In this study, the authors present robust tuning rules for an event-based control architecture for the automatic regulation of the depth of hypnosis in anaesthesia. The authors' control system uses propofol and remifentanil coadministration as control variables and the bispectral index as controlled variable. The control system is based on a PIDPlus controller combined with an event generator that detects significant variations of the BIS signal, thus providing strong filtering of the noise. A fixed ratio between the drug infusions allows the anaesthesiologist to explicitly regulate the opioid–hypnotic balance of the anaesthesia. The tuning rules are developed by solving a min–max optimisation problem that optimises the worst-case scenario over a given data set of patient models. A gain scheduling strategy yields optimal performance in both the induction and the maintenance phases of anaesthesia. Finally, through the Monte Carlo method, they validate the effectiveness of the proposed approach on a general population, and the robustness to the intra- and inter-patient variability for different infusion balances.

The periodic event-triggered control (PETC) and self-triggered control (STC) for networked singular systems under denial-of-service (DoS) attack and deception attack are studied. Due to the fact that DoS attack is able to prevent the control input from transmitting and deception attack falsifies the control input as a non-linear disturbance, a closed-loop system is constructed with different control inputs based on the switched system method. Next, the attention is focused on the design of PETC and STC schemes. PETC scheme adopts the input delay approach to transform the closed-loop system into a switched singular time-delay system and adjusts the triggering intervals by the frequency and duration of cyber-attacks. STC scheme relies on a reduced-order system derived from the original singular system and utilises the current sampled information to predict the next triggering instant. Then, exponential stability criteria are derived by codesigning the triggering parameter and controller gain. Finally, a small-signal version of the structure-preserving power network model is given to demonstrate the effectiveness of the proposed methods.

In this work, the fault estimation (FE) problem is studied for continuous-time non-linear switched systems with time-varying delay over fading channel under average dwell time switching. A novel FE method based on the intermediate estimator is used to eliminate the observer matching constraint condition, where an intermediate variable is introduced to estimate the state and fault simultaneously. Meanwhile, the fading channel of data transmission is modelled as Bernoulli distributed white sequences. Furthermore, because the observer matching conditions are eliminated by the intermediate estimator, both the wirtinger integral inequality and an advanced reciprocal convex combination method are utilised to provide a tighter estimation on continuous derivative of certain Lyapunov–Krasovskii function over fading channel, leading to a less conservative result. Moreover, the solution of the parameters for intermediate estimator is characterised in the feasibility of linear matrix inequality problem. Finally, two numerical examples indicate the proposed technique is valid and superior.

This study mainly focuses on the development of a second-order sliding mode-based meta-cognitive fuzzy neural network (MCFNN) control for power quality improvement, whereby an MCFNN is employed to learn modelling uncertainties. First, a second-order sliding mode control (SOSMC) is designed to track reference current for active power filter. Then, an MCFNN system with accurate approximation capability is further investigated to learn the unknown parts in SOSMC. Different from the existing predefined structure approaches, only necessary data can be extracted to adjust the structure and parameters of the networks in MCFNN. Subsequently, the Lyapunov stability analysis is presented to guarantee tracking performance and stability of the closed-loop system. Moreover, the excellent performance of the proposed MCFNN scheme is verified by simulation and experimental studies, and its remarkable characteristics are exhibited in comparison with other intelligent control schemes.

This work presents a new algorithm for flocking with a virtual leader by introducing a new sampling scenario, so-called multi-rate sampling. In the multi-rate sampling, the period of receiving data from different sources is different, but the updating time for all individuals is the same. Here, the authors assume that the period of receiving data from neighbour agents is T , and that from the virtual leader is an integer multiple of it, that is, mT . An upper bound for period T is attained from the upper bound of the energy function that guarantees the neighbouring network to be connected and collision to be avoided between agents. Also, an upper bound on m , which ensures the velocity of informed and uninformed agents to tend the virtual leader's velocity, is derived. The convergence analysis demonstrates that whatever the acquiring period of the virtual leader's information mT is further, then the convergence rate of the group's velocity to the virtual leader's velocity will be greater. Finally, to show the validity of the results, they present a simulation.

