Almost all of the available literature on secure state estimation focus on sensor attacks. Unlike the existing results, this study investigates the attack-resilient state estimation problem for continuous-time linear systems with sparse actuator attacks and process noises. It is assumed that, the attacker has limited resources and can only manipulate a certain number of actuators. Specifically, a novel switched observer is proposed with milder design conditions which are derived in terms of linear matrix (in)equalities. It is shown that, the observer not only provides an attack-resilient state estimation, but also guarantees that the resulting observer error system is with noise attenuation level which can be optimised. Finally, a simulation example of a linearised reduced-order aircraft system is provided to show the effectiveness of the proposed approach.

A tube-based robust model predictive control (MPC) is proposed to be applied in constrained linear systems with parametric uncertainty. An estimation method is applied in this proposed technique to adapt the system model at each sampling time and to reduce the conservatism nature of the tube-based MPC as the system model approaches the real model as time passes. By updating the subject model online through this newly proposed approach the performance of the system is improved. Asymptotic stability of the closed-loop system is established. The simulation results of a DC motor are applied to illustrate the effectiveness of this proposed controller in dealing with one practical system.

This study investigates an control problem for a class of stochastic non-linear systems where the measurement outputs subject to randomly occurring sensor saturations are transmitted through the network link and will inevitably encounter the random delays and multiple packet dropouts. The network-induced phenomena have the random nature which is governed by Bernoulli distributed stochastic variables. The existence of transmission delays will lead to the packets arriving at the receiver side with one or multiple or none at each sampling instants, which are stored in a finite buffer and are all used to update the observer. By employing stochastic analysis and Lyapunov functional approaches, an observer-based non-linear controller is designed via linear matrix inequality technique. The asymptotic stability with a given disturbance attenuation level is guaranteed by solving the feasibility of certain LMI. A simulation example is exploited to illustrate the usefulness and effectiveness of the proposed method.

This study is concerned with a stabilisation problem of a boundary controlled fractional reaction diffusion (FRD) system with mixed or Robin boundary conditions. The contribution of this study is to utilise boundary feedback control to stabilise the FRD system with mixed or Robin boundary conditions in terms of the backstepping method. Specifically, three backstepping-based boundary feedback controllers have been proposed to address the stabilisation problem of the FRD system with mixed or Robin boundary conditions, including Dirichlet, Neumann, and Robin backstepping-based boundary feedback controllers. Moreover, based on Lyapunov-based Mittag–Leffler stability theory, we prove that the FRD system with mixed or Robin boundary conditions is Mittag–Leffler stable by the proposed three backstepping-based boundary feedback controllers. Finally, the numerical efforts of the open-loop and the closed-loop solutions of the FRD systems with mixed or Robin boundary conditions are presented by two numerical experiments to verify the validness of our results.

Considering filter gains with additive interval variations, this study is devoted to the non-fragile filtering of linear systems with an event-triggered transmission. To take into account the influence of these variations thoroughly, a structured vertex separator is adopted to alleviate the computation burden. Combining the Finsler lemma, conditions of designing the non-fragile filter to ensure the required performance are formed by linear matrix inequalities. Compared to the norm-bounded method to handle the variations, the proposed method could provide less conservative results. Simulations are executed to show the validity of the proposed method.

A particularproblem in aerospace control and applications is the active target defence differential game (ATDDG), where an attacker missile tries to capture a target aircraft which is significantly slower than the attacker. A third agent is a defender missile which is fired by the Target's wingman. The defender's mission is to intercept the attacker in time to enable a successful target evasion and its survival. The problem is naturally posed as a zero-sum DG. The target and the defender form a team; their objective is to determine a cooperative strategy to maximise the terminal separation between the target aircraft and the point where the Attacker missile is intercepted by the Defender missile. The Attacker is the opposition and its task is to devise its own strategy to minimise the same terminal distance. The solution of the ATDDG provides the instantaneous optimal heading angles for each agent playing the game in order to achieve their objectives. Most importantly, the agents' strategies are state feedback laws. The assumption of simple motion dynamics of the agents yields their optimal headings which is adequate in a beyond visual range engagement, as it is currently envisioned to be the pertinent operational scenario.

