In this study, the problem of fault estimation observer design with finite-time convergence specification for continuous-time dynamic systems subject to external disturbances. First, the unknown input observer is constructed to achieve accurate estimation of the occurred fault and to guarantee robustness against the disturbance. Then a pole placement-based fault estimation observer is constructed using time-delay design such that the fault estimation error converges to zero in finite time. Unlike conventional literatures, the proposed fault estimator with finite-time convergence specification does not contain discontinuous sign function. Finally, simulation results of an aircraft application are presented to illustrate the finite-time convergence of the proposed fault estimation observer.

This study investigates the problem of event-triggered distributed predictive control (DPC) for multi-agent systems. To guarantee the stability of overall system, a constraint relevant to the triggering instant is imposed in the DPC optimisation problem, and the corresponding event-triggering condition with the information received from neighbouring agents is derived based on the input-to-state stability (ISS). In such a framework, the DPC optimisation problem is solved only when the triggering condition is satisfied, which reduces the communication consumption and lowers the computational load. Moreover, the recursive feasibility of DPC optimisation problem is proved and the sufficient conditions for ensuring the ISS of overall system are developed. Finally, a simulation example is provided to illustrate the effectiveness of the presented method.

This study investigates the problem of reconstructing actuator faults for descriptor systems via a PD-type learning observer. By synthesising the derivatives of the output estimation error into the P-type learning law, a novel PD-type learning observer is established to simultaneously reconstruct original system states and actuator faults. Stability analysis of the PD-type learning observer is explicitly provided. A systematic design method is also suggested based on a linear matrix inequality technique. Further, a robust PD-type learning observer is designed against process disturbances and measurement noises. At last, a simulation example is used to demonstrate the effectiveness of the proposed fault-reconstructing method.

In this study, the authors analyse some fundamental structural properties of linear time-invariant multivariable systems in the controller canonical form and present a direct method for the computation of bases and associated friends for output-nulling, input-containing and reachability subspaces in terms of the parameters of the system and the invariant zero structure, both in the non-defective and in the defective case. Using this analysis, it is possible to express the solvability conditions of important control and estimation problems in terms of easily checkable conditions on the system matrices.

The problem of static output feedback preview tracking control is proposed for a class of polytopic uncertain discrete-time systems by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) technique. First, the error system method of preview control theory is adopted and the difference operator is introduced, and then an augmented error system including previewed information is constructed, which transforms a tracking problem into a regulation problem. Then, a previewable reference signal is fully utilised through reformulation of the output equation for the derived augmented error system while considering the output feedback. Sufficient conditions for designing a robust static feedback preview controller are given in terms of solutions to a set of LMIs. Based on the criterion, a static output feedback controller with preview action is designed such that the output can asymptotically track the reference signal. Finally, the numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the study.

This study addresses the issue of control synthesis for discrete-time non-homogeneous Markov jump systems. Here, the concept of multiple boundary sets (BSs) is made to represent time-varying transition probabilities of the system operation mode, and another kind of probabilities is exploited to describe the switching among the multiple BSs. Overall, the stabilisation condition is first derived in terms of bilinear time-varying matrix inequalities with two kinds of probabilities that affect the evolvement of the modes. Then, to derive a finite number of solvable conditions from the stabilisation condition, this study introduces a relaxation technique capable of directly integrating some available constraints on the probabilities without resorting to any over-bounding technique.

This study is concerned with the stabilisation problem for a class of Caputo type fractional-order interval systems with perturbation. Employing Riemann–Liouville fractional integral sliding surface, a novel robust sliding mode control law is established to drive the dynamics of the system to the manifold s=0 in finite time. Based on linear matrix inequality criterions and stability theorems, the closed-loop system will asymptotically converge to the origin as time progresses. Meanwhile, the unknown perturbation is well adjusted on-line by the designed adaptive law. Furthermore, a new reaching law is introduced to reduce the chattering which is caused by the discontinuity of the switching function, and to improve the robustness and the stability of system. Besides, some results about the control and stabilisation of fractional-order interval systems are illustrated in this study; several comparisons with the related works are given to reveal the potential advantages of the proposed controller over the previous results. Finally, an example with numerical simulations is provided to show the validity and feasibility of the proposed method.

One of the unique global behaviours of a group of under-actuated autonomous vehicles is known as cyclic pursue, which requires a group of vehicles to uniformly distribute on circles and at the same time, to orbit around a centre point, while circumnavigation further requires those vehicles to circumnavigate a predefined target of interest. Such behaviours can also be called periodic formations. This paper further studies the periodic formations for multi-agent systems composed of a group of under-actuated autonomous vehicles and a target of interest by proposing a distributed strategy to maintain any required distance between two vehicles and desired angle difference between vehicle's heading and the line of sight that takes directly towards its pursuing vehicle. The authors' distributed control law, dependent only on the information of its pursuing vehicle and itself, can not only enable a network of autonomous vehicles to circulate around a target of interest, but also achieve any physically feasible periodic formations, which include forming regular polygons as a special case.

