The problem of model reference adaptive control is considered for a class of uncertain dynamical systems with non-linear delayed state perturbations. It is assumed that the time-varying delays are any non-negative continuous and bounded functions. In particular, it is only assumed that the non-linear delayed state perturbations are bounded in any non-negative non-linear functions which are not required to be known for the system designer. A new method is presented whereby a class of continuous memoryless robust adaptive controllers with a rather simple structure can be constructed. It is also shown that the proposed robust adaptive control schemes can guarantee that the current state of uncertain non-linear time-delay dynamical systems can track the state of a given delay-free reference model as far as possible. Finally, the simulations of a numerical example are provided to demonstrate the validity of the theoretical results.

Multirotor helicopters are very powerful flying robots used in many applications, but their lack is robustness. A fail in any of their rotors can drive the helicopter to fall. In this study two different micro-helicopter structures are analysed, a standard Quadrotor and a Hexrotor. An uncertainty model is generated and a robust controller is designed. The structured singular value μ _Δ is used to test the robust stability and performance of these two plants, obtaining better results for Hex than Quadrotor. At the end of the study, a set of flight tests, where some of the motors are partially damaged, is presented confirming the analysis of μ _Δ. Results of this study show Hexrotor as a very interesting structure for unmanned aerial vehiclesbecause of its stability and performance characteristics compared with Quadrotor.

The problem of sliding mode control is considered for a class of uncertain switched systems subject to actuator faults. It is assumed that there may happen degradation in each actuator channel. Besides, the authors relax the restrictive assumption that each subsystem shares the same input channel, which is different from some existing works. In this work, a weighted sum approach of the different input matrices is introduced to construct a common sliding surface. Moreover, by on-line estimating the loss of effectiveness of the actuators, an adaptive sliding mode controller is designed. This does not only compensate the effects of the actuator degradation effectively, but can also reduce the conservatism compared with some existing approaches which only utilise the bound of the gain variation. It is shown that the reachability of the specified sliding surface can be ensured, and a sufficient condition on the exponential stability of sliding mode dynamics is obtained via the average dwell time method. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

This study addresses the output feedback stabilisation problem of discrete-time linear systems with input delay. By viewing the difference between the current input and the delayed input as a special disturbance, full- and reduced-order extended state observers are constructed, respectively, to estimate both the state and the disturbance simultaneously. Then the composite control laws are synthesised to actively compensate the input delay by using the state and disturbance estimates. Different from existing predictor-based control approaches, the proposed controllers are memoryless, and the past input information are thus not needed. Moreover, it can be observed that the information on the size of the input delay is not involved in either the observers or the controllers. Finally, simulation results are provided to illustrate the advantages and effectiveness of the proposed approaches.

A novel design methodology of corrective control is proposed for fault-tolerance against transient faults in input/output asynchronous sequential machines. The main objective is to lessen controller complexity by proposing a structure of corrective control that employs no state observer, which is required in the former studies for input/output control of asynchronous machines. The form of the output feedback is also simplified as a unit character instead of bursts. Although the exact identification of the machine's state is infeasible, the proposed controller achieves immediate fault-tolerance against transient faults that cause unauthorised state transitions. As a case study, the authors apply the proposed control scheme to implementing configuration controllers for space-borne field programmable gate array with hardware redundancy in which single event upset faults may happen by the radiation effect.

This study considers the convergence analysis approach to iterative learning control (ILC) which is achieved based on two-dimensional (2D) Roesser systems. Stability results are proposed for 2D Roesser systems when they are subject to varying parameters with respect to independent time and iteration axes. It is shown that the convergence analysis of ILC for a class of non-linear systems can be performed based on the established stability results of varying 2D Roesser systems. Moreover, the presented convergence results of ILC can work with sufficient robustness against iteration-varying initial state shifts. Illustrative simulations are included to verify the established convergence results of ILC for non-linear systems.

This study investigates the containment control problem of second-order discrete-time multi-agent systems with Markovian missing data in actuators and one step network-induced time delay. The process of missing data from the controller to the actuator is modelled by a homogeneous, finite-state and discrete-time Markov chain. The authors first discuss the containment control problem for the case when all the elements of the transition probability matrix are completely known, then the result is extended to a more general case with only partially known transition probabilities. The distributed control protocol with one step time delay is proposed. Based on the stochastic Lyapunov–Krasovskii functional method, sufficient conditions in terms of a set of matrix inequalities are given to guarantee that the states of all the followers asymptotically converge to the convex hull formed by the corresponding states of the leaders in mean square sense. A cone complementary linearisation algorithm is used to obtain the control gains. Finally, two numerical simulations are provided to show the effectiveness of theoretical results.

In this study, the authors investigate the state response for continuous-time antilinear dynamical systems. First, they propose the concept of matrix anti-exponential function, and then derived some nice properties of this new function. With the matrix anti-exponential function as an effective tool, they obtain a closed-form expression for the state response of continuous-time antilinear systems. Finally, they derived an expression with finite terms for the proposed matrix anti-exponential function, which will be useful for numerical implementation.

This study is concerned with the finite-time synchronisation control (FTSC) of complex networks with discontinuous and continuous node dynamics. Two types of controllers (including continuous and discontinuous ones) are designed to ensure synchronisation of networks based on non-smooth analysis. Many sufficient criteria are given to guarantee FTSC by utilising the famous finite-time stability theorem. Compared the new obtained results with the previous literatures, the FTSC is discussed firstly when the node dynamics as well as the controllers are both discontinuous. Meanwhile, the upper bound of the settling time for synchronisation can be estimated. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.