This study investigates the adaptive neural dynamic surface control (DSC) of output constrained non-linear systems, subject to unknown system dynamics and uncertain control direction. A Nussbaum-type dynamic gain algorithm is used to handle the effect of unknown control direction. Integral barrier Lyapunov functions (iBLFs) are directly utilised to tackle the effect of output constraint. The prominent feature of iBLFs is that the feasible initial output signals are relaxed to the whole constraint range compared with pure tracking errors-based barrier Lyapunov function. Also, the DSC technology is developed to avoid the explosion of complexity in traditional control design, and adaptive neural networks are adopted to estimate the uncertainty that comprises the unknown system dynamics and parametric uncertainties. By utilising Lyapunov synthesis, it is proven that the proposed control is able to guarantee semi-global uniformly ultimately bounded of all signals in the closed-loop system. Simulation results are provided to verify the effectiveness of the proposed approach.

A robust output feedback active fault-tolerant leader-following controller for a class of non-linear multi-agent systems is presented. It is assumed that the states of the followers are not available; therefore, a local observer is constructed to estimate the states of each agent. In addition, the non-linear dynamics of agents may include uncertainties and the control input of the leader dynamics is unknown to all followers. Moreover, taking advantage of wavelet neural networks (WNNs), an online fault estimation scheme is developed which can effectively approximate the unknown actuator faults. The proposed decentralised observer-based robust cooperative controller is capable of compensating for the effects of unknown time-varying additive actuator faults, the model uncertainties, and the unknown input of the leader simultaneously. The stability analysis and convergence results that guarantee boundedness of all closed-loop signals are investigated via Lyapunov's direct method. To demonstrate the effectiveness of the proposed approach, a network of single-link manipulators is studied. As the results verify, the proposed WNN-based fault estimation scheme can properly approximate the unknown actuator faults, which results in efficient compensation in the fault-tolerant control design to achieve cooperative tracking objectives.

In this study, decentralised adaptive control is investigated for a class of discrete-time non-linear hidden leader–follower multi-agent systems (MASs). Different from the conventional leader–follower MAS, among all the agents, there exists a hidden leader that knows the desired reference trajectory, while the follower agents know neither the desired reference signal nor which is a leader agent. Each agent is affected from the history information of its own neighbours. The dynamics of each agent is described by the non-linear discrete-time auto-regressive model with unknown parameters. In order to deal with the uncertainties and non-linearity, a projection algorithm is applied to estimate the unknown parameters. Based on the certainty equivalence principle in adaptive control theory, the control for the hidden leader agent is designed by the desired reference signal, and the local control for each follower agent is designed using neighbourhood history information. Under the decentralised adaptive control, rigorous mathematical proofs are provided to show that the hidden leader agent tracks the desired reference signal, all the follower agents follow the hidden leader agent, and the closed-loop system eventually achieves strong synchronisation in the presence of strong couplings. In the end, the simulation results show the validity of this scheme.

In this study, neuro-fuzzy-based identification procedure for Hammerstein model with coloured noise is presented. Separable signal is used to realise the decoupling of the identification of dynamic linear part from that of static non-linear part, and then correlation analysis method is adopted to identify the parameters of the linear part. Furthermore, by combining multi-innovation and gradient search theory, multi-innovation-based extended stochastic gradient approach is derived for improving the parameters estimation accuracy of the non-linear part and the noise model. In addition, the convergence analysis in the martingale theory illustrates that the parameter estimation error will converge to zero under the persistent excitation condition. Finally, two simulation results demonstrate that the proposed approach has high identification accuracy and good robustness to the disturbance of coloured noise.

A new concept of accepting performance degradation, which evaluated by converging rate and stability, is proposed for switched systems. The relation between the converging rate of the whole switched system and the eigenvalues of each subsystem is established, based on which the accepting performance degradation is evaluated quantitatively in the presence of process and actuator faults. The derived results are further verified by the simulation of an application to the highly manoeuvrable technology vehicle model.

