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A complex dynamical network (CDN) can be considered as the composition system with the nodes subsystem (NS) and the links subsystem (LS), and both subsystems are coupled with each other. In this paper, two vector differential equations (VDE) are used to describe the dynamical behaviours of NS and LS, respectively, in which the dynamical behaviour of NS is considered as the VDE with the second derivative term (SDT). This paper mainly focuses on the dynamics of LS, which is represented as VDE with the intuitive topologic feature of outgoing links, and investigates the design of the tracking controller for NS and the auxiliary tracking objectives (ATO) for LS. Firstly, the dynamical models of NS and LS in CDN are proposed, and the corresponding assumptions are given. Secondly, based on Lyapunov stability theory, the controller of NS and the ATO of LS are designed so that the state of NS can asymptotically track the given reference signal. Finally, the effectiveness of the proposed control strategy in this paper is verified by the numerical simulation example with N two-links robots. Abbreviations: ATO: auxiliary tracking objectives; CDN: complex dynamical network; LS: links subsystem; MDE: matrix differential equation; NS: nodes subsystem; SDT:second derivative term; VDE: vector differential equation; [ABSTRACT FROM AUTHOR]

To improve the ride comfort of the vehicle and the high-efficiency control requirements of the suspension, this paper proposes a time-delay control strategy and the idea of using a linear motor as the actuator. This paper analyses the damping characteristics of the time-delay control strategy in the time domain and frequency domains. A linear equivalent excitation method is proposed to optimise the optimal time-delay control parameters under complex excitations. The stability of the system is analysed. The damping effect of time-delay control active suspension is verified by numerical simulation. An experimental hardware platform of a linear motor and active suspension was built further to verify the effectiveness of the time-delay control strategy. The experimental results show that the relative errors of root mean square values of experimental and simulation results are within 16% under each working condition. The experimental results verify the effectiveness of the simulation results. [ABSTRACT FROM AUTHOR]

This paper suggests a new dynamic sliding mode controller incorporating a disturbance observer for controlling integrating processes with time delay. Here, a new reaching law has been introduced to expedite the system response without evoking chattering. The convergence of this law is also studied. Additionally, the whole system stability is proved using the Lyapunov stability theory. This paper also proposes a new disturbance observer to improve the disturbance rejection and to help suppress chattering further. The suggested observer has only one parameter to be designed. Therefore, this observer can easily be implemented. Several simulation examples and a real-time application are considered to prove the superiority of the suggested controller over the reported controllers in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate various stabilisation problems of a hybrid system of elasticity, consisting of a thin tape, which moves axially between two sets of rollers. We present a control solution, which works simultaneously, for three variants of the tape model. In particular, we design boundary feedback control laws via Lyapunov's second method. The resulting closed-loop system for the general case is then analysed, where we prove the existence and uniqueness of solution using the semigroup theory of linear operators; furthermore, we prove the exponential decay of the solution via a frequency domain theorem. The stabilisation of the two other special cases is derived implicitly from the general case proofs presented in the paper. Finally, the paper is concluded by presenting computer simulations to support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time consensus control for a class of multi-agent systems subject to unknown bounded disturbances under undirected topology. Firstly, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid the non-differential problem. Secondly, a distributed fixed-time control protocol is designed, which can realise the fixed-time convergence and improve the system convergence rate independent of the system's initial state. Thirdly, the dynamic event-triggered mechanism is proposed, such that the triggering frequency of events is reduced and communication energy consumption can be saved. The stability analysis is presented by employing the Lyapunov theory and the Zeno phenomenon is excluded. Finally, the simulation examples are presented to show the effectiveness and advantages of the proposed method in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes Brenke-type polynomials for uncertainty approximation in adaptive control of cooperative electrically driven manipulators. The contribution of this paper is reducing the number of signals needed in the construction of the regressor vector for uncertainty approximation due to the simplicity of Brenke-type polynomials in comparison with other alternatives. It is verified that uniformly bounded stability of the tracking/approximation errors can be assured if the Brenke-type polynomials are utilised as regressors. Moreover, it has been assumed that velocity signals are not available for feedback. Different trajectories, including simple and highly complicated and fast paths, have been tested in simulation results. The results are also compared with four state-of-the-art powerful approximation methods to show the accuracy and efficiency of the proposed controller structure. [ABSTRACT FROM AUTHOR]

