In this study, a new distributed filtering approach is proposed for the load frequency control of uncertain non-linear power systems with cyber-physical attacks. Specifically, the non-linear power system is firstly modelled under interval type-2 Takagi–Sugeno fuzzy framework and the uncertainty therein is captured by designing corresponding membership functions. Both denial of service cyber attack and physical sensor attack are considered and modelled as independent Bernoulli process. Based on the Lyapunov stability theory, less conservative sufficient conditions have been derived to guarantee the robustly mean-square asymptotic stability with an average performance standard for the dynamic filtering error system. Moreover, artful matrix transformation techniques have been adopted to decouple the intertwined matrix variables in designing the distributed filter gains. In simulations, a three-area non-linear power system with internal uncertainties is used to validate the robustness of the proposed distributed filtering strategy to system parametric uncertainties and cyber-physical attacks.

In this study, a novel adaptive hybrid fuzzy system-wavelet neural network (FS-WNN) approximator is developed for control of uncertain non-linear multiple-inputs and multiple-outputs systems. The main idea is to use two different universal approximators to approximate each unknown non-linear function of the dynamic system. The first approximator is a FS and the second approximator is a WNN. Each approximator approximates the system's unknown functions independently. Then, the two approximations of the same function are combined using a modulation technique. The used modulation attributes to the first approximation a scaling factor and attributes its complementary factor to the second approximation to synthesise a hybrid optimal approximation of the function. Thus, system unknown functions are accurately approximated using the novel adaptive hybrid approximator that gathers the advantages of both approximators. The adaptation laws of the developed hybrid approximator are derived using Lyapunov's direct method to ensure the stability of the closed loop system. A simulation study is given to evaluate the performance of the proposed hybrid FS–WNN approximator in comparison with the FS and WNN approximators in indirect adaptive control of a two-link robot manipulator.

In this study, the distributed optimisation for solving resource allocation problem with both local bound and equality constraints is studied. A continuous-time multi-agent system with communication time-delay is proposed for the resource allocation. First, to reduce communication cost, a new modified multi-agent system is proposed inspired by previous work. Next, based on the system, the communication time-delay is considered to reduce the communication cost and match real situation. Then, by choosing proper parameters, sufficient conditions are derived for convergence to the optimal solution of the distributed optimisation. Moreover, delay-free case is also considered, which proves that the system is convergent based on directed communication graph by choosing proper parameters. Finally, simulation results demonstrate the characteristics of the system.

In this study, a novel output feedback model predictive control based on ellipsoidal set-membership state estimation is proposed for systems with unknown but bounded external disturbances. The set-membership state estimation is utilised to estimate the current system states for the optimisation of model predictive control such that the actual states are not required. Ellipsoidal set-membership estimation guarantees that the real system state lies in the ellipsoid originated from the estimated state. The control inputs computed by solving the optimisation problem recursively regulate the system state to converge to a domain containing the origin. All the quadratic matrix inequality conditions are conservatively approximated as linear matrix inequality conditions such that the optimisation problems can be solved by using semi-definite programming. System constraints are analysed over all the prediction horizon and transformed into linear matrix inequalities for the direct incorporation into the optimisation. Simulation examples demonstrate the effectiveness of the proposed approach.

In distributed control systems, a local regulator does not have complete knowledge of the whole system. Therefore, some information is transmitted between local regulators through communication lines. The delays in communication lines are not negligible and they can make the closed-loop system unstable or impose a limit on the achievable control performance. Due to the process and communication delays, controllers cannot reject all disturbances. Although there has been a plethora of literature available for assessing the control performance in the presence of process time delay, no similar study has been conducted for distributed control systems in the presence of communication delays. In order to address this problem, a new solution for performance assessment of distributed control systems, which takes communication delays into account, is proposed here. Further, the corresponding minimum variance controller is also derived under the distributed control framework with communication delays.

