In this study, the problem of fault detection (FD) observer design for discrete-time Lipschitz non-linear systems with finite-frequency specifications is investigated. The finite-frequency and indices are introduced to measure the robustness to unknown disturbances and the sensitivity to faults, respectively. Based on the use of a reformulated Lipschitz property, the non-linear error dynamics are transformed into a linear parameter varying (LPV) system. A new lemma is proposed to characterise the system performances in finite-frequency domain. To reduce the conservativeness of the multi-objective problem, slack variable techniques are used to obtain the sufficient conditions for the design of FD observer which are derived in terms of linear matrix inequalities (LMIs). The proposed design method can provide less restrictive LMI conditions and achieve a better FD performance than the existing one in full frequency domain. Two numerical examples are given to show the effectiveness and superiority of the new results.

A flexible crane system with vibrating and varying cable is investigated in two-dimensional space. Two partial differential equations and four ordinary differential equations derived by the Hamilton's principle are used to describe the dynamics of the flexible crane system. The dynamic model of the crane system considers the variation of the tension of the cable. Boundary control design is given to suppress vibrations of the flexible crane system. The Lyapunov's direct method is employed to prove the uniform ultimate boundedness of the states of the cable system. The effectiveness and performance of the proposed control schemes are depicted via numerical simulations.

This study addresses the filter design issue for fuzzy Markov stochastic systems with sensor failures and packet dropouts. A more general failure model is used for Markov systems to better describe the sensor failures, and the packet dropouts are assumed to obey a series of Bernoulli processes which are formed into a diagonal matrix. Sufficient condition is established to guarantee that the filtering error system is stochastically stable and achieves the given performance. The parameters of the filter are then derived by solving linear matrix inequalities. Simulation results are given to demonstrate the usefulness and availability of the proposed method.

A novel memory scheduling robust fault detection filter (FDF) is proposed for a class of discrete-time polytopic uncertain systems with fading channel communication networks. The main merit of this filter-based fault detection method is that it can significantly improve the robustness of FDF to attenuate influences from external disturbance, channel fading and model uncertainty on fault detection accuracy. Designing such FDF involves three main stages. First of all, a memory scheduling FDF structure is proposed based on the utilisation of weighted historical filter's states over interval instants, and a residual error system is formulated based on time partition and state augmented approaches. Then, the parameter-dependent Lyapunov method is further utilised to analyse the stochastic stability of the residual error system with the help of Finsler equivalent transformation. In the following, a two-stage optimisation algorithm combined with scalar parameters method is constructed to design memory scheduling FDF in a less conservative linear matrix inequality manner. Finally, a random numerical verification with 300 test systems and a case study of an industrial continuous-stirred tank reactor are exploited to show the effectiveness of obtained results.

This study addresses the distributed state and output feedback coordinated tracking problem for multiple Euler–Lagrange systems with a moving leader in the presence of non-linear uncertainties under a directed topology graph. The authors first design a distributed coordinated tracking control scheme by full-state feedback, where each follower can only share information with its neighbours. Next, the adaptive neural networks are applied to deal with the model uncertainties due to their superior approximation capability. To deal with the absence of velocity sensors, then they propose a distributed output feedback coordinated tracking control law combined with a high-gain observer. The uniform ultimate boundedness of all the state errors can be guaranteed in the sense of Lyapunov stability theory. Furthermore, the leaderless synchronisation problem is solved using the proposed control schemes. Finally, simulation examples are presented to illustrate the feasibility of the theoretical results.

The main purpose of this study is to present a simple design method to synthesise the adaptive robust controllers for a class of uncertain strict-feedback non-linear systems with delayed state perturbations and external disturbances. In this study, such a simple design method is presented so that (i) the presented design method is easy to understand for the system designers; (ii) it is not necessary to know any information on the upper bound functions of non-linear delayed state perturbations and the non-linear functions due to the derivatives of the fictitious control functions to construct some state feedback control schemes; and (iii) the resulting adaptive robust control schemes are simple and easy to implement in practical engineering control problems. The adaptive robust controllers synthesised by the presented design method have a rather simple structure, and can guarantee the uniform exponential boundedness of the considered uncertain strict-feedback non-linear time-delay systems. A numerical example is provided to illustrate the authors' simple design procedure and the corresponding simulations are made to demonstrate the validity of the theoretical results.