In this study, a novel iterative algorithm is proposed for solving coupled Lyapunov equations appearing in continuous-time Itô stochastic systems with Markovian jump parameters. In this algorithm, some tunable parameters are introduced, and thus a combination of the information in both the last step and the current step can be utilised to update the estimation of the unknown matrix variables. The monotonicity and boundedness of the proposed algorithm are analysed, and the convergence condition for this algorithm is also given. Due to the use of the latest updated information, the proposed algorithm can achieve better convergence performance than the existing iterative algorithm by appropriately choosing the tuning parameters. An illustrative example is employed to show the effectiveness of the proposed algorithm.

This study addresses the input-to-state stability (ISS) and integral ISS (iISS) of non-linear systems with distributed-delayed impulses. Based on Lyapunov method and the analysis technique proposed by Hespanha et al., the authors derive some sufficient condition for ISS/iISS, which depend on the distributed delays existing in impulses. They prove that the given system is uniformly ISS/iISS under the average dwell time conditions. Finally, the effectiveness of the proposed results is evidenced by two illustrative examples.

This study investigates the mean square exponential (MSE) synchronisation problem for the multi-agent systems with multiplicative noises, where the communication topologies among the agents are directed and time varying. The phenomenon of randomly varying coupling delay is considered and described by a Bernoulli distributed white sequence with known probability, thereby better reflecting the practical system dynamics. Network topologies proposed in this study are directed and time varying which intrinsically characterise the random communications between agents. By exploiting the graph theory and the coordinate transformation method, the MSE synchronisation problem for the stochastic multi-agent network is converted into a robust MSE stability problem for the transformed system. Then by constructing a Lyapunov functional and utilising the properties of Kronecker product, both delay-independent and delay-dependent sufficient conditions are derived guaranteeing the transform system to be robustly stable in the mean square. The criteria established are in the form of matrix inequalities which can be solved and checked easily. Finally, simulation examples are provided to illustrate the validity for the obtained results.

This study presents a non-linear trajectory tracking controller for quadrotors without velocity and angular velocity measurements. The rotation matrix is utilised to represent the quadrotor attitude. Based on the hierarchical control strategy, the position and attitude loops are investigated separately, where two novel auxiliary systems are, respectively, introduced to obviate usage of the velocity and angular velocity information in the corresponding control developments. In addition, a criterion for choosing the position loop control parameters is established to ensure the singularity-free extraction of the command rotation matrix. Further, an attitude control scheme with the initial condition constraint is exploited to ensure the attitude tracking error converging to the desired equilibrium all the time. In terms of the hierarchical system synthesis theory, it is demonstrated that the quadrotor, with the proposed controller, is able to accomplish trajectory tracking manoeuvres with asymptotically stable property. Finally, simulations verify theoretical results.

This study presents a novel constraints transformation-based robust adaptive dynamic surface control (DSC) scheme for tracking control of a class of uncertain non-linear systems with output constraints. The considered systems are in semi-strict feedback form that contain not only parametric uncertainties, but also general non-linear function uncertainties as well as unknown input gains. In the proposed approach, a constraints transformation technique is firstly introduced to convert the original constrained system into an equivalent one without constraints. By ensuring the stability of the transformed system, it suffices to guarantee the constraints are not transgressed. To attain this, a decoupled DSC design methodology is then developed to stabilise the transformed system and a systematic design procedure is established. Through rigorous analysis, it is shown that the proposed control scheme can achieve output tracking objective and guarantee that all the closed-loop signals remain bounded while simultaneously preventing the prescribed output constraints from being violated. Simulation studies illustrate the efficiency and feasibility of the proposed approach.

Kalman filters for discrete-time linear systems with censored measurements have been developed, of which the Tobit Kalman filter has been shown an effective candidate. In this study, the authors expand the Tobit Kalman filter to discrete-time linear systems with time-correlated multiplicative measurement noise. By introducing several new terms including the estimates for the products of multiplicative measurement noise and the state as well as their error covariance matrices, the proposed filter can be implemented in a recursive manner. A numerical example involving radar tracking is provided to show the effectiveness of the proposed filter.

The integral inequality approach has been widely used to obtain delay-dependent stability criteria for dynamic systems with delays, and finding integral inequalities for quadratic functions hence plays a key role in reducing conservatism of corresponding stability conditions. In this study, an improved integral inequality which covers several well-known integral inequalities is introduced, and improves thereby stability for linear systems with time-varying delay. Three numerical examples are given to demonstrate the effectiveness and superiority of the proposed method.

This study deals with a fundamental issue of evaluating the performance of widely used fault detection and diagnosis (FDD) schemes within a closed-loop framework. The focus is to examine how certain implemented controller would impact on the FDD performance and how such performance can be further improved. For this purpose, the authors consider the FDD problem for a class of linear discrete-time systems (with and without unknown disturbances) under typical proportional–integral control using observer-based methods. It is revealed that some existing observer-based FDD approaches are no longer applicable in the closed-loop situation due to the feedback control. To solve the problem, by appropriately modifying the structure and re-designing the parameters of the observers, it is proven that the dynamics of closed-loop residuals can be made identical with those of the residuals obtained with known control inputs at each time step. A numerical example is provided to show the effectiveness of the proposed algorithm.