This study considers the bipartite containment problem for a class of descriptor multi-agent systems (MASs) under a structurally balanced graph. A new bipartite containment control protocol acting on each follower is proposed on the basis of designing a singular observer, where relative output information is utilised. By employing the stability theory of descriptor systems and multiple Lyapunov function technique, some sufficient criteria are derived to guarantee observer-based bipartite containment of descriptor MASs. The feasibility of obtained theoretical results is finally verified via performing simulations.

This study is concerned with reinforcement learning enhanced by two-time scale approximations. Many systems arising in applications are large and complex. To treat these problems, it is often beneficial, and sometimes necessary, to reduce the dimensionality and aggregate states that are ‘close’ to each other. In this study, the authors propose a two-time scale reinforcement learning method for such an aggregation process. In particular, they present how to classify states that are ‘close’ and demonstrate the effectiveness of the authors' state aggregation based two-time scale methods. Thus the problem can be considered as using learning for identifying the system. A production planning problem with failure-prone machines is used throughout this study to illustrate the main ideas, key steps and results. Monte Carlo simulations are used to generate the random environment.

Parameter estimation is an important tool for modelling a real system. This study considers the parameter estimation problem of a multi-input multi-output state-space system with unmeasurable states. By employing the negative gradient search and cutting down redundant parameter estimates, the authors derive a partially-coupled generalised stochastic gradient (PC-GSG) algorithm to estimate the parameters. Considering the unmeasurable states, they present a new state observer which replaces the unknown parameters with their estimates to generate state estimates. By combining the PC-GSG algorithm and the new state observer, they obtain a state observer based partially-coupled generalised stochastic gradient (SO-PC-GSG) algorithm to estimate the parameters and states. In order to eliminate the interference of the coloured noise and strengthen the performance of the SO-PC-GSG algorithm, they propose a state observer based filtering PC-GSG algorithm by means of the data filtering technique. Finally, the effectiveness of the proposed algorithms is investigated in a simulation study.

The output regulation problem for pure-feedback non-linear systems with prescribed performance (PP) driven by an external linear system with unknown parameter are investigated. First, an observer with a disturbance signal is designed to observe unmeasured system states. Secondly, fuzzy logic systems (FLS) are used to approximate unknown non-linear non-affine functions. Thirdly, a fuzzy internal model is obtained to reject disturbance, and an adaptive fuzzy output feedback algorithm is proposed based on dynamic surface control (DSC) technique and backstepping method. Simultaneously, an L function is constructed so that the overall property (steady-state property and dynamic property) of the tracking error are constrained by PP functions. The results explain that the proposed control algorithm can make sure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and the tracking error is semi-globally PP uniformly ultimately bounded (SPPUUB). Finally, two examples are given to show the validity of the results.

In this study, near optimal tracking of a class of non-linear systems is addressed. Adaptive (approximate) dynamic programming (ADP) approach is used to calculate the optimal control in closed form. ADP has been widely used to resolve optimal regulation and tracking problems of non-linear control systems. Despite advances in the so called supervised and unsupervised ADP techniques for optimal tracking, they have a main draw back. That is, the optimal controller needs to be recalculated for every particular reference trajectory. The main goal of this work is to address this issue for a class of non-linear systems. Finally, this approach is applied on a Delta robot and the performance of the method is analysed experimentally.

This study addresses the event-based control of networked switched systems subject to cyber attacks. A novel mode-based event-triggered mechanism is proposed, which is capable of characterising non-periodic denial-of-service (DoS) attacks. A switching control law is employed in each subsystem to weaken the negative effects caused by DoS attacks. The time sequences of system switchings, event triggerings and intermittent DoS attack behaviours are fully investigated, which yields a resultant closed control system. Then, by using piecewise Lyapunov functional methods, sufficient conditions are formulated to guarantee the concerned system exponentially stable. Meanwhile, the co-design methods for switching controllers and event-triggering parameters can be developed. Finally, a numerical simulation example and a practical example of a second-order oscillating circuit are presented to verify the proposed methods.

