State estimation problem for power systems has long been a fundamental issue that demands a variety of methodologies depending on the system settings. With the recent introduction of advanced devices of phasor measurement units (PMUs) and dedicated communication networks, the infrastructure of power grids has been greatly improved. Coupled with the infrastructure improvements are three emerging issues for the state estimation problems, namely, the coexistence of both traditional and PMU measurements, the incomplete information resulting from delayed, asynchronous and missing measurements due to communication constraints, and the cyber-attacks on the communication channels. In this study, the authors aim to survey some recent advances on the state estimation methods which tackle the above three issues in power grids. Traditional state estimation methods applied in power grids are first introduced. Latest results on state estimation with mixed measurements and incomplete measurements are then discussed in great detail. In addition, the techniques developed to ensure the cyber-security of the state estimation schemes for power grids are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out.

This paper investigates the disturbance decoupling problem for Boolean control networks. Firstly, using the matrix semi-tensor product, the logical dynamic equations of Boolean control networks are converted into discrete time linear equations. Secondly, the solvability of the disturbance decoupling problem is analyzed based on the structure matrices of BCNs, and a method for design state-feedback controllers is put forward to deal with this problem. Two necessary and sufficient conditions for the disturbance decoupling problem of BCNs are obtained. Then an algorithm is provided to design controllers for calculating the disturbance decoupling forms of Boolean control networks. Finally, an illustrative example is given to describe the proposed algorithm.

This study proposes a systematic control design approach to consider jointly the event-triggered communication mechanism and state-feedback control for switched linear systems. The systems determine the necessary samplings of the feedback signal by constructing predefined events that can reduce redundant signal transmission and updates. Specifically, the first main step in the design is to construct sufficient conditions for stability analysis in the form of linear matrix inequalities to utilise fully the idea of average dwell time. With the proposed event-triggering mechanism, the design renders the resulting switched closed-loop system finite-time bounded. Subsequently, the authors present the conditions for finding the parameter of the event-triggered sampling mechanism and the state-feedback sub-controller gains. Then, the results for the full state feedback control case are further extended to systems incorporating observer-based state-feedback control motivated by practical applications. For each case, an estimate of the positive lower bound on the inter-execution times is further derived to avoid Zeno behaviour. A numerical example is presented to illustrate the effectiveness of the proposed methods.

This study addres,ses a distributed optimal integrated tracking control method with disturbance rejection for separate kinematic and dynamic uncertain non-holonomic mobile mechanical multi-agent () systems. Initially, based on the graph theory, the overall tracking systems of agents are defined and the distributed optimal tracking problem of separate kinematics and dynamics is transformed into an equivalent distributed optimal regulation problem of the integrated affine system. Then, neural network (NN)-based adaptive dynamic programming and cooperative differential game theory is utilised for control, in which only one NN is required for each agent. The NN weight-tuning law and the online algorithm is developed to approximate the value function, and synchronously update both optimal control and worst disturbance laws in only one iterative loop. The tracking errors and function approximation errors are proven to be uniformly ultimately bounded using Lyapunov theory. Finally, as applications of the proposed method, control of the wheeled mobile multi-robot system is discussed. The effectiveness of the method is demonstrated by the results of the comparative numerical simulation.

This study investigates event-triggered proportional–derivative (PD) control for systems with network-induced delay. Based on the Lyapunov–Krasovskii functional, the PD sampled-data controller design condition is derived in terms of linear matrix inequality (LMI) which include the integral-based event-triggering condition. As the derivative term of the proposed PD control may lead excessively frequent triggering, an integral-based triggering is firstly adopted to reduce the required sampled control input in this study. The proposed triggering condition with integration is converted as LMI with quadratic augmented vector by applying a new quadratic generalised free-weighting matrix inequality which provides a free selectable vector. Numerical simulation shows the effectiveness of the proposed event-triggered PD control with the integral-based event-triggering condition.

In this study, the problem of output regulation with passive performance control is investigated for a class of switched stochastic delay systems by using an average dwell time approach. It is assumed that the system under consideration is subject to the existence of time delays in both states and the regulators switching signal which causes asynchronous switching between candidate regulators and subsystems. By construction of a Lyapunov–Krasovskii (L–K) functional, sufficient conditions for the existence of the corresponding regulators are derived from the cases where the states are measurable and unmeasurable, respectively. Then, a switching signal is designed based on the upper bounds of the time delays. Finally, simulation examples are provided to illustrate the feasibility and efficiency of the proposed method.

Using the linear representation of symmetric group in the structure vector of finite games as its representation space, the inside structures of several kinds of symmetric games are investigated. First of all, the symmetry, described as the action of symmetric group on payoff functions, is converted to the product of permutation matrices with structure vectors of payoff functions. Second, in the light of the linear representation of the symmetric group in structure vectors, the algebraic conditions for the ordinary, weighted, renaming and name-irrelevant symmetries are obtained as the invariance under the corresponding linear representations. The semi-tensor product of matrices is a fundamental tool in this approach.