This study investigates a distributed leader-following consensus problem for a class of high-order uncertain non-linear multiagent systems. For the uncertain non-linear terms in the systems, the authors propose a less conservative Lipschitz condition, which the Lipschitz growth parameters are unknown. By using the adaptive method, the unknown Lipschitz growth parameters are estimated asymptotically. Furthermore, to lower the frequency of controller updates, a new dynamic event-triggered control strategy with the novel dynamic variable is constructed based on the event-triggered method. The distributed consensus protocol is proposed based only on the relative state information of neighbouring agents and the protocol can ensure that the Zeno-behaviour no longer occurred. Based on the Lyapunov stability theory, it is strictly proved that the state variables of the followers can track asymptotically those of the leader. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed theoretical results.

In the presence of the unmodelled dynamics and external time-varying disturbances, letting an underactuated underwater vehicle track a reference trajectory correctly without knowledge of the vehicle's linear velocity is a challenging problem. This study reports a solution to this problem by proposing a linear velocity observer that is based on available states. Furthermore, a fuzzy observer-based tracking controller is designed, where fuzzy logic systems are resorted to approximate the model uncertainties and disturbances. Theoretical analysis demonstrates that the vehicle can converge to a neighbourhood of the reference smooth trajectory, hence achieving a global state that is uniformly and ultimately bounded. In order to validate the performance of the proposed controller, numerical examples are presented. They show that the linear velocity observer can be used to estimate the actual linear velocity and the underwater vehicle is able to track the reference trajectory closely.

This study investigates the problem of reliable mixed /passive control for Takagi–Sugeno (T–S) fuzzy semi-Markovian jump systems under different event-triggered schemes. An asynchronous fuzzy fault-tolerant controller is designed to deal with the actuator failures, which results in the closed-loop system is stochastically stable with a prescribed mixed /passive performance level even if the actuator failures appear. In order to relieve the transmission pressure over the network, the authors utilise different event-triggered schemes and compare their ability of network resource saving. In addition, there is a difference between the system modes and the controller modes to formulate the asynchronisation phenomena. By implementing the delay system method, in combination with the free-weighting matrix and Lyapunov–Krasovskii functional, some conditions on the performance analysis are established to ensure the stochastic stability of the system. Then, controller gain matrices and event-triggered matrices can be obtained simultaneously based on a group of feasible linear matrix inequalities. Finally, simulations are given to show the availability of the proposed method.

In an electronically controlled VE distributive pump, the fuel quantity actuator (FQA) is a significant component. It is responsible for governing the quantity of fuel being injected into diesel-type engines. There exist non-linearities in the system, and usually, non-linearities are neglected in modelling and control design, which makes the performance of the closed-loop system degrade. Therefore, the authors take the non-linearities of the rotary electromagnet and offsetting spring into consideration and establish the more detailed mathematical model in this study. Besides, the FQA system always confronts disturbances caused by external torque and input voltage variation in the real working condition. Furthermore, to deal with the non-linearities and reject the disturbances, a generalised proportional integral observer (GPIO)-based backstepping control approach is presented. By using a GPIO, the state estimations and disturbances estimation can be obtained at the same time. In addition, a theoretical analysis of the closed-loop system is given, showing its asymptotic stability, even under acting lumped disturbance. The introduced control scheme exhibits satisfactory performance in terms of transient behaviour and disturbance rejection. Finally, a set of simulation and experimental tests are carried out to validate the feasibility as well as efficiency of the proposed control framework.

This study investigates a novel disturbance observer-based distributed sliding mode control (DOB-DSMC) strategy for the multimotor web-winding system in the presence of model uncertainties and external disturbances. First, a disturbance observer is developed for each subsystem to generate the disturbance estimations, which can be incorporated in the controller to counteract the disturbances. After that, by choosing appropriate coordination variables, a DOB-DSMC is designed, which ensures that the system states converge to the sliding surface in finite time. The proposed controller can not only reduce the effect of coupling between continuous subsystems on states but also restrain the influence of uncertainties and external disturbances. It only requires a smaller control input than linear control. The controller gain matrices are obtained by solving linear matrix inequalities, which are obtained by the control theory and Lyapunov stability theory. Finally, some simulations and experimental tests are performed on the three-motor web-winding system to test the performance of the proposed DOB-DSMC method.