Switched models whose dynamic matrices are in block companion form arise in theoretical and applicative problems such as representing switched ARX models in state-space form for control purposes. Inspired by some insightful results on the delay-independent stability of discrete-time systems with time-varying delays, in this work, the authors study the arbitrary switching stability for some classes of block companion discrete-time switched systems. They start from the special case in which the first block-row is made of permutations of non-negative matrices, deriving a simple necessary and sufficient stability condition under arbitrary switching. The condition is computationally less demanding than the sufficient-only existence of a linear common Lyapunov function. Then, both non-negativity and combinatorial assumptions are dropped, at the expense of introducing conservatism. Some implications on the computation of the joint spectral radius for the aforementioned families of matrices are illustrated.

The safety of a vehicular platoon is seriously threatened in the presence of actuator saturations, (possibly fast) time-varying non-linear uncertainties. Meanwhile, the string stability and the strong string stability cannot eliminate the potential safety hazard caused by large initial error conditions. This study focuses on safety-guaranteed distributed control of the vehicular platoon with a bidirectional communication topology and the constant time headway policy. The authors formulate bilateral inequality constraints on the spacing error between adjacent vehicles to represent the collision-avoidance and compact formation performance. A novel state transformation technique is proposed to convert the bounded spacing error space to an unconstrained state space. On the basis, Comprehensive equality constraints for the transformed states are established by integrating the information of proximal (preceding and following) vehicles. In addition, an anti-windup compensation method is utilised to handle actuator saturations. Then an adaptive constraint-following controller is designed to render the uniform boundedness and uniform ultimate boundedness performance of the transformed state. As a result, the string stability, the strong string stability, the collision-avoidance and compact formation are guaranteed despite the presence of actuator saturations and complex uncertainties. Numerical simulations are performed to validate the effectiveness of the proposed control scheme.

This study solves the problem of observer-based output feedback stabilisation of a coupled time-fractional reaction–advection–diffusion system with space-dependent coefficients. In light of the backstepping approach, the Mittag–Leffler convergent observer is derived to enable stabilisation by output feedback. By the fractional Lyapunov method, the Mittag–Leffler stability of the estimation error system is then established. Using the separation principle yields a stabilising output feedback controller, with which the closed-loop stability is proved. Finally, the feasibility of the proposed approach is tested by fractional numerical examples when the kernel matrix equation has not the explicit solution.

This study proposes a new active fault-tolerant control (FTC) and fault estimation scheme for a non-linear octorotor system. The proposed method utilises the idea of an online control allocation (CA) scheme to fully engage the rotors redundancy based on the information from the fault estimation unit. The nominal performance is first achieved using non-linear dynamic inversion (NDI) technique and then to incorporate the robustness, an adaptive non-linear sliding mode control is united with a baseline NDI controller. The proposed method is used to attain the desired altitude and attitude tracking control of an octorotor system. Furthermore, to control the un-actuated states (called internal dynamics) of octorotor system, a separate integral sliding mode-based NDI controller is designed that provides the translational axes control by generating the desired roll and pitch commands. Simulations on the non-linear model of octorotor system validate the dominant performance of the proposed scheme compared to the existing methods in the literature.

This study is concerned on the design of a quasi-linear parameter varying (qLPV) proportional–integral (PI) controller for twin rotor multiple-input multiple-output systems (TRMS). The non-linear model is represented as a qLPV polytopic plant with an affine dependence on a non-linear parametric function of the pitch angle. This representation retains the exact model as opposed to the conventional linearisation around an operating point. Due to the availability of the pitch angle measurement, the non-linear parameter can be obtained in real-time and the controller is designed using qLPV technique. To deal with limited control input for such systems, the proposed controller design also considers the actuator saturation that yields controller with practical gains without any additional gain bound criterion. Further, the transient tracking performance is also considered in the design by using closed-loop eigenvalues assignment in desired damping regions. The control synthesis problem is formulated in the form of linear matrix inequalities for gain based performance criterion. The designed controller is validated on a two-degree of freedom helicopter experimental setup. Finally, to demonstrate the effectiveness of the proposed design, a comparative analysis is done with the existing algorithms. Also, the efficacy of the decentralised controller vis-a-vis the centralised one is presented.