This paper deals with the robust state feedback stabilizability problem of linear time-invariant (LTI) systems in the presenceof polytopic uncertainty. The paper contributes two major results involving (i) necessary and sufficient conditions to simultaneouslycheck positivity and robust stability of an uncertain LTI system (ii) the development of a design algorithm to solve the mainstabilizability problem. This problem is not easy to deal with because it is not a convex problem. To cope with this issue, a designalgorithm is proposed that checks the design space of the stabilizer parameters, divides it into smaller subspaces, checks thefeasibility of the corner points of the design subspaces, removes the detected total infeasible design subspaces, and shrinks theremaining parts to solve the design problem, iteratively. The proposed algorithm is applied to the cancer chemotherapy applicationand the results demonstrate its efficacy to control the model considering the positivity condition. [ABSTRACT FROM AUTHOR]

The eigenstructure of imaginary axis eigenvalues of a Hamiltonian matrix is of importance in many fields of control systems, for example, in stability analysis of linear Hamiltonian systems, computation of the solutions of an algebraic Riccati equation (ARE), existence of a Lyapunov function for LTI systems, etc. The dynamical system consisting of all stationary trajectories for an optimal control problem – often called the Hamiltonian system – is known to admit, in its state space dynamical equation, a Hamiltonian matrix for the system matrix. In each of these cases, defectiveness of imaginary axis eigenvalues of a Hamiltonian matrix turns out to be of crucial importance. For example, defectiveness causes unboundedness of the oscillatory stationary trajectories in the Hamiltonian system. A characterisation of the ARE solutions in terms of Lagrangian invariant subspaces of the Hamiltonian matrix when the imaginary axis eigenvalues are defective has been addressed in the literature for the controllable case. This paper focuses on the general case of uncontrollable systems; we formulate conditions under which the imaginary axis eigenvalues of the Hamiltonian matrix are non-defective: this is central for solutions corresponding to imaginary axis eigenvalues to not become unbounded. We provide conditions on the so-called ϵ -characteristic of the non-defective imaginary axis eigenvalue: this helps in the characterisation of Lagrangian invariant subspaces. We formulate conditions under which a passivity-based Hamiltonian matrix is normal (i.e. it commutes with its transpose), and we link normality of such Hamiltonian matrices with all-pass behaviour. In summary, this paper formulates results that link defectiveness of imaginary axis eigenvalues of Hamiltonian matrix to solvabilities of Lyapunov and Algebraic Riccati equations, controllability/observability, ϵ -characteristic and sign-controllability. We consider examples in the area of bounded-real transfer functions and RLC circuits, both controllable and uncontrollable, to study applicability of the results of this paper. [ABSTRACT FROM AUTHOR]

This paper studies the global attitude stabilization of a rigid body, a task that is subjected to topological obstacles. As a result of these obstructions, continuous feedbacks cannot globally stabilise the rigid body attitude. Therefore, this paper presents an observer-based hybrid controller to overcome these restrictions. Consequently, a new kind of synergistic potential function is designed which induces a gradient vector field to globally stabilise a given set. Moreover, the gradient of the proposed potential functions is utilised to derive a hybrid observer. Furthermore, this paper considers two types of constraints: angular velocity constraint and torque constraint. Afterward, these constraints are formulated in terms of the Linear Matrix Inequalities (LMI) optimisation problem to perform constraints satisfaction. Besides, this paper introduces a novel hybrid quantiser to deal with the problem of the low-price wireless network. Finally, a comparative study in simulations is provided to assess the performance of the proposed scheme. [ABSTRACT FROM AUTHOR]

Distribution-dependent stochastic differential equations (DDSDEs, in short), also called as McKean–Vlasov SDEs, are a special class of SDEs and have some concrete applications in mean-field control, mean-field games and complex networks. Stability plays fundamental role among the theory and applications for DDSDEs. In this paper, we discuss a class of distribution-dependent stochastic differential equations driven by time-changed Brownian motions (TDDSDEs, in short). The main aim of this paper is to establish the stability for TDDSDEs. Sufficient conditions are provided to guarantee the solutions to be stable in different senses with regard to a part of the variables in terms of a Lyapunov function. Two examples are given to show the usefulness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a novel distributed controller that solves the leader-follower and the leaderless consensus problems in the task space for networks composed of robots that can be kinematically and dynamically different (heterogeneous). In the leader-follower scenario, the controller ensures that all the robots in the network asymptotically reach a given leader pose (position and orientation), provided that at least one follower robot has access to the leader pose. In the leaderless problem, the robots asymptotically reach an agreement pose. The proposed controller is robust to variable time-delays in the communication channel and does not rely on velocity measurements. The controller is dynamic, it cancels-out the gravity effects and it incorporates a proportional to the error term between the robot and the controller virtual position. The controller dynamics consists of a simple proportional scheme plus damping injection through a second-order (virtual) system. The proposed approach employs the singularity free unit-quaternions to represent the orientation of the end-effectors, and the network is represented by an undirected and connected interconnection graph. The application to the control of bilateral teleoperators is described as a special case of the leaderless consensus solution. The paper presents numerical simulations with a network composed of four 6-Degrees-of-Freedom (DoF) and one 7-DoF robot manipulators. Moreover, we also report some experiments with a 6-DoF industrial robot and two 3-DoF haptic devices. [ABSTRACT FROM AUTHOR]