This study proposes a fault estimation (FE)-based fault-tolerant control (FTC) strategy to maintain system reliability and achieve desirable control performance for a 3-DOF helicopter system with both actuator drift and oscillation faults and saturation. The effects of the faults and saturation are combined into a composite non-differentiable actuator fault function, which is approximated by a differentiable function and estimated together with the system state using a non-linear unknown input observer. An adaptive sliding mode controller based on the estimates is developed to compensate the effects of the faults and saturation. Taking into account the bi-directional robustness interactions between the FE and FTC functions, an integrated design approach is proposed to obtain the observer and controller gains in a single step, so as to achieve robust overall FTC system performance. In fault-free cases, the proposed strategy can be considered as a new approach for anti-windup control to compensate the effect of input saturation. Comparative simulations are provided to verify the effectiveness of the proposed design under different actuator fault scenarios.

A controller design method is presented for one-sided Lipschitz Markovian jump systems with partially unknown transition probabilities. By using the proposed controllers, it can be guaranteed that the state trajectories starting from a given region remain in it (without disturbances) or a bigger one (under disturbances), where the local one-sided Lipschitz and quadratically inner-bounded conditions can be satisfied. In addition, an observer-based controller is designed to stabilise the system without the requirement that the system states are measurable. Finally, two examples are given to illustrate the effectiveness of the proposed scheme.

The focuses of this study are the vibration control and constraint problems of an input and output constrained flexible marine riser system, in which system parametric uncertainties are taken into account. Through the combination of integral-barrier Lyapunov function (IBLF), backstepping technique and adaptive technique, an adaptive Lyapunov-based barrier control with an auxiliary system is developed aiming at achieving the control purposes of vibration suppression and constraint satisfaction, where the auxiliary system is to compensate for the input saturation, IBLF is to solve the output constraint and adaptive laws are to handle the parametric uncertainties. In addition, disturbance observer is designed in the barrier term of IBLF, which could attenuate the effects of unknown boundary disturbance. With the proposed control, the uniform boundedness and stability of the closed-loop system are easily achieved. Finally, the significance of the proposed control is demonstrated via numerical simulation.

A control scheme for boost power converters based on current-mode control is given. The proposed methodology relies on the design of two feedback loops. An outer loop for steady state error compensation using a proportional-integral action and a non-linear inner loop for current tracking. A dynamic backstepping controller with a well-defined region of attraction, ensuring asymptotic stability via a Lyapunov function, is achieved. The closed-loop system performance is evaluated through experimental results for a 130 W boost power converter with the controller implemented in a dSPACE platform, where precise regulation, tracking and robust behaviour with respect to large unknown load variations are proven successful.

In this study, the problems of stabilisation for interval type-2 polynomial fuzzy systems with time-varying delay and parameter uncertainties are investigated. The objective is to design a state-feedback interval type-2 polynomial fuzzy controller such that the closed-loop control system is asymptotically stable. The conditions for the existence of such a controller are delay dependent and membership function dependent in terms of sum-of-squares (SOS). Based on a basic lemma to deal with the delay terms, the authors formulate and solve the problem with more flexibility due to imperfect premise matching that the number of rules and premise membership functions are not necessary the same between the interval type-2 polynomial fuzzy model and interval type-2 polynomial fuzzy controller. Piecewise linear membership functions approximations enclosing the original lower and upper membership functions are employed to facilitate the stability analysis. A numerical example indicates the effectiveness of the derived results.

This study will investigate the distributed linear quadratic (LQ) control problem for discrete identical uncoupled multi-agent systems with a global performance index coupling the behaviour of the multiple agents. An existence condition to the optimal distributed LQ controller is given first. In general, such condition can be checked by solving a discrete algebraic Riccati equation through a numerical method. When the condition fails to hold, a suboptimal distributed controller design method is proposed for a class of LQ performance. The solution can be obtained by solving two local algebraic Riccati equations whose dimension is the same as a single agent. The stability condition is given in terms of the spectrum of a matrix representing the desired sparsity pattern of the distributed controller. Comparing to the centralised control, the computation and communication complexity is much lesser. Finally, the suboptimality is parameterised, and can be measured by solving a Lyapunov equation.

In this study, the adaptive tracking control is investigated for a class of stochastic pure-feedback non-linear time-delay systems with output constraint and asymmetric input saturation non-linearity. First, the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation model, and the barrier Lyapunov function is designed to cope with the output constraints. Then, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to address the effects of the unknown time-delay terms, and the neural network is employed to approximate the unknown non-linearities. At last, based on Lyapunov stability theory, a robust adaptive neural controller is proposed, which decreases the number of learning parameters and thus avoids the over-estimation problem. Under the designed neural controller, all the closed-loop signals are guaranteed to be 4-moment (or 2 moment) semi-globally uniformly ultimately bounded and the tracking error converges to a small neighbourhood of the origin for bounded initial conditions. Two simulation examples are presented to further illustrate the effectiveness of the designed method.