In this study, a novel control strategy of a three-inline array tethered spacecraft formation is proposed, based on a simplified non-linear model around the equilibrium point. The formation stability is analysed by using an interconnected system approach which deeply reveals the coupling characteristic among three spacecraft. It is shown that both individual control laws of spacecraft and the coupling effects can achieve the stability. The problems of fault-tolerant control and fault propagation are further discussed. Simulation results validate the effectiveness of the proposed methods.

This study presents a successful application of a model predictive control (MPC) design approach based on linear parameter-varying (LPV) models subject to input/output constraints to control a utility-scale wind turbine. The control objectives are to allow the wind turbine to extract from the wind the rated power taking into account the wind speed variation, to reduce mechanical loads and power fluctuations and to guarantee the stability of the system for the whole range of operation. A modified min–max MPC-LPV scheme is proposed to compute online the optimal control input at each sampling instant by solving an optimisation problem subject to linear matrix inequality constraints. To reduce the conservatism of the original MPC scheme due to the overbounding associated with affine parameter-dependence, the full block S-procedure with a linear fractional transformation formulation is used. The performance and the efficiency of the proposed MPC-LPV algorithm is validated via simulation and compared with the original scheme and other conventional controllers.

A new model reduction (MR) method is developed for continuous-time switched linear parameter-varying (LPV) systems based on time-weighted gramians. Using time-weighted energy functionals and parameter-independent multiple Lyapunov functions, the time-weighted controllability and observability gramians are obtained. With a balanced transformation matrix optimally derived, the authors show that a balanced realisation can be achieved for the original switched LPV systems. A series of low-order models for different weighting factors are yielded by state truncation or singular perturbation techniques. The reduced-order models can preserve the stability. The feasibility and effectiveness of the proposed MR method are illustrated by two examples including a three spring-mass system.

This study investigates sliding mode control (SMC) for non-linear networked control systems (NCSs) subject to packet disordering as well as external disturbances. The main objectives of the proposed method are to predict packet disordering and to stabilise the NCSs in case of the unknown packet disordering in the future. Firstly, linearisation of non-linear systems and the technology of adopting the newest control input with a stochastic parameter are employed to model the system as a linear Markovian jumping system. Secondly, with the application of a time series prediction model, the phenomenon of disordering better under the novel measurement is portrayed. Then, robust SMC is designed by solving the linear matrix inequalities (LMIs). Finally, examples with sampled disordering packets are simulated to illustrate the effectiveness and advantages of the proposed method.

This study investigates the problem of sampling period assignment and design of digital state feedback controllers for systems subject to time-varying sampling periods and uncertain delays. The system is controlled through a communication network, where the sampling period and the network-induced delay are bounded in a known interval. The sampled system is described by a linear parameter-varying discrete-time model obtained by means of the Cayley–Hamilton theorem. The proposed discretisation procedure improves the current approaches in the literature and allows the design of controllers that are robust to the delay and depending on the sampling period defined by a scheduling policy in a scenario with concurrent access to the communication network by multiple plants. The gain-scheduled linear quadratic controller is designed by means of linear matrix inequalities. The policy to access the network is dynamic and formulated as an optimisation problem. Numerical experiments illustrate the efficiency and the validity of the proposed approach.

This study investigates the aerodynamic effects and the tracking control problem of quadrotor-type unmanned aerial vehicles. The authors first present the on-line identification of the aerodynamic parameters by using the recursive least squares algorithm based on the measurement outputs of the accelerometer. Then, the non-linear discrete-time trajectory tracking controllers with aerodynamic compensation have been designed. Through identifying and compensating the external aerodynamics on line, the simulation results show that the tracking performance has been enhanced, especially when the vehicle is in some flight envelopes where the aerodynamics have significant effects on the quadrotor dynamics, such as the large-acceleration flight regime.

In this study, the authors investigate the problem of finite-time output regulation for a class of mismatched uncertain n-dimensional integrator, in which only the output signal is measurable and the higher derivatives of the matched and mismatched disturbances are bounded by time-varying functions. Based on a finite-time extended state observer, an output feedback controller is constructed. It is shown that even in the presence of mismatched uncertainties, whose high-order derivatives are bounded by positive functions, the output of the system can be regulated to zero in finite time without requiring the knowledge of full-state signals. An application to mass-spring mechanical systems is given to illustrate the effectiveness and attractive properties of the authors' proposed controller.