This paper describes a general physical background that originates integro-differential problems with specific reference to aero-elastic coupling, and offers two techniques of control for this class of problems. The central result of the paper is that integro-differential equations with kernel exponential series admit an optimal solution described, in turn, by a Volterra integral equation in terms of the control. Numerical simulations show how controls prevent the flutter instability of a two-dimensional wing and a wind turbine blade. [ABSTRACT FROM AUTHOR]

The high computationally expensive nature of nonlinear optimisation algorithms leads to limitations of its use in a real-time era. So, this is the main challenge against researchers to develop a fast algorithm that is used in real-time computations. This paper proposes a fast nonlinear model predictive control algorithm that utilises a parallel particle swarm optimisation with synchronous and asynchronous methods inclusion, that handles nonlinear optimisation problems with constraints. The additional divide and conquer approach of the proposed algorithm improves the speed of computation and disturbance rejection capability which proves its efficacy in real-time applications. A highly nonlinear fast dynamic real-time inverted pendulum system with hybrid embedded hardware platform (ARM + FPGA) is used to validate the performance of this algorithm under constraints. The solution presented in the paper is computationally feasible for smaller sampling times i.e. in miliseconds and it gives promising results with synchronous and asynchonous parallel PSO compared to the state-of-art PSO algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the achievable delay margin using lead-lag filter structures for Electric Power Steering systems. We propose an approximation of the delay margin as an explicit function of filter parameters. Our results provide useful guidelines for adjusting the different filter parameters to ensure system stability in the presence of a time delay. Simulation results show that the proposed filter structures can attenuate vibrations and improve steering feel and road feel. As a consequence, the influence of the delay on the system can be minimised with little performance degradation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential contraction and expansion of regime-switching diffusions. The focus is on the behavior of the distance from one solution to another solution, rather than with respect to some equilibrium point. The moment and almost sure exponential contraction and expansion are investigated. General criteria and easily verifiable conditions for the moment and almost sure exponential contraction and expansion are obtained. The contribution of the Markovian switching to the exponential contraction and expansion is revealed. Several examples together with numerical experiments are provided for demonstration. The convergence of contracting observers with noisy measurements under Markovian switching and the connection between exponential contraction and global attractivity of stochastic population systems are presented. [ABSTRACT FROM AUTHOR]

The development of intelligent prostheses has effectively improved the life of amputees. However, the current prosthetics mainly focus on restoring the basic mobility of amputees, without considering the use habits of the wearer and the diversity of arm movements, which makes the unknown interference and complex control requirements in daily life an obstacle to the use of prosthetics. To solve this problem, this paper proposes a combination method of adaptive control algorithms of bionic arm shoulder joint based on DDPG to realise intelligent control of the shoulder joint of upper limb prosthesis. Based on using adaptive control to reduce the interference of external variables, the accuracy of the joint module system is improved through reinforcement learning. The results show that the controller has a good effect on improving the dynamic performance of the mechanical system and can be widely used in bionic mechanical control. [ABSTRACT FROM AUTHOR]

This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals which are called event times. Sufficient conditions are established to guarantee asymptotic stability of the resulting impulsive systems. It is worth mentioning that the event times are different from the impulse times, that is, the control signals are updated at each event time but the actuator performs the impulsive control tasks at a later time due to time delays. The effectiveness of our theoretical result with the proposed scheme is illustrated by three examples. [ABSTRACT FROM AUTHOR]

This paper proposes a nonlinear controller strategy for the frequency regulation of a hydraulic turbine regulating system (HTRS). An immersion and invariance (I&I) technique is utilised to develop the desired control law. The derived control method is used to guarantee that the equilibrium point is asymptotically stable. Furthermore, it can ensure that all overall closed-loop system trajectories are bounded. The feasibility and effectiveness of the technique are demonstrated using a nonlinear dynamical system of an HTRS connected to a single-machine infinite bus (SMIB) power system. The simulation results demonstrate that the technique is capable of regulating the frequency and improving dynamic performance despite large disturbances. It is capable of rapidly reducing oscillations and surpasses two known nonlinear controllers, namely the synergetic control and the backstepping control techniques. Additionally, despite the fact that the HTRS's parameters vary, the proposed technique is capable of providing consistent control performance. As a result, the presented controller is insensitive to variations in the system's parameters. [ABSTRACT FROM AUTHOR]