For controller design, exogenous disturbance, which commonly exists in real applications, is an important factor to be considered. However, the existing results on constrained model predictive control (MPC) design for Markovian jump linear systems (MJLS) mainly focused on the disturbance-free case. This motivated to study constrained MPC synthesis for MJLS with bounded additive disturbance. By projecting the desired closed loop trajectories onto a set of predetermined trajectories, the adopted predictive control law is a sum of these corresponding stabilising control laws. Constraints are guaranteed by restricting the augmented state into a maximal output admissible set. Then the MPC algorithm is given by optimising the infinite horizon sum of deviation of the quadratic cost from its steady-state value. Under the MPC algorithm, the long run average cost is proved to be less than or equal to its steady-state value, which equals to the optimal one when one of the constituent control laws is chosen to be the optimal control law. The optimisation and analysis of determination of projection coefficients have also been discussed. Finally, a numerical example is given to illustrate the proposed results.

In this study, the robust optimal filtering problem is investigated for a class of linear time-varying systems with stochastic uncertainties. A new model is presented that accounts for both stochastic parameter uncertainties and noise. On the basis of the new model, a robust optimal filter is proposed. It takes stochastic uncertainties into full consideration, but does not depend on any specific structure of uncertainties. By resorting to linear system theory and utilising stochastic analysis methods, the filter gain is designed such that the estimation error covariance is minimised at each time step. The authors' developed filtering algorithm is recursive, and therefore suitable for real-time online applications. In the end, two simulation studies are performed to illustrate the effectiveness and applicability of their proposed strategy.

This study investigates the consensus problem for general linear multi-agent systems (MAS) via observer-based dynamic output feedback event-triggered control. Assume that the relative state information is unknown for each agent and only the relative output feedback between neighbouring agents can be measured. To solve the consensus problem, the authors develop a novel observer-based event-triggered approach to design a dynamic relative output feedback control. Two event-triggering time sequences are constructed. One is the relative output to the observer and another is the observer error to the controller. One can prove that under the proposed control strategies, the consensus problem can be solved via linear matrix inequalities as well as Riccati inequality if the communication graph of the MAS is connected. Furthermore, the Zeno-behaviour of triggering time sequences can be avoided. Finally, the effectiveness of the proposed strategies is illustrated by a numerical example.

The bipartite consensus problem for integrator multi-agent systems over signed fixed digraphs is investigated in the presence of measurement noise. A time-varying consensus gain is introduced and then a stochastic type protocol is proposed, whose performance is analysed using the state transition matrix of the closed-loop system. Necessary and sufficient conditions for ensuring a mean square bipartite consensus protocol are obtained in the presence of noise. Furthermore, in the absence of noise it is shown that these conditions are also necessary and sufficient for ensuring the bipartite consensus except for the quadratic integrability of the consensus gain. It is found that the signed digraph being structurally balanced and having a spanning tree are the weakest assumptions on connectivity for achieving bipartite consensus regardless of the measurement noise. In particular, if the signed digraph is structurally unbalanced, then under some mild conditions, the states of the closed-loop system converge to zero in mean square, regardless of the initial states.

This study is devoted to control of fluid networks subject to random disturbance. Adopting stochastic differential equation theory, an improved model is presented to incorporate not only the non-linearities induced by fan branch but also random disturbances. On the basis of the model, combining decentralised control and adaptive control techniques, the mean square exponential stability is proposed. According to the proposed stability, the desired equilibrium of fluid flows could be ensured by setting controllers just related to links. Two engineering examples are provided to show the effectiveness of the proposed method.

In this study, a predictor-based output feedback control design is proposed for sampled systems with input delay subject to disturbance. An extended state observer (ESO) is first constructed to simultaneously estimate the system state and disturbance based on only the output measurement. Then a filtered predictor is constructed by using the estimated state and disturbance to compensate the input delay so as to improve the disturbance rejection performance. For the presence of a constant or asymptotically stable disturbance, a robust H infinity feedback control design based on state prediction and disturbance estimation is proposed to realise no steady-state output error, despite mismatched disturbance. When there exists a time-varying disturbance with deterministic dynamics, such as a sinusoidal type, the proposed predictor can achieve a small prediction error by properly tuning the filter, such that the existing observer-based feedback control methods for delay-free systems can be directly adopted to stabilise such a system with input delay. Moreover, the output error bounds in the presence of time-varying disturbance are quantitatively analysed for using the ESO-based predictor feedback and anti-disturbance predictor feedback, respectively. Two illustrative examples are given to demonstrate the effectiveness and merit of the proposed method.