This study develops a scheme of an adaptive fuzzy dynamic surface control (DSC) for a non-linear non-strict feedback system with immeasurable states. By utilising the universal approximation property of a fuzzy logic system, a state observer is designed to estimate the unmeasured states. Based on the back-stepping DSC design technique, an adaptive fuzzy output feedback control design method is developed. The proposed method can overcome the ‘explosion of complexity’ problem, and also can eliminate the limitation of the measurable states. It is proved that the control method can guarantee that all the signals in the closed-loop system are bounded and the system output can track the given reference signal well. The simulation results are provided to demonstrate the effectiveness of the proposed control method.

This study studies the output tracking control of a class of sandwich-like systems with state-dependent deadzone non-linearity between two cascaded subsystems (e.g. the gear transmission systems). An exact differentiator-based backstepping control for such a sandwich-like non-linear system is proposed. The proposed controller utilises the high-order sliding mode robust exact differentiator to compensate the impact of non-strict feedback coupling term due to the sandwiched deadzone. The stability of the closed-loop system is guaranteed to be uniform-ultimately bounded and the output tracking error converges to a residual set. Finally, two simulation examples are provided to demonstrate the tracking performance and effectiveness of the proposed controller.

In this study, the authors developed a novel universal approximator by the integration of Petri networks into type 2 fuzzy neural networks (T2FNN). T2FNN involve large number of rules, which result in heavy computational burden and great computation time. By incorporating Petri layers to optimise the number of rules; these two drawbacks could be very well overcome. Moreover, a new inference type 2 fuzzy system was developed to reduce the time consumed in the iterative K–M inference procedure, and to increase the approximation accuracy. The proposed inference engine is based on the use of an adaptive modulation of the upper and the lower outputs. The Petri type 2 fuzzy neural networks (PT2FNN) approximator was used to approximate the adaptive control for uncertain single-input single-output non-linear system. The stability of the closed-loop system was proven and demonstrated using the Lyaponov approach. Comparative studies of the proposed PT2FNN approximator with type 1 fuzzy neural network and T2FNN were performed. The performances of PT2FNN over the two types of the fuzzy system were shown on the inverted pendulum system.

An integral–proportional derivative (I–PD) control strategy for integrating plus time-delay processes is proposed. The proposed scheme consists of an inner PD loop and an outer I-loop for taking care of the servo as well as the regulatory action. Explicit formulas for tuning of the proposed controller are derived in terms of gain margin, phase margin and critical gain. Moreover, pole-placement and frequency loop-shaping design methods are also explored for designing the I–PD controller. Simulation results show the superiority of the proposed I–PD controller over conventional P/PI/PID ones for integrating processes. The design is also validated through experiments on a temperature control process.

This study provides a new parameterisation for a special class of nested-saturation controllers, in which some multiplying coefficients appear before saturation functions. In an existing saturation scheme for the chain of integrators, the saturation levels and the multiplying coefficients are separately assigned in two stages, namely determined in the reduction analysis of saturated terms and the stability analysis of a reduced system. In the new parameterisation, it is in the saturation reduction analysis that the mentioned parameters are already determined. Such a convenient parameterisation is also applied to the uncertain multiple integrators and some mechanical systems.

In this paper, the stability analysis for interval type-2 (IT2) polynomial fuzzy-model-based (PFMB) control system using the information of membership functions is investigated. To tackle uncertainties, IT2 membership functions are used in the IT2 polynomial fuzzy model and IT2 polynomial fuzzy controller. The stability of IT2 PFMB control system is investigated based on the Lyapunov stability theory and both sets of membership function independent (MFI) and membership function dependent (MFD) stability conditions are derived on the basis of the sum-of-squares (SOS) approach. To make the stability conditions MFD, the boundary information of IT2 membership functions is used in the stability analysis. To extract richer information of IT2 membership functions, the operating domain is partitioned into sub-domains. In each sub-domain, the boundary information of IT2 membership functions and those of the upper and lower membership function are obtained. Furthermore, to further relax the conservativeness, a switching polynomial fuzzy controller, together with the informations obtained in each sub-domain, is employed in investigating the stability analysis. Numerical examples and simulation results are given to demonstrate the validity of MFD and MFD switching methods.