Lyapunov-based approach to sampled-data set stabilisation of constrained delayed Boolean control networks (DBCNs) is investigated in this paper. The main mathematical tool is semi-tensor product (STP) of matrices. Since the sampling interval is selected from a finite set, the STP method is adopted to convert the dynamics of constrained DBCNs under nonuniform sampled-data control into a switched Boolean network (SBN). It is worth noting that the switches can only occur at the sampling instant. Using the techniques of Lyapunov function and average dwell time, several sufficient conditions are proposed for the global stability of SBN. Moreover, by virtue of reachable set approach, a procedure is established to design state feedback sampled-data stabilisers for constrained DBCNs. The obtained results are applied to the cell survival regulation of apoptosis networks. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive neural tracking control problem for a class of stochastic nonlinear systems with time delays and full-state constraints in a unified framework for the first time. The time-delay terms of the controlled systems are compensated by novel Lyapunov–Krasovskii functionals. The asymmetric barrier Lyapunov function (BLF) is adopted to guarantee that the full states are always restricted within prescribed constraints. RBF neural networks are utilised to approximate the lumped unknown functions in the design process. Furthermore, the dynamic surface control (DSC) technique is employed to simplify the process of control design significantly. Stability analysis shows all closed-loop signals are SGUUB, and full-state constraints are not violated. Finally, simulation results confirm the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The Dynamic Weighting Control Allocator (DWCA) was introduced by Sadien et al. (Control Engineering Practice, 2019) to solve the allocation problem raised by the yaw control of an on-ground aircraft. It handles the classical tradeoff between virtual reference inputs realisation and control power minimisation. But it also offers three specific features. First, the actuators reach saturation almost simultaneously, which allows an efficient recovery in case of failure. Then, several industrial requirements are taken into account, such as implementation ease, low computational cost and compatibility with certification constraints. And finally, the actuators can be prioritised, the last ones being used sparingly (to avoid overheating, fatigue, maintenance cost...) only when the virtual reference inputs cannot be realised by the first ones only. But despite its attractiveness, the DWCA is limited to the 1-dimensional case, which means that only one degree of freedom can be controlled. This is not sufficient to deal with today's challenges in the aeronautical and automotive fields, for example, where certain control problems are inherently multi-dimensional. With the progressive advent of autonomous cars, new concepts of light hybrid or electric vehicles are, for example, emerging, where both hydraulic and electric actuators are mounted on each wheel to improve the combined management of speed and steering. In this context, this paper introduces a non-trivial generalisation of the DWCA, which retains the various characteristics and advantages of the initial version and can be used in the multi-dimensional case. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of control laws for Discrete Event Dynamic Systems (DEDSs) represented by Timed Event Graphs (TEGs) under Generalized Marking Constraints (GMCs). The behaviour of TEGs is described using linear equations while GMCs are expressed by weighted inequalities in Min-Plus algebra. We formulate the problem in terms of control linear Min-Plus models. Hence, an algebraic method to calculate control laws ensuring the respect of GMCs is suggested. And once sufficient conditions are satisfied, we propose casual feedbacks to guarantee these marking specifications. Besides, the proposed control strategy is applied to a dual-armed cluster tool, a well-known industrial application. [ABSTRACT FROM AUTHOR]

In this paper we deal with the problem of strong stabilisation for a class of distributed semilinear systems by means of a nonlinear feedback control. The systems under consideration evolve in a Hilbert space and present periodic time-varying state delay. We first give a proof for the existence and uniqueness of the solution for the considered systems. Then, under a null controllability condition, we establish the stabilisation result and provide an explicit optimal decay rate estimate. The particular case of such systems for which the linear part generates a differentiable semigroup is also investigated. Some illustrating applications to hyperbolic and parabolic equations are displayed. Finally, a conclusion and some perspectives are given. [ABSTRACT FROM AUTHOR]

