This study proposes an adaptive control scheme for global tracking of a class of switched non-linear systems involving unknown saturated-like Prandtl–Ishlinskii (PI) hysteresis. The switching information is assumed to be unobservable. A bound estimation approach is introduced to circumvent the obstacle caused by unknown switching and PI hysteresis. It is shown that under arbitrary switching, the proposed controller guarantees all signals of the overall closed-loop system are globally uniformly bounded, and the tracking error can converge to an arbitrarily small residual set. The proposed control scheme is tested on a typical wing rock system in the face of persistent aerodynamic parameter changes. Simulation results demonstrate suppression of the wing rock and exhibit better transient performance in comparison with some existing method.

Implementation of immersion and invariance theorem for antagonistic actuated robots becomes increasingly difficult as non-linearity of elastic torque exists. This inherent difficulty is mainly driven by the need to solve the partial differential equations (PDEs) in the immersion conditions. In this work, forwarding-based dynamic surface control (DSC) for designing asymptotically tracking control laws is developed for a tendon-driven joint with mismatched external disturbances. At each step of the design, by defining a lower-order target system, the required mappings can be transformed into the virtual control inputs so that the prescribed transient performance is realised. Based on forwarding combined with DSC, all virtual controls are connected in sequence and high-frequency noises can be suppressed. This technique not only avoids solving the PDEs, but also avoids computing mappings and their analytic derivatives. In particular, global boundedness of all signals in the robotic systems can be ultimately guaranteed by the internal stability of filters. Controller performances are demonstrated by simulating an actuated robot with one joint.

The wind turbine generator system (WTGS) is usually linearised around operating points, and traditional control techniques concentrate on local dynamic response nearby each operating point. However, the actual wind speed is switching frequently between different operating points, which could cause a serious negative influence on the stability and dynamic response of WTGS. To overcome this disadvantage, this study proposes a systematic method to combine the switching rule into the control design to improve the dynamic response of the mechanical side of WTGS. Through modelling the WTGS driven by the switching wind speed into a class of linearised Markovian jump controlled systems, the regional pole placement technique is developed for such a class of systems and applied on improving the dynamic response of WTGS. Combined with the H _∞ control, the proposed method can achieve better wind energy conversion efficiency and reduce the power volatility efficiently. Through combining the analysis on the actual historical wind speed into the control design, simulation results for a 2 MW wind turbine show the effectiveness of the proposed method.

This study is concerned with the dynamic output feedback control problem for fast sampling discrete-time singularly perturbed systems using the singular perturbation approach. Sufficient conditions in terms of linear matrix inequalities (LMIs) are presented to guarantee the existence of a dynamic output feedback controller for the corresponding slow and fast subsystems, respectively. The controller gains and the corresponding coefficient matrices can be obtained via solving the proposed LMIs. Thus, not only the high dimensionality and the ill condition are alleviated, but also the regularity restrictions attached to the Riccati-based solutions are avoided. The theoretical result demonstrates that the composite dynamic output feedback control designed through those of the slow and fast subsystems can stabilise the full-order discrete-time singularly perturbed systems. Finally, two real world practical examples are provided to show the effectiveness of the obtained results.

This study investigates the problem of robust model predictive control for positive systems under a new model predictive control framework. A robust model predictive control method is presented in this study for uncertain positive systems. A state-feedback control law that robustly stabilises the underlying system is designed by using linear programming. Different from the traditional model predictive control technique, the authors' proposed model predictive control framework employs a linear infinite horizon objective function and a linear Lyapunov function rather than quadratic performance indices and quadratic Lyapunov functions commonly used in the literature. Compared with existing design techniques for positive systems, the present approach owns the following advantages: (i) it gives a locally optimal control strategy which approaches to actual operation conditions and the control law is designed by solving a locally optimal control problem at each time step, (ii) it can explicitly deal with constraints of the systems, and (iii) the controller can be easily designed via linear programming without any additional constraints. An practical example is provided to verify the validity of the theoretical findings.