In this study, an innovative technique to design an observer-based finite-time output feedback controller (FT-OFC) is proposed for a class of non-linear systems. This controller aims to make the state variables converge to a small bound around the origin in a finite time. The main innovation of this study is to transform the non-linear system into a new time-varying form to achieve the finite-time boundedness criteria using the asymptotic stability methods. Moreover, without any prior knowledge of the upper bounds of the system uncertainties and/or disturbances, and only based on the output measurements, a novel time-varying extended state observer is designed to estimate the states of the non-linear system as well as the uncertainties and disturbances in a finite time. In this way, the time-varying gains of the extended state observer are designed to converge the observation error to a neighbourhood of zero while remaining uniformly bounded in finite time. Subsequently, an observer-based time-varying control law is designed to make the system globally uniformly bounded in finite time. Finally, the efficiency of the proposed FT-OFC for a disturbed double integrator system with unknown measurement noise is illustrated by numerical simulations.

This study investigates a parametric method to design a dynamic compensator for descriptor high-order quasi-linear (DHQ) systems. Utilising the solution to generalised high-order Sylvester equations, a more unified parametric form of the dynamic compensator is developed to improve the control effects. Meanwhile, normalisation design by using the dynamic compensator is also considered for DHQ systems such that the closed-loop regularity can be maintained easily and effectively. Whether the closed-loop form is singular or not, it has an expected eigenstructure. Finally, an example is provided to verify the parametric method is feasible and reliable.

The fixed-time master–slave trajectory tracking control problem of the human-in-the-loop teleoperation systems with mixed communication delays (including time-varying delays and random delays), parametric uncertainties, and external disturbances is discussed in this study. Based on the non-singular terminal sliding mode control technique, a novel neuro-adaptive fixed-time control algorithm is designed to solve the above-mentioned problem. Moreover, to improve the steady-state performance of the presented control algorithm, the combination of the radial basis function neural networks, parametric adaptive laws and fixed-time control method is newly-designed and used to reduce the effects of parametric uncertainties and external disturbances. By employing the Lyapunov argument, the sufficient conditions on the control parameters for guaranteeing the fixed-time stability of the controlled teleoperation system are derived. Besides, the authors also present the upper bound of the settling time and prove that it is independent of the initial condition. Finally, several simulation examples are performed to verify the effectiveness of the theoretical results.

This study synthesises modelling techniques and dynamic state estimation techniques for the simultaneous estimation of the muscle states, muscle forces, and joint motion states of a dynamic human arm model. The estimator considers both muscle dynamics and motion dynamics. The arm model has two joints and six muscles and contains dynamics both of the muscles and of the motion. We develop an optimally tuned extended Kalman filter using noisy measurements of joint angles with standard deviation 2.87, of joint velocities with standard deviation 6.9/s, and of muscle activations with standard deviation 10% of their peak values, and then simultaneously estimate joint angles, joint velocities, muscle forces, joint moments, and muscle states. The standard deviations of estimation errors (SDEE) are no more than 0.07° for joint angles, 1/s for joint velocities, 0.6 mm for muscle–tendon lengths, and 0.1 Nm for joint torques. The results are compared with a previously developed static optimisation method, and verify the effectiveness of the proposed estimator in providing lower SDEE for both muscle and motion dynamics of the human arm model compared to the static optimisation method.