This study investigates dynamic output-feedback control for linear systems by using an event-triggered output-feedback with quantisation. The event-triggering scheme is considered both in an event-driven sampling case and the case of periodic event-triggered transmission based on periodical verification of the event condition. A hybrid system model as well as a time delay model are developed for the two event schemes, respectively, to facilitate analysis and design. To obtain an asymptotical stability performance, the quantiser utilised is logarithmic and of infinite level. For the two design methods, conditions to guarantee the asymptotic stability of the closed-loop systems are established in terms of linear matrix inequalities, and the explicit expressions of the dynamic controller are given. Numerical examples are given to show the feasibility and efficiency of the theoretical results.

This study addresses the input–output feedback linearisation and the internal dynamics stability of an underactuated autonomous underwater vehicle (AUV) in three-dimensional space. By taking the coordinates of a virtual reference point in front of AUV system as the output equation, the input–output feedback linearisability of AUV kinematics and dynamics is guaranteed. A non-linear controller is designed to make the reference point track a desired trajectory which is generated by an open-loop path planner. Then, it is shown that the resulting internal dynamics of the system is stable. Neural network approximation capabilities and adaptive techniques are also adopted to compensate for unknown vehicle parameters, and constant or time-varying disturbances induced by waves and ocean currents. A Lyapunov-based stability analysis is used to show uniform ultimate boundedness of tracking errors. Finally, simulation results are provided to illustrate the effectiveness of the proposed control system as a qualified candidate for real implementations in offshore applications.

This study addresses the cooperative fault-tolerant tracking control problem for a class of multi-agent systems subject to mismatched parameter uncertainties, external disturbances and actuator faults including loss of effectiveness, outage and stuck. The communication network is undirected connected graph with a fixed topology. It is assumed that the actuator efficiency factors, the upper bounds of the unparametrisable time-varying stuck faults and disturbance, are unknown. Different from the traditional centralised fault-tolerant tracking control problem, only part of the follower nodes can obtain the information of leader directly. On the basis of the local state information of neighbouring agents, a novel cooperative fault-tolerant tracking control scheme by using adaptive mechanism is proposed. By introducing the estimates of controller parameters driven by neighbourhood tracking errors, it is shown that not only the actuator faults in the follower nodes can be compensated, but also the global tracking objective can be achieved. Furthermore, it is proved that all closed-loop signals are bounded and all follower nodes asymptotically tracking to the leader can be achieved in the presence of actuator faults, external disturbances and mismatched parameter uncertainties. Finally, a numerical example is given to show the effectiveness of the proposed control scheme.

In this study, a bespoke sliding mode non-linear observer and a linear controller framework is proposed for achieving robust formation control of a cluster of satellites in the case of a circular reference orbit. Exploiting the structure of the satellite dynamics, a non-linear observer is proposed based on super-twist sliding mode ideas. The observer estimates the states and any unknown bounded disturbances in ‘finite time’. The stability properties of the observers are demonstrated using Lyapunov techniques. A distributed controller, based on the estimated states and the relative position output information, depending on the underlying communication topology, is proposed. A polytopic representation of the collective dynamics which depends on the eigenvalues of the Laplacian matrix associated with the communication topology is used to synthesise the gains of the proposed control laws. A simulation example is used to demonstrate the efficacy of the proposed approach.

In this study, a recursive singularity-free, fast terminal sliding mode control method, which is able to avoid the possible singularity during the control phase, is applied for a finite-time tracking control of a class of non-holonomic systems. The reaching control law is proposed to guarantee the existence of the sliding mode around the fast terminal sliding surface and zero-tracking errors are achieved in finite time with an exponential decay rate. Simulation results are illustrated on three benchmark examples of chained-form non-holonomic systems: a wheeled mobile robot, an under-actuated rigid body and a front-wheel-drive car. The results demonstrate that the proposed control law achieves favourable tracking performance for non-holonomic systems.

This study is concerned with the leader-follower formation control of non-holonomic mobile robots without communication. A pan-controlled camera is the sole sensor used by the follower to observe the leader. A new vision-based formation system without range states is proposed, which eliminates the need of inter-robot range estimation. An adaptive formation controller and an adaptive camera controller are designed in the presence of unknown leader's velocities and vision-related parameters. A parameter projection algorithm is integrated into the controllers to bound the control inputs. The camera controller ensures the stable observation of the leader's features. Thus the camera constantly provides visual measurements for the formation controller which guarantees the formation maintenance. Simulation and experimental results verify the effectiveness of the proposed active vision-based formation control approach.

The stability analysis of reset control systems is challenging when reset time instants are uncertain, because such uncertainties may damage or even destabilise the system. This study considers reset control systems with uncertain output matrix, and presents sufficient conditions for the quadratic stability and finite gain ℒ₂ stability of the closed-loop reset systems. Then, the results are extended to piecewise quadratic stability, which is much less conservative. The design of the reset controller is also discussed. All the results are given as linear matrix inequalities by using a lemma about multi-convex function. Several examples are given to show the effectiveness of the obtained results.

This study investigates the problem of finite-time attitude stabilisation in probability for a class of stochastic spacecraft systems. Based on the stochastic finite-time stability theorem, a continuous control law is proposed to guarantee the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. A simulation example is given to illustrate the effectiveness of the proposed method.