This study investigates the stability and stabilisation problems for a class of neutral stochastic systems with Markovian jumping parameters. First, stability conditions are derived based on mode-dependent Lyapunov–Krasovskii functionals. Second, a novel delay state-feedback controller is considered to stabilise the stochastic system; novel conditions for designing desired controllers are presented in terms of linear matrix inequalities. The results are then extended to the robust stabilisation problem for uncertain neutral Markovian jump systems. Finally, numerical examples and simulation results are provided to show the effectiveness of the proposed design methods.

This study is concerned with the event-based security control problem for a class of discrete-time stochastic systems with multiplicative noises subject to both randomly occurring denial-of-service (DoS) attacks and randomly occurring deception attacks. An event-triggered mechanism is adopted with hope to reduce the communication burden, where the measurement signal is transmitted only when a certain triggering condition is violated. A novel attack model is proposed to reflect the randomly occurring behaviours of the DoS attacks as well as the deception attacks within a unified framework via two sets of Bernoulli distributed white sequences with known conditional probabilities. A new concept of mean-square security domain is put forward to quantify the security degree. The authors aim to design an output feedback controller such that the closed-loop system achieves the desired security. By using the stochastic analysis techniques, some sufficient conditions are established to guarantee the desired security requirement and the control gain is obtained by solving some linear matrix inequalities with non-linear constraints. A simulation example is utilised to illustrate the usefulness of the proposed controller design scheme.

In this study, a novel online fault compensation control scheme based on policy iteration (PI) algorithm is developed for a class of affine non-linear systems with actuator failures. The control scheme consists of a PI algorithm and a fault compensator. For fault-free dynamic models, the PI algorithm is developed to solve the Hamilton–Jacobi–Bellman equation by constructing a critic neural network, and then the approximate optimal control policy can be derived directly. Alternatively, the actuator failure is reconstructed adaptively to achieve online fault compensation without the fault detection and isolation mechanism. The closed-loop system is proved to be asymptotically stable via Lyapunov's direct method. Two numerical simulation examples are given to demonstrate the effectiveness of the proposed fault compensation control scheme.

In this study, the authors study the input delay compensation problem for discrete-time linear systems with both state and input delays. Under the assumption that the original time-delay system without input delay can be stabilised by state feedback, a nested predictor feedback controller is established to predict the future states such that the arbitrarily large yet exactly known input delay in the original system is completely compensated. Consequently, it is shown that the closed-loop system consisting of the original time-delay system and the nested prediction feedback controller is asymptotically stable. Under an additional assumption, an explicit nested predictor feedback controller without involving any nested summations is also established. Finally, two numerical examples are carried out to illustrate the obtained theoretical results.

The event-triggered consensus problem with agents described by double integrator dynamics is addressed in this study. The authors consider the problem of non-consistent packet losses where the broadcast channel from one agent to its neighbours can drop the event-triggered packets of information, where the transmitting agent is unaware that the packet was not received and the receiving agents have no knowledge of the transmitted packet. They also consider the constraints associated with communication delays. In this study, they consider directed graphs, and they also relax the consistency on the packet dropouts and the delays. By relaxing the consistency they allow the dropouts and delays for a packet broadcast by one agent to be different for each receiving node. Under these constraints, an event-triggered consensus protocol is designed for the agents to achieve consensus asymptotically while reducing transmissions of measurements. In addition, positive inter-event times are obtained which guarantee that Zeno behaviour does not occur.

The adaptive control problem of a class of time-varying non-linear systems with uncertainties and input delay is addressed via a Hamiltonian approach in this study. The delay is assumed to be a constant and the uncertainties are small parametric perturbations. First, the non-linear system is equivalently transformed into a Hamiltonian system form and the Casimir-like function is proposed to help shaping the Hamiltonian as a candidate of Lyapunov function in the extended systems. Second, the adaptive control problem is investigated based on the time-varying dissipative Hamiltonian system with input delay. The feedback controller is designed to guarantee the stability of the closed-loop system for all admissible uncertainties, as well as constant delay. Sufficient conditions are presented to ensure the rationality of the proposed control law, which are derived based on Lyapunov function method. Stabilisation problem is also considered while there are no uncertain parameters in the delay non-linear systems. Finally, several examples are presented to illustrate the effectiveness of the results obtained in this study.

In this study, the authors address the problem of robust output feedback hierarchical control for a class of uncertain non-linear systems. The proposed approach is to design an output interface dynamic which is connected to the non-linear system and a linear abstract system. In order to deal with the uncertainties, they resort to the notion of internal model from output regulation. Finally, the unknown point mass system illustrates their approach.