This study addresses the gain-scheduled control problem for discrete-time delayed non-linear parameter-varying (NLPV) and linear parameter-varying (LPV) systems. First, by constructing the parameter-dependent Lyapunov–Krasovskii functional and employing multiple auxiliary functions, delay-dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay-dependent linear matrix inequality conditions for the static output-feedback control design and state-feedback control design for delayed NLPV are provided. Second, the results obtained for discrete-time delayed NLPV systems are modified in a simple way to deal with discrete-time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

This work investigates the static output feedback sliding mode control (SMC) design problem of uncertain non-linear systems with Rice fading channels. The interval type-2 Takagi-Sugeno fuzzy modelling approach is exploited to express non-linear dynamics with uncertain parameters. As the wireless network between the sensor and the controller may be subject to channel fading, the premise variables are probably altered during their propagations. In such cases, a key issue is to synthesise a desired SMC law for stabilising the controlled non-linear systems. To this end, new membership functions are constructed via employing the fading measurements and the desired SMC law are subsequently synthesised. To deal with the disturbances in communication channels, the notion of input-to-state stable in probability (ISSiP) is utilised and sufficient criteria are deduced to guarantee the ISSiP of the resultant closed-loop systems and the reachability of the prescribed sliding surface. Finally, a simulation example illustrates the designed control strategy.

In this technical note, the problem of observer-based controller design is considered for sensor networked systems subject to distributed hybrid-triggered transmission scheme and input quantisation. A novel observer model based on coupled transmission signals from multi-channel is first proposed to estimate unavailable state variables and exploited in the feedback protocol. In order to provide a trade-off between saving network resources and improving system performance, a distributed hybrid-triggered transmission scheme with communication delays is adopted to update the observer input signals. For the sake of further reducing the occupancy of network resources, the control input signal is quantised by a logarithmic quantiser. Then, by making use of the Lyapunov stability theory, the sufficient conditions guaranteeing the system asymptotically stable are presented. Moreover, the explicit expressions of observer and controller parameters are achieved by solving a set of linear matrix inequalities. Finally, two simulation examples are provided to illustrate the rationality of the proposed control method.

Symbolic planning techniques rely on abstract information about a continuous system to design a discrete planner to satisfy desired high-level objectives. However, applying the generated discrete commands of the discrete planner to the original system may face several challenges, including real-time implementation, preserving the properties of high-level objectives in the continuous domain, and issues such as discontinuity in control signals that may physically harm the system. To address these issues and challenges, the authors proposed a novel hybrid control structure for systems with non-linear multi-affine dynamics over rectangular partitions. In the proposed framework, a discrete planner can be separately designed to achieve high-level specifications. Then, the proposed hybrid controller generates jumpless continuous control signals to drive the system over the partitioned space executing the discrete commands of the planner. The hybrid controller generates continuous signals in real-time while respecting the dynamics of the system and preserving the desired objectives of the high-level plan. The design process is described in detail and the existence and uniqueness of the proposed solution are investigated. Finally, several case studies are provided to verify the effectiveness of the developed technique.

In this study, a distributed model predictive control (MPC) method based on extended state observer is proposed for a class of large-scale interconnected systems by using a reduced state-space decomposition strategy. Firstly, the full state of the system is divided into internal state and external state to decrease computation and communication burden, where the former one is used for local optimisation, and the latter one is used to exchange with its neighbours. Based on the receding optimisation strategy, a reduced state-space decomposition iterative algorithm is proposed, and the convergence of the proposed algorithm is given. To improve the disturbance rejection capability of the system, an extended state observer is designed to estimate the disturbance by using a pole assignment method. By applying a feedforward compensation strategy, a composite controller is derived by combining with local MPC controller and compensation controller, then the input-to-state stability is analysed for the closed-loop system. Finally, an example of a ship engine room power system is given to demonstrate the effectiveness of the proposed method.