This study investigates the sampled-data containment control problem for linear multi-agent systems with multiple leaders under undirected or directed network topology. First, by means of the decomposition method, the containment control problem is transformed into the simultaneous stability analysis issue of certain subsystems. Then, the solution of a class of differential equations, which plays a key role for the addressed problem, is exploited by using the contradiction method. Together with a novel Lyapunov function, sufficient conditions are established to guarantee that all the followers move into the convex hull spanned by the leaders. The proposed results are dependent on the information of the system dynamics, the coupling strength as well as the eigenvalues of topology matrix. Furthermore, the established results are specialised to both the leader–following case and the traditional consensus case. Finally, simulations are given to illustrate the theoretical results derived in this study.

The design of robust controllers for continuous-time (CT) non-linear systems with completely unknown non-linearities is a challenging task. The inability to accurately identify the non-linearities online or offline motivates the design of robust controllers using adaptive dynamic programming (ADP). In this study, an ADP-based robust neural control scheme is developed for a class of unknown CT non-linear systems. To begin with, the robust non-linear control problem is converted into a non-linear optimal control problem via constructing a value function for the nominal system. Then an ADP algorithm is developed to solve the non-linear optimal control problem. The ADP algorithm employs actor-critic dual networks to approximate the control policy and the value function, respectively. Based on this architecture, only system data is necessary to update simultaneously the actor neural network (NN) weights and the critic NN weights. Meanwhile, the persistence of excitation assumption is no longer required by using the Monte Carlo integration method. The closed-loop system with unknown non-linearities is demonstrated to be asymptotically stable under the obtained optimal control. Finally, two examples are provided to validate the developed method.

This study addresses the problem of quasi-synchronisation of fractional-order memristor-based neural networks (FMNNs) with time delay in the presence of parameter mismatches. Under the framework of fractional-order differential inclusions and set-valued maps, quasi-synchronisation of delayed FMNNs is discussed and quasi-synchronisation criteria are established by means of constructing suitable Lyapunov function, together with introducing some fractional-order differential inequalities. A new lemma on the estimate of Mittag–Leffler function is derived first, which extends the application of Mittag–Leffler function and plays a key role in the estimate of synchronisation error bound. Then, linear state feedback combined with delayed state feedback control law is designed, which guarantees that for a predetermined synchronisation error bound, quasi-synchronisation of two FMNNs with mismatched parameters will be achieved provided that the feedback gains satisfy the newly-proposed criteria. The obtained results extend and improve some previous published works on synchronisation of FMNNs. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.

Leader-following consensus is investigated for second-order continuous-time multi-agent systems with limited communication data rate in this study. The network communication topology is directed and static. Using the sampled position and velocity data, a corresponding discrete-time system, whose leader-following consensus is proved to be equivalent to that of the original system, is given. A distributed protocol is proposed based on dynamic encoding and decoding. A necessary and sufficient condition is given for the existence of such communication and control protocol to ensure the achievement of leader-following consensus, if the upper bound of the communication data rate is predetermined. Two algorithms are also presented to achieve the leader-following consensus if the communication data rate is unfixed or limited, respectively. Finally, simulation examples are given to verify and illustrate the theoretical analysis.

This study provides a solution to the problem of applying the active disturbance rejection control (ADRC) approach to the tracking control of pure feedback non-linear systems with large uncertainties. The design is based on the backstepping technique, and in each step two extended state observers (ESOs) are designed, one to approximate the derivative of the virtual control generated from the last step, while the other to estimate the system uncertainty. A key feature of the developed backstepping ADRC is that the activations of the ESOs are delayed successively. It is proved that under the new backstepping scheme, the closed-loop signals are guaranteed to be semi-globally uniformly ultimately bounded and the output tracking error can be made arbitrarily small.

In blast furnace ironmaking operation, the molten iron temperature and the silicon content ([Si]) are two key molten iron quality (MIQ) indices. The measurement, modelling and control of these indices have always been of importance in metallurgic engineering and automation. In this study, data-driven methods for online prediction and control of multivariate MIQ indices are proposed by integrating hybrid modelling and control techniques together. First, a data-driven hybrid method that combines canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modelling inputs from multitudinous factors. Then a data-driven online model for prediction of MIQ is established by recursive subspace identification (R-SI) with forgetting factor. Unlike the conventional SI modelling, the proposed R-SI-based online modelling only identifies subspace matrices for a data-driven input–output model without explicitly estimating the system matrices, which can reduce the computation complexity. Finally, a predictive controller is designed to maintain the MIQ indices at an expected level by using the developed MIQ prediction model as an online predictor. Since the parameters of the predictor are updated adaptively by the latest process data, the predictive controller can produce more reliable and stable control performance. Experiments using industrial data have verified the superiority and practicability of the proposed methods.