This paper addresses the output feedback adaptive resilient control problem for a class of stochastic nonlinear systems under sensor and actuator attacks. By applying a linear state transformation, the original system is transformed into a new one for which output feedback control becomes possible. The Nussbaum function is exploited to overcome the unknown control direction problem generated by uncertain control coefficients and adversary attacks. Based on the available compromised output signal and the states reconstructed by a new extended state observer, an output feedback adaptive resilient control scheme is proposed for such systems by combining the neural-networks-based approximation approach, backstepping technique and some special methods. The proposed controller can guarantee that all signals in the closed-loop system are semiglobally bounded in probability and the stabilisation error variables remain in an adjustable vicinity of origin. Finally, the effectiveness and applicability of the proposed control methodology is verified by two illustrative examples. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time boundedness (FTB) of linear time-invariant systems that are affected by a disturbance generated by an exosystem. By using a time-invariant quadratic Lyapunov function, Finsler's lemma and a dual system approach, new sufficient linear matrix inequalities (LMIs) conditions are given for analysis and synthesis for FTB. These results are extended: first, to finite-time stability (FTS) of linear time-invariant systems, second, to their input–output FTS associated, or not, to FTB. All the conditions are given in terms of LMIs, which make them easily tractable. Finally, the computational efficiency and the conservatism reduction of our approach are illustrated through an illustrative example. [ABSTRACT FROM AUTHOR]

This paper proposes a model-free super-twisting terminal sliding mode controller (MF-STTSMC) for the n-DOF upper-limb rehabilitation exoskeleton in the presence of external disturbance and backlash hysteresis. This ultra-local model-based control scheme consists of a sliding mode disturbance observer (SMDO) and a super-twisting non-singular fast terminal sliding mode controller (ST-NFTSMC). The ultra-local model is used to approximate the origin complex exoskeleton system in a short sliding time window, which avoids the requirement for accurate modelling and decreases the difficulty of controller design. To compensate for the lumped uncertainties, the SMDO is constructed to achieve finite-time observation and zero estimation error. Besides, to realise finite-time convergence of sliding surface and tracking error with less chattering, the ST-NFTSMC is proposed by employing a super-twisting algorithm. Furthermore, the stability of a closed-loop system with MF-STTSMC is ensured by using the Lyapunov theorem. Finally, to validate the proposed strategy, co-simulations of 7-DOF iReHave upper-limb exoskeleton are realised by using SolidWorks, SimMechanics, and Matlab/Simulink. Compared to time-delay estimation-based intelligent proportional-derivative control (TDE-iPD), α-variable adaptive model-free controller (α-AMFC), and inclusive and enhanced time delay controller (IETDC), the higher performances of the proposed MF-STTSMC are demonstrated. [ABSTRACT FROM AUTHOR]

This paper studies the problems of stability and stabilisation for time-varying delay systems. A flexible augmented Lyapunov–Krasovskii functional (FALKF) including some triple integral terms and delay-product-type quadratic terms is first constructed, in which the upper and lower limits of integral terms are flexible. Compared with some existing ones, the information of time-varying delay can be fully utilised. A parameter-dependent reciprocally convex inequality (PDRCI) is proposed, which covers some existing ones as its special cases. Based on the FALKF and PDRCI, a less conservative stability condition is obtained to ensure the time-varying delay systems to be asymptotically stable. By using a matrix inequality decoupling technique, the corresponding controller for the closed-loop systems is derived. Compared with some existing works, the constraints on introduced slack matrices are avoided. It directly provides extra free dimensions in the solution space. Two examples are employed to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper develops a distributed consensus control protocol that guarantees consensus tracking and global optimality with respect to a positive quadratic performance index for identical general linear multi-agent systems on an undirected graph. By using the previewable future reference signal, the consensus tracking control problem is converted into a preview control based optimal problem. The inverse optimality theory is introduced to overcome the difficulty of designing a distributed optimal controller, which is caused by the fact that the communication topology always interplays with the system dynamics and subsequently the global information is usually required in a conventional optimal controller design. First, a distributed optimal controller for tracking a reference signal with stable mode is designed. Then, an internal model based distributed optimal controller is further designed to track a time-varying reference signal. The structured quadratic performance indexes are derived for both cases, respectively, and based on which, two distributed optimal tracking control protocols are implemented to guarantee the asymptotic stability of the augmented systems only using local information. Simulation results show that an appropriate preview length can effectively improve the tracking performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with reset controller design and $ \mathcal {L}_2 $ L 2 -gain stability of piecewise-affine systems under the framework of hybrid systems. Firstly, stability conditions of piecewise-affine systems under dynamic state-feedback control are established through bilinear matrix inequality conditions. Secondly, a reset controller with reset rules under the hybrid systems framework is proposed in the sense of Lyapunov and sufficient conditions for exponential and $ \mathcal {L}_2 $ L 2 -gain stability of the closed-loop systems are provided. Different from the piecewise-affine systems with the dynamic state-feedback controller, the reset controller is designed such that the $ \mathcal {L}_2 $ L 2 -gain performance of piecewise-affine systems can be enhanced. Thirdly, an LMI approach is proposed to avoid the difficulty of solving the bilinear matrix inequalities. Furthermore, robustness to inflations of the flow and jump sets is established, and robustness to the norm-bounded uncertainties is proposed. Finally, numerical simulations including a robot arm system, an inverted pendulum system and the Chua's circuit system are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper investigates the secure state estimation problem of the cyber-physical systems (CPSs) in the presence of malicious attacks. Considering the destructiveness and stealthiness of the attacker, a novel stochastic transmission scheme, in which the repeater generates transmission data by randomly combining some measurement values, is proposed to ensure the effectiveness of the attack detector. A filter equipped with the $ \chi ^2 $ χ 2 detector and the stochastic transmission scheme is proposed to conduct the secure state estimation. The attack probability condition of the estimation error being mean-square bounded is given, which indicates that stochastic transmission scheme has a limited effect on the filter. Some numerical simulations are given to illustrate the effectiveness of the proposed transmission scheme. [ABSTRACT FROM AUTHOR]

