Lyapunov finite-time stability theorems with the homogeneity theory. Numerical simulation experiments on a spin- particle system show the effectiveness of the results obtained in this study.

This study explores the unified stability problem for a class of continuous-time switched non-linear systems, in which the non-linearities are described by the Takagi-Sugeno (T-S) fuzzy models. The ‘unified’ means that the switched system can be arbitrarily composed of either stable or unstable subsystems. Firstly, mode-dependent average dwell time switching strategies are introduced, and the fast switching strategy is improved by a mode-dependent bounded maximum average dwell time. Then, the subsystems are reclassified into ‘switching-stable’ and ‘switching-unstable’ subsystems. The state divergence will be absorbed by the ‘switching-stable’ subsystems. Moreover, by constructing a time-scheduled multiple Lyapunov function, the unified stability conditions are established. Finally, the effectiveness of the achieved results is validated by numerical examples.

The observability of discrete-time multi-agent systems (MASs) with switching topology under the framework of leadership coordinated control is studied. Based on the switched control system theory, some algebraic properties on observability of discrete-time MASs with switching topology are given. Moreover, on the basis of the eigenvalues and eigenvectors of the system matrices, an effective algebraic characterisation on the observability of discrete-time MASs is established based on fixed topology. The observability of some special topological graphs is also studied. Finally, numerical example and simulations are given.