This study investigates the tracking control problem of strict-feedback systems with parametric uncertainties and asymmetric non-smooth saturation as well as actuation faults. By combining a well-defined smooth function with a Nussbaum-type function, robust adaptive and fault-tolerant control scheme is developed, which, as compared with most existing methods, exhibits several attractive features such as, capable of dealing with strict feedback systems with time-varying unknown control gain and parametric uncertainties; able to cope with asymmetric and non-smooth input saturation without requiring the prior knowledge of bound of input saturation; able to accommodate unexpected actuation faults; and structurally simple and computationally inexpensive. The proposed control schemes can guarantee all of the signals in the closed-loop system are semi-globally uniformly ultimate bounded. Finally, a simulation experiment is utilised to demonstrate the feasibility of the proposed design approach.

This study proposes a vision-based motion estimation and target tracking algorithm for a quadrotor unmanned aerial vehicle circumnavigation around a moving mobile target whose velocity is unknown and time varying. In this study, the authors assume that the quadrotor is equipped with onboard downward-looking camera, as a means to determine position of the quadrotor relative to the target. The proposed circumnavigation control algorithm relies essentially on two distinct phases, namely the virtual target tracking and the circumnavigation phase. To prepare for these phases, a predefined sphere, with a desired radius having the moving target position as its centre, is constructed along with a virtual target point that can move on its surface. During the whole tracking procedure, the quadrotor is first commanded to reach the virtual target point located at the projection of the ground vehicle's position onto the surface area of the sphere. When the quadrotor's position and velocity approaches the virtual target point with a given accuracy, the second phase is initiated to provide the quadrotor with more precise guidance to start orbiting at a specific height from level ground around the moving target. In this manner, the virtual target point is given the ability to manoeuvre itself in a circular motion above the moving target. The developed orbit manoeuvre uses an estimate of the moving target's velocity, obtained from a predictor scheme able to achieve velocity estimation as fast as possible.

This study is concerned with stability analysis for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. By applying the idea of scalar function and augmented vectors, dealing with the positivity of a functional, a novel simple Lyapunov–Krasovskii functional is established. Then, fuzzy-weighting dependent matrices and the reciprocally convex approach are introduced to deal with two integral parts, convex analysis approach is used to solve the useful terms (which are ignored in previous methods), with the above methods some less conservative stability criteria is obtained. Finally, three numerical examples are provided to show the effectiveness and improvements of the proposed conditions.

In this study, a minimum jerk norm (MJN) scheme with an obstacle avoidance constraint is proposed and applied to a redundant robot arm, of which the joint jerks keep bounded for a human-friendly robot control. To achieve superior tracking performances of the redundant robot arm, the proposed jerk bounded MJN scheme is improved by the feedback control. More importantly, the effectiveness on obstacle avoidance of the proposed scheme is guaranteed by the variable-magnitude escape jerk theorem. Besides, for the purpose of implementation on the practical robot system, the corresponding discrete formulas with their theoretical analyses are presented. Then the proposed scheme is reformulated as a dynamical quadratic program which is solved by a piecewise-linear projection equation neural network. Furthermore, the path-tracking simulation and comparison substantiate the effectiveness and accuracy of such a scheme with the smooth and human-friendly joint variables applied to the obstacle avoidance of a six degrees of freedom jerk bounded robot arm. At last, the experimental application conducted on a practical redundant robot arm system further shows the physical realisability and the safety of the proposed scheme.

A robust iterative learning control (ILC) method is proposed for industrial batch processes with input delay subject to time-varying uncertainties, based on a two-dimensional (2D) system description of batch process operation. To compensate the input delay, a 2D state predictor is established to predict the augmented system states, such that a 2D ILC design is developed for the ‘delay-free’ 2D system based on using only the measured output errors of current and previous cycles. Delay-dependent stability conditions for the resulting 2D system are established in terms of matrix inequalities by defining a comprehensive 2D Lyapunov–Krasovskii functional candidate along with free-weighting matrices. By solving these matrix inequalities using a cone complementarity linearisation method, the ILC controller is explicitly derived together with an adjustable H infinity performance index. An important merit is that perfect tracking can be realised for a batch process with arbitrarily long input delay if the delay-free part of the 2D system can be stabilised, in no presence of time-varying uncertainties. Moreover, the time integral of tracking error can be added as an extended 2D system state for ILC design to eliminate steady-state output error for all batches. An illustrative example of injection moulding process is given to demonstrate the effectiveness of the proposed method.