This paper presents an interpolatory framework for model order reduction of linear time-invariant (LTI) systems over limited time intervals of the form $ [0,\tau ] $ [ 0 , τ ] , with $ \tau \lt \infty $ τ < ∞. We give a new proof for deriving interpolation-based first-order necessary conditions for time-limited $ H_2 $ H 2 optimality. Based on these optimality conditions, we propose a time-limited rational Krylov framework for time-limited rational interpolation. The interpolatory framework is used to present an iterative algorithm that yields reduced-order models satisfying the optimality conditions approximately. The distance to optimality is quantified in terms of the interpolation errors. The errors depend primarily on the interpolating model's poles and the time interval size. We test the proposed algorithm in three numerical examples and compare its performance with various time-limited model reduction algorithms available in the literature. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the problem of the exponential synchronisation for delayed neutral-type multi-weights complex networks (DNMCNs) with regime-switching jump diffusion under aperiodically intermittent control. Compared with the related works, hybrid time delays and regime-switching jump diffusion are introduced into neutral-type networks which can better simulate more complicated practical applications. The introduction of regime-switching jump diffusion increases the difficulties of synchronisation analysis in comparison with the Markovian jump diffusion. Meanwhile, it is noteworthy that we firstly extend the availability of aperiodically intermittent control scheme to handle the synchronisation issue with DNMCNs. On the basis of a technique that combines the Lyapunov method and graph theory, some sufficient criteria to synchronise DNMCNs via intermittent control are obtained. Finally, an oscillator system is considered as the application, and the corresponding numerical simulations are proposed to validate the applicability of the obtained theorems and show the effectiveness. [ABSTRACT FROM AUTHOR]

Model predictive control is a popular choice for systems that must satisfy prescribed constraints on states and control inputs. Although much progress has been made in distributed model predictive control, existing algorithms tend to be computationally expensive. This limits their use in systems with fast dynamics. In this paper, we propose a new distributed model predictive control algorithm that we term as instant distributed model predictive control (iDMPC). The proposed algorithm employs a realisation of the primal-dual algorithm in the controller dynamics for fast computation. We show that the closed-loop system trajectories with the proposed iDMPC algorithm converge asymptotically to a desired reference. To ensure the satisfaction of the state constraints during the transient, we also include an explicit reference governor in the feedback loop. [ABSTRACT FROM AUTHOR]

In this paper, the control issue of adaptive fault-tolerant is studied for a class of stochastic nonlinear systems with multiple faults and full state constraints, with multiple faults including the actuator faults and the external system fault. The problem with full state constraints are solved by constructing a logarithmic barrier Lyapunov functions (BLFs). By integrating multi-dimensional Taylor network (MTN) technology into the backstepping process, a new adaptive MTN-based fault-tolerant controller is designed. On the basis of considering multiple faults, the proposed control strategy can ensure that all signals in the closed-loop system are semi-global ultimately uniformly bounded (SGUUB) in probability, and all states of the system are constrained within the given boundary. Finally, three simulation examples are given to illustrate the effectiveness and practicability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

