With the widespread use of wheeled mobile robots (WMRs) in various applications, new challenges have arisen in terms of designing its control system. One of such challenges is caused by wheel slippage. This study proposes a new method for haptic teleoperation control of a WMR with longitudinal slippage (not including sliding). In this teleoperation system, the mobile robot's linear velocity follows the master haptic interface's position. The proposed teleoperation controller also includes an acceleration-level control law for the mobile robot such that the velocity loss caused by slippage is compensated for. Information about the magnitude and timing of slippage is displayed to the human operator through haptic (force) feedback. Despite the functional benefits of displaying slippage information as haptic feedback to the user, there are system stability related concerns that have been addressed using the proposed controller. Experiments of the proposed controller demonstrate that it results in stable bilateral teleoperation with a satisfactory tracking performance.

This work focuses on the construction of rigid formation from non-rigid ones in the two-dimensional space. Analogously to operations of Henneberg sequence aiming to guarantee the minimal rigidity of formation, two new operations are introduced, allowing one to sequentially build any rigid graph by connecting non-rigid ones. A systematic construction sequence is developed based on proposed operations, and is shown to be able to restore rigidity by introducing minimum number of new edges during the construction process. Further applications of the proposed operations are also presented, one of which is successfully employed in the problem of persistence analysis of directed graphs, and can verify the persistence of a given graph with a speed two times faster comparing with existing solution.

The design of sliding switching surfaces consist in finding a manifold where the controlled system dynamics are asymptotically stable. This problem has been studied for a long time, during which a wide range of designing approaches has been proposed, which can be classified into two research methodologies; the first one corresponding to eigenvalues designing approaches and the second one is based on optimal approaches. In addition, some research approaches only can be applied to specific type of systems, e.g. single-input single-output systems or continuous time systems. Finally, the performance or the level of the achieved accuracy among the different approaches varies significantly. The proposed approach facilitates the task of designing sliding surfaces applied to multi-input multi-output (MIMO) linear systems. The presented methodology introduces a switching surface for MIMO linear systems through a simple equation that allows both eigenvalues placement design or optimal methods without any coordinate system representation transformation. In addition, a design parameter is also included for the adjustment of the non-ideal dynamics. Moreover, this approach guarantees high accuracy of the system dynamics, either for arbitrary eigenvalues assignment or for optimal switching surface definitions. In addition, these benefits are attained using a single switching surface equation. An illustrative example is included to show the advantages of the proposed design methodology.

This study presents fractional-order system modelling and control for a permanent magnet synchronous motor (PMSM) velocity servo system. Fractional-order model of the PMSM velocity servo system is obtained theoretically for an improved modelling precision. To identify the parameters of the proposed fractional-order model, an enhancement of the classic Levy identification method with weights is applied. In a real-time PMSM velocity servo plant, the fractional-order model is identified according to the experimental tests using the presented algorithm. The fact that the fractional model is more accurate than traditional integer-order model is substantiated using by the mean square error performance index. Two H _∞ stabilising output feedback controllers are designed for velocity servo using a simple scheme according to the identified fractional-order model and the traditional integer order one, respectively. The experimental test performance using these two designed H _∞ controllers is compared to demonstrate the advantage of the proposed fractional-order model of the PMSM velocity system.

This study studies the leader–following consensus problem for a class of multi-agent systems with unknown non-linear uncertainties. It is proved that the global consensus can be achieved by distributed feedback controller subject to actuator saturation for switching topologies and time-varying delays. Sufficient conditions in terms of linear matrix inequalities are derived to ensure that all following agents could reach consensus asymptotically with a leader, which provide the allowable upper bound of communication delay. Stability analysis is mainly based on algebraic graph theory, non-linear analysis and Barbalat's lemma. Numerical simulations are given to demonstrate the effectiveness of the main results.

Designing an observer for Takagi–Sugeno (T–S) fuzzy systems in the presence of uncertainties is a great challenge for researchers. Owing to the uncertainties, it is hard to design an observer to make the state estimation error converge to zero asymptotically. To resolve this problem, the authors consider the uncertainties to be unknown inputs and apply the unknown inputs method. The existing literature concerning observer design for T–S fuzzy systems using the unknown inputs method generally have only a single output matrix. In addition, the method of converting uncertainties into unknown inputs requires a matching condition which includes a common constant matrix to match all uncertainties in all local models of T–S fuzzy system. Therefore, the above two constraints lead the observer design to be very conservative. To overcome the above drawbacks, a special transformation is used to transform the original T–S fuzzy system into a new system form, and then they propose a method to synthesise an observer for an uncertain T–S fuzzy system which allows different output matrices and relaxes the matching condition of the uncertainties for all local models. Finally, two examples are presented to demonstrate the efficiency of the proposed method.

In this study, the authors deal with inertial measurement units subject to uncertainties. They propose an extended robust Kalman filter (ERKF) in a predictor–corrector form to estimate a rigid body attitude. The filter is developed based on regularisation and penalisation whose approaches present the advantage of encompassing in a unified framework all state and output uncertain parameters of the system. The ERKF is tuned based on two degree of freedom which belong to a certain interval known a-priori, useful for online applications. The attitude estimation system proposed takes into account a rigid body model formulated in terms of quaternions. Experimental results are presented based on a comparative study among the ERKF, the standard extended Kalman filter and an 𝓗_∞ filter.