This study investigates the output tracking problem for a class of Takagi–Sugeno fuzzy systems subject to periodic signals and actuator saturation via equivalent-input-disturbance (EID) technique. In particular, to ensure the periodic signals tracking, a state-space repetitive control structure is considered. Further, the EID technique is utilised to improve the disturbance rejection performance without any prior knowledge of the disturbance and inverse dynamics of the plant. By constructing a suitable Lyapunov–Krasovskii functional and using the Wirtinger-based integral inequality, a new set of sufficient conditions is derived in terms of linear matrix inequalities (LMIs) which ensures the stability of the addressed system. In addition to that by using a Lyapunov level set, saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimisation problem. Moreover, the designed fuzzy repetitive controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation, but also in the presence of any actuator faults, saturation and dead zone. Finally, the proposed method is validated through two numerical examples to illustrate the effectiveness and superiority of the developed controller design.

In this study, two novel iterative algorithms are presented to solve the Lyapunov matrix equations appearing in discrete-time periodic linear systems. In both algorithms, a weighted combination of the estimation in the last and the current steps is used to update the estimation of the unknown matrices. It is shown that the sequences generated by the proposed algorithms with zero initial conditions monotonically converge to the unique positive definite solution of the periodic Lyapunov matrix equation if the associated system is asymptotically stable. Finally, a numerical example is used to illustrate the effectiveness of the proposed algorithms.

In this study, a simple Lyapunov-based adaptive model predictive control (MPC) is proposed to stabilise a class of unconstrained non-linear systems with constant parametric uncertainties. In the proposed MPC design, the uncertain parameters are estimated online with an adaptive updating law, and the estimated parameters are guaranteed bounded. A Lyapunov-based constraint is employed in the adaptive MPC to ensure the stability of the closed-loop system. By using the control Lyapunov function-based constraint, terminal penalties in traditional MPC can be avoided, such that computational burden is significantly reduced. Both theoretical results and numerical examples demonstrate that, with the proposed adaptive MPC, states of the closed-loop system can be stabilised, while the adaptive estimated parameters are bounded.

This study deals with the problem of passivity and passification for switching Markovian jump systems with time-varying delay and generally uncertain transition rates. The considered systems could be viewed as Markovian jump linear systems governed by a piecewise-constant transition rate matrix, which is subject to a high level average dwell time switching. The time delay is considered as time-varying and meets the requirements of the upper and lower bounds. The generally uncertain transition rates cover uncertain transition rates and partly known transition rates as two special cases. First, sufficient conditions, which guarantee the exponential mean-square stability and stochastic passivity of the underlying systems, are presented by resorting to average dwell time approach. Second, the design of the stabilising controller is given further. Moreover, an improved controller design method, which could provide efficiency and practicability, is further developed. All the proposed conditions are given in the form of linear matrix inequalities. Finally, practical examples illustrate the validity of the obtained results.

This study is concerned with adaptive model-based event-triggered control of an uncertain continuous system with external disturbance. The proposed framework incorporates two important control techniques for reducing communication burden and regulating the states of the system online in control network, that is, adaptive model-based networked control system and event-triggered control (ETC). An adaptive model of the plant is capable of generalising the zero-order hold implementation in traditional ETC schemes, while also providing stability thresholds that are robust to model uncertainties. In the adaptive model-based controller, the authors present an update law to estimate the parameters of the adaptive model at triggered instant. After revisiting the adaptive model property in the context of event-triggered communication, an event-triggered condition is proposed using the Lyapunov technique. The stability condition of the proposed approach does not need explicit knowledge of the plant parameters, but are given only in terms of the parameters of the adaptive model and some bounds in the model uncertainties. In addition, lower bound on transmission periods are provided. Meanwhile, stability with respect to external disturbance is examined. A real-time simulation example is presented to demonstrate the effectiveness of the theoretical results.