The problem which is concerned with filter-based neural control for switched uncertain nonlinear systems with incomplete measurement is studied in this paper. Filters are used to estimate unknown states, while neural networks approximate unknown functions. Data loss, saturation and other problems often occur during data transmission. An appropriate control law is designed by a backstepping method to solve this problem. Through using the average dwell time, it is proved that the switching system tends to be stable in a certain time. The analysis of probabilistic stability is also carried out to ensure that the system can achieve uniformly ultimately boundedness. Finally, the effectiveness of the previous design is proved by simulation. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a Novel Modified Super-Twisting sliding mode control (NMST-SMC) with an integral terminal sliding surface. The NMST-SMC algorithm was applied for a wind energy conversion system based on an induction generator. Firstly, integral terminal sliding surfaces are designed for rotor flux, voltage and current subsystems. Secondly, reaching control laws are added in the equivalent control law to enhance the tracking performance of the rotor flux, stator current, DC bus voltage and gridside current loops. To increase the system performance, a modified super-twisting controller is added. This suggested control scheme is aimed to reduce the total harmonic distortion (THD), strong robustness and stability to voltage faults, and fast dynamic response to power step change. The stability of the proposed controller is proved using the Lyapunov theory. The numerical simulation results of the proposed control strategy are compared to others to prove its effectiveness. [ABSTRACT FROM AUTHOR]

This paper investigates the σ-error pth $ (p>0) $ (p > 0) -moment stability and synthesis problems for a class of discrete-time semi-Markov jump singular systems (DTSMJSSs). In view of the Lyapunov functions approach, we first derive the σ-error pth $ (p>0) $ (p > 0) -moment stable behaviour of interested systems. Based on semi-Markov kernel approach and the techniques of eliminating power of matrices (EPMs), we then obtain several LMI conditions for σ-error mean square stability. Subsequently, due to the time-varying singular E-matrix in DTSMJSSs, two different forms of controller gain are exploited in order to design stabilising state-feedback strategies. In particular, computational analysis and comparison of the proposed control schemes are provided, which shows the numerical complexity of the proposed control schemes is vastly lower than that of the existing literature. Finally, an example has been performed to verify the obtained analytical results. [ABSTRACT FROM AUTHOR]

In this paper, event-triggered control for uncertain delayed neural networks (DNNs) with actuator saturation against deception attack is discussed. We propose a novel framework into which an event-triggered mechanism (ETM), actuator saturation, system uncertainty, and deception attack are combined. In the framework, the discrete ETM is employed to determine whether the sampled signal should be transmitted to controller so as to save network bandwidth, a random occurrence deception attack model satisfying Bernoulli distribution is introduced to construct the system robust, and actuator saturation is considered due to the actual complex network environment. Based on the framework, we discussed the stochastic stability of a novel delayed neural network model in a closed-loop system. By resorting to the appropriate Lyapunov–Krasovskii functional (LKF), we derive some new sufficient conditions for the stochastically stable of the system and obtain the gain of the system controller using efficient linear matrix inequality (LMI) method. Finally, a numerical example, in the end, demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive output feedback control design problem for a class of nonlinear systems with unknown state time delays by combining the dynamic gain and neural network. A novel reduced-order dynamic gain observer is introduced to estimate the unmeasured system states. Radial basis function neural networks (RBF NNs) are used to approximate unknown functions. An adaptive NN output feedback controller is designed based on the backstepping technique. By arranging the proper Lyapunov–Krasovskii functional, we prove that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, a physical example and a numerical example are given to prove the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the state-dependent switching design problem for impulsive switched linear systems under dwell-time constraints. All conditions are presented as optimisation problems that are convex for some fixed set of scalars. Applications to sampled-data systems are presented and illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper addresses the output feedback optimal consensus tracking control problem for a class of nonlinear multi-agent systems (MASs) with unknown internal dynamics and input saturation. Firstly, an adaptive observer is designed to reconstruct the unmeasurable states using neural networks (NNs) based on the augmented dynamic model. Subsequently, a novel distributed feedforward controller is proposed using the backstepping method, where an auxiliary state is introduced to deal with the input saturation problem. Unlike the traditional recursive design technique, the procedures we take can reduce the consensus tracking control problem into the optimal regulation issue, which is then solved by the adaptive dynamic programming (ADP) method. Therefore, the designed consensus control protocol consists of a distributed feedforward controller and a distributed optimal feedback controller. Moreover, the stability of the MASs is guaranteed by the Lyapunov theory. Numerical simulation on multi-missile guidance problem demonstrates the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we consider an evolution linear control system. First, by using Weiss–Staffans perturbation results we prove that, under suitable conditions, our evolution system is well posed. Next, we give a characterisation of observability of the evolution system via some spectral condition. We also provide sufficient condition to ensure the stability of the system in the periodic case. As applications, we consider concrete problems including wave equation in one dimension. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm to verify whether a finite game is a coset weighted potential game (WPG) without pre-knowledge on its coset weights. This algorithm can also provide a recursive method to calculate the unknown coset weights. Then we give the concept of near coset WPGs based on evolutionary equivalence between two finite games, and its algebraic verification is obtained. Finally, the application of near coset WPGs to game-theoretical optimisation of multi-agent systems is discussed, which can improve the applicability of potential games in multi-agent optimisation problems. [ABSTRACT FROM AUTHOR]