This study is concerned with the optimal control and scheduling problem for linear networked control systems with communication constraints and security issues. The communication channel, which connects remote sensors with a controller, has limited transmission capability and may suffer denial of service attacks from an external attacker. Unlike most existing cyber-attack-related literature which presumed a prior well-designed control or estimating strategy on which triggering and jamming strategies were established, in the present work, optimal strategies of the controller, the trigger as well as the external attacker are considered simultaneously under the renowned linear quadratic criteria. A designer, who can jointly devise the controller and the trigger, aims to improve the system's performance while the attacker's goal is just the opposite. With the assumption that the trigger and the attacker have limited opportunities to send or attack, a zero-sum static game of complete information is first utilised to investigate the optimal strategies for both players, i.e. the designer and the attacker. The existence of Nash equilibrium (NE) point, i.e. the combination of optimal strategy for each player, is proven afterwards. Finally, the property of none pure-strategy NE in a special case is provided with rigorous proofs. A numerical example is employed to demonstrate how to derive the optimal strategies for the designer and the attacker.

This study is about fault detection observer design in finite-frequency domain for Lipschitz non-linear systems with actuator fault. To make the generated residual sensitive to fault while robust against disturbance, the authors derive design conditions for the fault detection observer to achieve fault sensitivity performance in finite-frequency domain and disturbance attenuation performance. The authors further transform the design conditions as a set of linear matrix inequalities to facilitate the observer design. Besides, some extra design degrees of freedom parameters are provided in the proposed method to further reduce some conservatism. Numerical simulations of a single-link flexible joint robot are conducted to verify the effectiveness of the proposed approach.

This study addresses a distributed filtering problem for discrete-time Takagi–Sugeno fuzzy complex networks with sensor saturation, where nodes and filters are connected via a shared communication network. It is supposed that each node's output measurement transmitted to its filter according to Round-Robin scheduling protocol. Based on a non-parallel distributed compensation strategy, distributed filters are constructed, where the coupling matrix between filters could be different from the one between nodes and the parameters of the filters depend on current and delayed membership functions. The augmented filtering error system is represented as a discrete-time fuzzy system with time-varying delays. By applying a novel nonquadratic Lyapunov functional that depends on current and delayed membership functions, and combined with a Abel lemma-based finite-sum inequality, distributed regional filters are designed such that the local and exponential stability of the augmented filtering error system is ensured and the performance requirement is satisfied. Numerical examples illustrate the effectiveness and less conservatism of the proposed method.

This study is concerned with the problem of composite anti-disturbance control for attitude manoeuvre and vibration reduction in the presence of external disturbances. By employing finite-time integral sliding manifold, a novel finite-time integral sliding mode disturbance observer is constructed to estimate the lumped disturbances in finite time, where the lumped disturbances include external disturbances and coupling terms between system states and flexible modal. Based on the estimation values, a composite anti-disturbance controller is proposed via backstepping method. Simulation results are employed to demonstrate the effectiveness of the proposed technique.

This study addresses the stabilisation problem via decentralised controllers for continuous-time positive fractional-order (FO) interconnected systems. By virtue of the positivity, a necessary and sufficient condition is first derived for asymptotic stability of the interconnected closed-loop system. Then, necessary and sufficient conditions for designing a decentralised state-feedback controller are formulated in the form of a linear programming problem which can be effectively solved by using various convex optimisation algorithms. The effectiveness of the obtained theoretical results is demonstrated by a numerical example in positive FO circuits.

This paper considers the cooperative fault-tolerant output regulation problem for linear multi-agent systems with actuator faults. It is assumed that the actuator faults are loss of effectiveness faults. A new lemma is introduced to ensure the transmission zero condition for the systems with actuator faults. Based on this lemma, the unique solution of the output regulation equations is achieved. Moreover, a distributed adaptive observer and a distributed state feedback controller with time-varying gains are designed to compensate the actuator faults. In addition, it is shown that the cooperative fault-tolerant output regulation problem can be solved under the proposed controller. Finally, a simulation example is presented to show the validity of the proposed controller.