The authors present an integrated approach for designing low-order multi-objective controllers for linear time-delay systems (TDSs), combining recently developed methods for reduction of delay systems and fixed-order control design, respectively. As a benchmark problem for process control applications, a model of an experimental heat transfer setup is used, which serves to motivate the adopted combination of model reduction and control technique. The former corresponds to a Krylov based reduction procedure, which is generalised to multiple-input-multiple-output systems with state, input and output delays, and allows the adaptive construction of an accurate low-order linear time-invariant approximation of the original linear TDS. Concerning the latter, a fixed-order controller is synthesised for the delay-free approximation, exploiting a recently proposed linear matrix inequality based framework for fixed-order controller design, and validated on the original model. In this way, the systematic overall design procedure, which is grounded in convex optimisation, complements approaches based on directly optimising stability and performance measures as a function of the controller parameters, which may lead to highly nonconvex, even non-smooth optimisation problems. The successful design of a fixed-order multi- controller is validated on the benchmark problem, confirming the potential of the adopted approach for realistic industrial applications.

This study investigates the design of an optimal linear estimator for a class of discrete-time linear systems with correlated stochastic parameter matrices and noises. The considered systems are endowed with the following two main features: (i) cross-correlated stochastic matrices involved in the state and observation equations are assumed and (ii) the process and observation noises have cross-correlation at the same time instant. A decorrelation framework is established to reconstruct such systems. With the equivalent transformation of original dynamic systems resulting from decorrelating operations, the optimal linear recursive filter in the minimum mean square error sense is developed by employing the results of Kalman filtering. The discrete-time linear systems with multiple packet dropouts are modelled as a particular case, and then the proposed filter is applied directly to estimate the system state, while a comparative analysis between the new method and the existing approaches is provided. Simulations demonstrate the effectiveness of the presented algorithm.

This study investigates the leader-following consensus problem for non-linear multi-agent systems with semi-Markov switching topologies. The dynamics of the leader agent and the follower agents is described by a general linear system. Since the transition rates of the semi-Markov switching topologies are time-varying, they are more general and practicable than the classic Markov switching topologies. A novel consensus protocol based on outdated states is proposed for multi-agent systems. By a system transformation, the consensus problem of multi-agent systems is converted into the stability problem of semi-Markov switching systems. The controller design condition is derived utilising the semi-Markov jump system theory and algebraic graph theory, which can guarantee that the multi-agent systems achieve a consensus with an exponential decay rate. A numerical example is given to illustrate the effectiveness of the proposed method.

This study investigates the synchronisation problem of a class of output-coupling complex networks whose nodes are in the output feedback form and contain unknown non-linear functions. To tackle the unknown parameters in the non-linear nodes, adaptive dynamic output feedback controllers are designed. By employing the linear matrix inequality technique, several sufficient conditions are derived to ensure the global asymptotic synchronisation for the resulting closed-loop systems. An illustrative numerical example is given to show the effectiveness of the main results.

The authors investigate the control problem for autonomous vehicle with both the uncertain kinematics and dynamics. The authors propose a triple-step control scheme to realise the objective of the path following irrespective of the uncertain kinematics and dynamics. The proposed control strategy has the desirable modularisation property that yields an explicit expression without the expense of complicated control structure. The performance of the proposed controller is shown by benchmark simulations.

This study addresses robust attitude tracking of a spacecraft without unwinding by considering external disturbances and uncertain inertia parameters. Quaternion is used to represent the relative attitude for attitude tracking, thus the closed-loop system has two equilibria. A desired equilibrium is determined from them according to the sign of the initial relative attitude quaternion such that less rotation is required for attitude tracking. A backstepping scheme based on similar skew-symmetric structure is adopted to design the attitude controller. Two compensation terms are introduced to deal with the uncertainties. A parametric condition is provided to guarantee that the attitude tracking has an exponentially convergent speed without unwinding. The related parametric regulation is addressed for response speed, robustness and disturbance attenuation. It is shown that arbitrarily fast response and any specified tracking precision can both be achieved by regulating the related parameters of the proposed controller. Compared with the related research, a variable gain term is included in the proposed controller. Accordingly, the controller has relatively slower gain in the system response, thus large control amplitude is avoided. Furthermore, the controller has much higher gain in the steady state such that much higher control precision can be obtained for a given control amplitude when compared with other attitude tracking controllers. Simulations are carried out to validate the effectiveness of the proposed attitude controller.

This study addresses the control synthesis of positive switched systems in both continuous- and discrete-time contexts. First, a novel design approach to the state-feedback controller of continuous-time positive switched systems without time delay is presented by virtue of multiple linear copositive Lyapunov functions associated with linear programming. Then, the design approach is extended to discrete-time positive switched systems. It is shown that the presented approach is less conservative than existing ones through comparisons. Furthermore, the approach is developed to the stabilisation of positive switched systems with time delay. Some discussions on the presented approach are provided to show potential applications in corresponding control issues of positive switched systems. Finally, two examples are given to illustrate the theoretical findings.