In this paper, the matched-pole–zero model which has been widely used for discretisation of a single-input–single-output control system described in transfer-function forms is extended to be applicable to the system in state-space forms. The matched-pole–zero model is classified as the discrete-time model, where poles and transmission zeros are mapped into the discrete-time domain according to the same discretisation law defined by a certain algebraic relationship. In order to obtain the matched-pole–zero model, the paper presents an equivalent reconfiguration, which transforms a system into an internal feedback structure around a subsystem based on the principle of control zeros. Discretisation of the subsystem produces a discrete-time model, where transmission zeros are mapped according to the desired law. The proposed matched-pole–zero model is obtained by modifying the pole placements of this discrete-time model. As long as the direct-term matrix of the underlying system is nonsingular, the proposed model can be obtained algorithmically and is applicable to a multi-input-multi–output system without any modification. The paper provides numerical examples verifying that the proposed matched-pole-zero model preserves the unique characteristics of the underlying system due to the zeros, such as the blocking and the decoupling properties, and causes smaller discretisation errors than the comparable matched-pole–zero model.

The consensus problem for a class of multi-agent systems with switching jointly connected topologies via periodic event-triggered control is studied. The distinguishing feature of such system is that the eigenvalues of system matrix can contain positive real parts. Due to the coexistence of unstable system matrix and disconnected topologies, the agents can diverge from each other across some periods even if the control input is imposed on them. To overcome this difficulty, a periodic-sampling time unit (PSTU) approach is introduced to analyse the local convergence or divergence property within each sampling time unit based on the periodic event-triggering control. Then the stabilisation property of switching behaviours is utilised to compensate the divergence within each switching interval via the dwell time technique. It is interesting to see that each switching period is considered to consist of finite number of PSTUs. Then by confining a pair of lower and upper bounds on the dwell time, the overall consensus can be reached. Further, a novel class of event-dependent discretised Lyapunov functions are utilised to describe the error characteristics and computable conditions for the overall consensus can be derived. Finally, the effectiveness of the proposed result is illustrated by a numerical example.

This study investigates the adaptive fault-tolerate control for strict-feedback non-linear system, in which actuator and sensor faults may happen simultaneously. Moreover, the additive and multiplicative faults are considered, which cover the bias, drift, loss of accuracy, and loss of effectiveness faults. Under the multiple sensor faults, a modified backstepping technique involving in the faulted states is proposed by utilising the fuzzy approximation to the unknown non-linear functions. Later, the adaptive fuzzy fault-tolerant control strategy is designed to ensure the practical fixed-time stability of the closed-loop system. Meanwhile, the convergence time is independent of the initial states of the system, and the control performance can be ensured for arbitrary bounded initial states in this study. Finally, the Buck converter circuit is employed to demonstrate the effectiveness of the proposed fault-tolerant control scheme.

In this study, adaptive prescribed finite-time stabilisation of uncertain single-input and single-output non-linear systems is considered in the presence of unknown states, unknown parameters, external load disturbance, and non-symmetric input saturation. A prescribed finite time disturbance observer is designed to approximate the unmeasured external disturbance. Also, a non-singular prescribed finite time terminal sliding mode control is proposed for the closed-loop control of the system with the non-symmetric input saturation. Extended Kalman filter algorithm is employed for the real-time estimations of the states and unknown parameters of the system. Moreover, a particle swarm optimisation algorithm is used to obtain the design parameters of the proposed disturbance observer and controller. To show the performance of designed control scheme, the proposed approach is employed to guarantee prescribed finite time stabilisation of non-linear vibration of a non-local strain gradient nanobeam. The Galerkin projection method is used to reduce the non-dimensional form of the governing non-linear partial differential equation of Euler–Bernoulli nanobeam to the ordinary differential equation. Finally, numerical simulations are performed to illustrate the effectiveness and performance of the developed adaptive control scheme for the vibration control of nanobeam in comparison with the conventional sliding mode control.

In this study, a sampled-data networked control system over a multipath routing-enabled network is investigated, where each delivered signal in a path suffers a random delay. For such a system, the mean square stabilisation problem is considered under the joint design of the event-driven strategy on the actuator side and the control policy on the decision-maker side. The contributions of this study are twofold. First, by pre-defining an application time as an event-triggering parameter, the sampled-data system is transformed into a stochastic form with input delay and packet dropout. When the probability distribution of random delay is known a priori, the close form of packet dropout rate is proposed and a set of necessary and sufficient stabilisation conditions are developed simultaneously. When is unknown, the reduced system is an uncertain dynamic system. Utilising matrix polynomials, a verifiable criterion is derived for stabilising the uncertain system, which is also necessary and sufficient. Second, for the scalar system, the close form of allowable sampling period bound is developed in terms of and system parameters.