This paper derives the limit of the Kalman filter and smoother as the inverse of the process noise covariance tends to zero (the zero informational limit) in the case that there is direct feedthrough (of full column rank) of the process noise input to the measurements. Two forms of the filter in the limit are derived with the second being a standard Kalman filter without unknown inputs. The latter form is used to derive necessary and sufficient conditions for convergence and stability of the filter. These consist of a controllability condition and a minimum phase condition. The filter and smoother are applied to an automotive example to estimate an unknown road profile. The example illustrates the usefulness of the stability and convergence conditions to inform the choice of a suitable set of sensors. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of stabilisation for a class of distributed semilinear systems. The considered systems present a state time delay and evolve in Banach spaces. A new stabilising feedback control is proposed. Two kinds of stabilizability, namely exponential and weak stabilizability, are investigated. An explicit estimate of the energy decay rate is given. Some illustrating applications to parabolic and hyperbolic equations with numerical simulations are considered. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time annular domain stability and stabilisation for the positive systems. A new analysis method is proposed to obtain less conservative finite-time annular domain stability criteria and its superiority to modified Gronwall inequality is analysed. Moreover, conditions for the existence of state feedback and observer-based controllers that guarantee the closed-loop system to be positive and finite-time annular domain stable are given under the linear programming framework. Finally, two numerical examples are provided to show the effectiveness and superiority of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the integration of input move-blocking into the framework of suboptimal model predictive control. The blocked input parameterisation is explicitly considered as a source of suboptimality. A straightforward integration approach is to hold back a manually generated stabilising fallback solution in some buffer for the case that the optimiser does not find a better input move-blocked solution. An extended approach superimposes the manually generated stabilising warm-start by the move-blocked control sequence and enables a stepwise improvement of the control performance. In addition, this contribution provides a detailed review of the literature on input move-blocked model predictive control and combines important results with the findings of suboptimal model predictive control. A numerical example supports the theoretical results and shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Motivated by some landslide models, and related estimation challenges, this paper presents an optimal estimation method for state and parameter in a special class of so-called ODE–PDE system based on the adjoint method for discrete-time asynchronous measurements. This system is described by a pair of coupled Ordinary Differential Equation (ODE) and Partial Differential Equation (PDE), with a mixed boundary condition for the PDE. The coupling appears both in the ODE and in the Neuman boundary condition of the PDE. For this system, initial conditions or state variables and some empirical parameters are assumed to be unknown and need to be estimated. The Lagrangian multiplier method is used to connect the dynamics of the system and the cost function defined as the least square error between the simulation values and the available measurements. The adjoint state method is applied to the objective functional to get the adjoint system and the gradients with respect to parameters and initial state. The cost functional is optimised, employing the steepest descent method to estimate parameters and initial state. This general approach is illustrated by two application examples corresponding to two different landslide models that validate the presented optimal estimation approach. The first one is about state and parameter estimation in an extended sliding-consolidation landslide model, and the second one is in the viscoplastic sliding-consolidation landslide model. [ABSTRACT FROM AUTHOR]

The paper addresses the exact linearisation of flat nonlinear discrete-time systems by generalised static or dynamic feedbacks which may also depend on forward-shifts of the new input. We first investigate the question which forward-shifts of a given flat output can be chosen in principle as a new input, and subsequently how to actually introduce the new input by a suitable feedback. With respect to the choice of a feasible input, easily verifiable conditions are derived. Introducing such a new input requires a feedback which may in general depend not only on this new input itself but also on its forward-shifts. This is similar to the continuous-time case, where feedbacks which depend on time derivatives of the closed-loop input – and in particular quasi-static ones – have already been used successfully for the exact linearisation of flat systems since the nineties of the last century. For systems with a flat output that does not depend on forward-shifts of the input, it is shown how to systematically construct a new input such that the total number of the corresponding forward-shifts of the flat output is minimal. Furthermore, it is shown that in this case the calculation of a linearising feedback is particularly simple, and the subsequent design of a discrete-time flatness-based tracking control is discussed. The presented theory is illustrated by the discretised models of a wheeled mobile robot and a 3DOF helicopter. [ABSTRACT FROM AUTHOR]