In this study, a high gain observer with delayed driving control signal is designed for synchronisation of fractional-order chaotic systems. The method consists in using two cascade high gain observers in order to compensate for the delay transmission signal from the transmitter to the receiver. For large delay, a fractional-order chain observer composed by high gain cascade delayed observers is proposed. The last observer of this chain estimates the state at the current time while previous observers estimate delayed states. Convergence of the proposed observer is proven. Application to the synchronisation of fractional-order chaotic systems is given. Computer simulations show the effectiveness of the proposed approach.

This study is concerned with the fault-tolerant (FT) formation control problem with a guaranteed performance for non-linear multi-vehicle systems subject to actuator faults. The authors consider a practical situation: the information transferred between adjacent vehicles is disturbed and each vehicle is interfered by stochastic disturbance and measurement noise. For each vehicle, a decentralised state observer and an adaptive fault estimator are designed based on which a novel cooperative FT control (FTC) protocol is proposed to drive all the vehicles to the desired formation configuration. Taking the system noise into consideration, the error dynamics are modelled by stochastic differential equations, whose properties are used for designing and analysing the Lyapunov function in the framework of calculus. It is proved that the formation error system is mean-square asymptotically stable with a prescribed attenuation level in an sense by the proposed FTC scheme. The observer, estimator and controller gains can be obtained by solving algebraic Riccati inequalities. Finally, the theoretical results are illustrated by simulations and real experiments.

In this study, the authors propose a control structure for a class of linear time-invariant (LTI) systems with Lipschitz non-linearity and unknown time-varying input delay. This scheme considers the worst-case scenario in control design with truncated prediction feedback approach, and takes into account the information of the lower bound of delay in the stability analysis. A finite-dimensional controller is constructed, requiring neither the non-linear function nor the exact delay function. The truncated prediction deviation is minimised by employing the delay range, and then bounded by integral construction and related techniques. Within the framework of Lyapunov–Krasovskii functionals, sufficient delay–range-dependent conditions are derived for the closed-loop system to guarantee the global stability. Two numerical examples are given to validate the proposed control design.

There is spatio-temporal nature for many multi-agent systems such as infight hose-and-drogue aerial refuelling systems. To deal with consensus control of such cases, this study establishes a non-linear leader-following spatio-temporal multi-agent system modelled by partial differential equations. Initially, a boundary controller based on boundary coupling is studied to ensure consensus of the multi-agent system. A sufficient condition on the existence of the controller for consensus is presented in terms of linear matrix inequalities. To simplify the obtained result, a second boundary controller is studied and a simple sufficient condition of its existence is investigated. Finally, two numerical examples demonstrate the effectiveness of the proposed methods. The merits of the proposed controllers lie in making use of only spatial boundary communication and requiring actuators and sensors only at spatial boundary positions.

This study presents the consensus of a saturated second-order multi-agent system with non-switching dynamics that can be represented by a directed graph. The system is affected by data processing (input delay) and communication time-delays that are assumed to be asynchronous. The agents have saturation non-linearities, each of them is approximated into separate linear and non-linear elements. Non-linear elements are represented by describing functions. Describing functions and stability of linear elements are used to estimate the existence of limit cycles in the system with multiple control laws. Stability analysis of the linear element is performed using Lyapunov–Krasovskii functions and frequency domain analysis. A comparison of pros and cons of both the analyses with respect to time-delay ranges, applicability and computation complexity is presented. Simulation and corresponding hardware implementation results are demonstrated to support theoretical results.

This study addresses the issue of robust control for a class of discrete-time delayed non-linear systems in the presence of controller failure by using a probability-dependent method. Considering the stochasticity and inevitability of controller failure, they propose a notion of controller probabilistic failure. Based on the idea of switching, the studied systems are converted into a kind of stochastic switched systems. When the probability information is available, a probability-dependent switching strategy is developed by application of piecewise Lyapunov function and average dwell time approaches such that the system is exponentially mean square stable with weighted performance. At the same time, a probability-dependent weighted switching controller is designed. Moreover, the obtained results are also shown to be feasible when the probability information cannot be known accurately. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.