The authors propose a robust output feedback control for unknown non-linear systems with external disturbance. The main contribution of this study is that the proposed method guarantees the global uniform ultimate boundedness of the output tracking error using only output feedback for unknown non-linear systems with external disturbance. The key idea of the proposed method is that the plant non-linearities and external disturbance, and their derivatives are lumped into augmented state variables. The robust high order augmented observer (RHOAOB) is developed to estimate the lumped augmented state variables and full state. The benefit to using the RHOAOB is that the estimation error can be reduced without increasing the bandwidth of the RHOAOB. The backstepping controller is designed to guarantee the global uniform ultimate boundedness of the output tracking error occurred by the disturbance estimation error. To the best of the authors' knowledge, it might be the first attempt of the analysis of the estimation and output tracking performance of the RHOAOB-based controller with the measurement noise in both time and frequency domains. The analysis shows that very small estimation error is not necessarily required to obtain the precise output tracking using an input-to-state stability property. This merit results in avoiding the amplification of the measurement noise.

Control of grid assistance is proposed in this study for a renewable hydrogen generation system of simple and robust structure. Here, the grid connection serves the dual purpose of minimising the effect of wind power variations in the electrolyser supply as well as maximising the hydrogen production. To regulate the electrolyser current at its rated value, a cascade control scheme is posed. The feedback loop which commands the grid converter switching is of interest for the design. The min-projection strategy that stabilises a switched affine system is applied as the switching law. The analysis of switched equilibria and their stability is done by employing the concepts of Filippov inclusion and common Lyapunov function, respectively. The obtained theoretical results are corroborated by numerical simulation.

This study presents H _∞ control synthesis of a miniature unmanned aerial vehicle to improve its hovering capability in the presence of wind disturbances. By time-scale techniques, the six-degree-freedom flight system can be decoupled into subsystems in different time-scales: one including slow-varying translational dynamics and Euler angles, and another composed of fast-varying angular velocities. To avoid contradictions between subsystems, control specifications for subsystems are classified, respectively, in disjoint frequency ranges. Robust H _∞ controllers, applied directly to the original flight system, are formulated by composing the sub-controllers. To achieve desired handling and flying qualities, wind characteristics are considered, and a novel flexible strategy is then developed to ensure an adequate response in all flight modes under different weather conditions. The effectiveness and merits of the proposed methods are illustrated with a simulation example.

This study proposes one novel data-driven control strategy based upon the simultaneous perturbation stochastic approximation method with adaptive weighted gradient estimation for general discrete non-linear systems. A function approximator is used to construct the controller, and here, it is fixed as a neural network (NN), whose structure is fixed previously, while allowing its connecting weights to be updated. The control parameters are then the connecting weights of the NN controller. The biggest advantage of this data-driven control approach is that it can generate a control signal to affect system's future performance without establishing the plant's mathematical model first. In this novel approach, to improve the control ability and accuracy, an adaptive weighted gradient estimation method is designed to do the parametric estimation with convergence analysis. Non-linear tracking problems for typical discrete-time non-linear plants are introduced for simulation comparison tests, and the convergence and feasibility of this newly proposed data-driven control strategy are well demonstrated through the simulation results. Finally, empirical study on a simulated wastewater treatment system is carried out to further illustrate the effectiveness of this newly proposed approach.

A singularity-free non-linear controller is proposed for trajectory tracking of a model-scaled autonomous helicopter. The helicopter model is firstly decomposed into a nominal one with unmodelled dynamics. Based on the decomposed model, the controller is designed with the hierarchical inner–outer loop strategy. The outer position loop controller is designed with hyperbolic tangent functions, and criteria for controller parameter selections are developed to realise the position tracking and to obviate singularity in deriving the command attitude from the position loop controller. The inner attitude loop controller is designed based on barrier Lyapunov function and backstepping technique to achieve the attitude tracking without singularity during the tracking process. In addition, in order to improve the tracking performance, observers are employed to compensate the unmodelled dynamics. Simulation of two manoeuvres verify the proposed theoretical results.

This study considers incremental stability problem of switched non-linear systems with each mode being local incrementally asymptotically stable. A new concept named ‘steady-state inclusion’ is proposed to describe the relations among incremental stability regions of modes. Based on such a concept, sufficient incremental stability conditions of the switched systems are established, which cover the global incremental stability as a special case. The new result is applied to synchronisation problem of coupled identical systems with switching coupling.

In this study, the problem of disturbance-observer-based-control (DOBC) and L ₂−L _∞ resilient control for Markovian jump non-linear systems with multiple disturbances is investigated. The disturbances are divided into two parts: one part is produced by an exogenous system and the other part is supposed to lie in the space of L ₂[0,∞). A disturbance observer is designed to estimate the first one, and the disturbance estimation is introduced into L ₂−L _∞ resilient state feedback control law. Hence, by combining DOBC and L ₂−L _∞ control methods, a composite anti-disturbance controller is designed to attenuate and reject two kinds of disturbances. Some sufficient conditions are obtained by using Lyapunov function method and linear matrix inequalities technique. Finally, an application example is given to illustrate the effectiveness of the main algorithm.

This study is concerned with the problem of global robust finite-time stabilisation of a class of unknown pure-feedback systems with input dead-zone non-linearities. The pure-feedback non-linear system under consideration has a pseudo-affine property and is with non-linearly parameterised uncertainties. By adopting and improving the existing finite-time backstepping control approach, a robust finite-time stabiliser is given, which could ensure the global finite-time stability of the trivial solution of resulting closed-loop system. A numerical and a realistic examples are employed to demonstrate the effectiveness of the proposed method.

In this study, the estimation problem of periodically occurring faults is investigated for a class of non-linear time-varying systems. Unlike most existing results, the system subject to bounded disturbance and measurement noise is considered. A novel non-linear iterative learning (IL) observer is constructed by using previous output estimation errors and inputs for the purpose of fault estimation (FE). The estimated fault is updated through a novel designed IL law. The recursive analysis and robust control technology are used to prove the condition under which the ultimate boundedness of the FE error can be guaranteed. Finally, a simulation study on a practical manipulator is provided to demonstrate the effectiveness and applicability of the proposed FE scheme.