In this study, the authors tackle some control problems related to the class of continuous-time, stochastic linear time-varying systems with Markov switching. First, the annular stochastic finite-time stability problem is considered, and two sufficient conditions are derived by considering the Itô formalism. Both conditions require the solution of a feasibility problem based on differential linear matrix inequalities. The former turns out to be less conservative and, therefore, is exploited in the analysis context; however, it cannot be converted into a computationally tractable condition for feedback purposes. The latter, which is based on a more conservative assumption, allows us to solve the state-feedback design problem. They show that the proposed approach obtains less conservative results with respect to the previous literature. Moreover, the application of the methodology to the finite-time control of a satellite illustrates the effectiveness of the proposed approach when facing engineering problems.

This study is devoted to derive the singular Fornasini–Machesini (F-M) state-space model for a class of MIMO multidimensional (n-D) systems represented by non-causal multivariate transfer function matrices. It is shown, first, that the singular n-D F-M realisation can be generated by using the realisation methods of the standard n-D F-M models. Since the resulted realisations are usually non-minimal and deriving a minimal realisation is an extremely difficult problem, a model-order reduction method is developed. In particular, the common eigenvector approach is proposed, which significantly reveals the relationship among the reducibility, the eigenvalues and the eigenvectors associated with a given singular F-M state-space model. An example of spatially interconnected, hexagonal circuit is also given to illustrate some details and confirm the effectiveness of the proposed method.

This study investigates the robust formation tracking problems for uncertain multi-agent systems(MASs). The leader is assumed to be linear case and the dynamics of the followers can be modelled as a high-order linear system with heterogeneous uncertainties and external disturbances. Only part of the followers can get the states of the leader and the control input of the leader cannot be obtained by any followers. Based on the relative information among agents, robust formation tracking protocols are proposed to achieve the desired formation tracking. It can be proven that the formation tracking error can be made arbitrarily small if the formation tracking feasibility condition holds. Finally, a simulation example is provided to illustrate the obtained theoretical results.

The formation problem for a class of non-linear multi-agent systems (MASs) is considered under bounded disturbance and repetitive environment. The agent dynamics here is unknown and heterogeneous, and the disturbances are both time-varying and iteration-varying. Based on a novel disturbance-related dynamic linearisation technique, the agent dynamics is first transformed into an equivalent dynamic linearisation data model along the iteration axis. Then, distributed robust model-free adaptive iterative learning protocols are designed to drive the agents to the desired formation pattern. By theoretic analysis, the formation tracking error of the MASs is ultimately bounded and the result is further extended to an iteration-varying topology and pattern case. As a data-driven method, the protocol design has the feature that only the input and output data of neighbouring agents are used. Finally, numerical examples are presented to show the effectiveness and robustness of this method.

In this technical note, the authors address the finite-time consensus problem of a second-order multi-agent system (SOMAS) under an event-triggered control strategy. This problem arises from the case where actuators in a SOMAS fail to follow the ideal controller behaviour exactly, due to either the failure of an embedded processor to maintain the desired update rate or a large time constant in the actuators, while still trying to maintain some performance merits from the finite-time control theory. A decentralised event-triggered non-linear protocol is proposed based on only local information for the undirected and connected communication graph. The rigorous proof is then presented and shows that the consensus can be achieved in finite time even under event-triggered schemes. Owing to the event-triggered strategy, they proposed a technique that bounds the steady errors of agent states into a small region around zero in finite time and reduces the update frequency of actuators while excluding the Zeno behaviour. Finally, simulation results are provided to validate the correctness and effectiveness of the proposed method and demonstrate that it can adjust a composed performance metrics with respect to the convergent rate, consensus accuracy, and update frequency of actuators by tuning the parameters in the control protocol.

This note presents a strict proof for the state transition matrix of linear discrete time-varying stochastic systems, which corrects the errors of the previous references.