Due to the features of event-triggered control in exploiting and saving system resources, they have been widely applied in sensor networks, multi-agent systems, networked control systems and so on. In this study, the authors focused on robust event-triggered distributed model predictive control (RETDMPC). Subject to disturbances and parametric uncertainties, they first applied the min–max model to RETDMPC. The min–max RETDMPC methodology is used to guarantee the robustness of the system state by taking the worst possible case of unknown uncertainties into consideration. Furthermore, in this framework, a new cost function is developed in which unknown uncertainties are considered. Next, sufficient conditions are provided to ensure the feasibility and stability of their developed min–max RETDMPC. Finally, a practical example is given to illustrate the advantages of their algorithm by comparing to the conventional model predictive control.

The DC–DC converters usually interfaces renewable energy sources in DC microgrids which may be contaminated by harmonic perturbations that adversely affect performance, creates stability and protection problems in a DC grid system. In this paper, the authors propose the use of the popular proportional–integral–derivative (PID) controller to mitigate selected harmonics. The solution is obtained by computing the complete set of stabilising controllers and imposing a bound on the sensitivity function. Using matrix representation of conic sections, the geometric-based PID controller is derived in the controller parameter space. The main result finds a subset of the stabilising set in which the controller mitigate harmonics with prescribed levels of attenuation which are constructively determined for each frequency of the selected harmonics. Simulation and experimental results using a boost converter are provided for validation.

This study revisits the problem of attitude stabilisation for rigid spacecraft with actuator constraints in the framework of non-linear proportional–derivative (PD) control methodology. A simple single saturated PD (SSPD) control is proposed. The most appealing features of the proposed SSPD control are that it completely embeds the control action within only a single saturation function for every actuator and omits the elaborate discrimination of the terms that shall be bounded for the commonly-used saturated control and hence it is easy for practical implementation with an improved performance. Lyapunov's direct method is employed to show asymptotic attitude stabilisation. Two illustrative examples are presented to demonstrate the improved performance of the proposed approach.

Iterative learning control (ILC) is a high-performance technique for repeated control tasks with design postulates on a fixed reference profile and identical initial conditions. However, the tracking performance is only critical at few points in point-to-point tasks, and their initial conditions are usually trial-varying within a certain range in practice, which essentially degrades the performance of conventional ILC algorithms. Therefore, this study reformulates the ILC problem setup for point-to-point tasks and considers the effort of trial-varying initial conditions in algorithm design. To reduce the tracking error, it proposes a worst-case norm-optimal problem and reformulates it into a convex optimisation problem using the Lagrange dual approach. In this sense, a robust ILC algorithm is derived based on iteratively solving this problem. The study also shows that the proposed robust ILC is equivalent to conventional norm-optimal ILC with trial-varying parameters. A numerical simulation case study is conducted to compare the performance of this algorithm with that of other control algorithms while performing a given point-to-point tracking task. The results reveal its efficiency for the specific task and robustness against trial-varying initial conditions.

This study addresses the problem of exponential stability for switched singular state-delayed systems with switching induced state jumps, which has not been studied up to now. The considered state delay varies in a time-varying interval. On the basis of equivalent dynamics decomposition, a model of state jump at switching instants is firstly established under an assumption that the time length between arbitrary two adjacent switches is larger than the upper bound of the state delay. Then, a sufficient condition on exponential stability of the system under the reranged dwell-time switching constraint is presented. The key idea is the design of a dwell-time-dependent generalised Lyapunov function as well as a dwell-time-dependent function with respect to algebraic variables and application of the Razumikhin approach. The obtained stability condition exploits the lower bound and the upper bound of the dwell time. In addition, it is independent of the size of the state delay and allows the delay to be a fast time-varying function. Finally, two numerical examples are given to show the efficacy of the derived result.