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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]

The present paper is devoted to the optimisation of parabolic type differential inclusions (DFIs) given by polyhedral set-valued mappings. For this, an auxiliary problem with a polyhedral parabolic discrete inclusion is defined. With the help of locally adjoint mappings and comparison of matrix-coefficients of discrete and discrete-approximate problems, necessary and sufficient optimality conditions for polyhedral-parabolic discrete-approximate inclusions are skilfully constructed. Thus, using the discretisation method and the features of the polyhedral nature of the problem, we prove sufficient optimality conditions for a polyhedral parabolic DFI. At the end of the paper, the numerical results are presented. [ABSTRACT FROM AUTHOR]

This paper solves the problem of designing positive functional $ H_{\infty } $ H ∞ filters for positive linear time-delay systems. In fact, we propose a new positive reduced order $ H_{\infty } $ H ∞ filter for positive linear constant state time-delay systems for which the states remain in the nonnegative orthant of the state space, subject to disturbances and unknown inputs. This paper is a first attempt to design positive unknown inputs functional $ H_{\infty } $ H ∞ filter for such positive linear delayed systems. The proposed approach is based on the positivity of an augmented system composed of dynamics of both considered system and proposed filter, on the unbiasedness of the estimation error by the resolution of Sylvester equation and also on Lyapunov-Krasovskii stability theory; then conditions for the establishment of such filters are formulated in terms of an optimization problem. An algorithm that summarizes the different steps of the proposed positive functional $ H_{\infty } $ H ∞ filter design is given. Finally, numerical example and simulation results are given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper presents an end-user privacy and thermal comfort preserving approach for residential thermostatically controllable loads (TCLs) to provide demand response (DR) in grid services under uncertainties. Unlike the standard approach whereby a central utility-level control is used to control end-users loads, this paper splits the control effort between a central coordinating controller and local robust controllers. The Lagrangian relaxation (LR) method is applied by relaxing the power tracking constraint to obtain a hierarchical control framework with a local controller at each household level and a coordinating controller at the central utility level. Household-level local controllers are based on robust model predictive control (MPC) that relies on minimum household-specific information while accounting for thermal model parameter uncertainties and forecast errors associated with exogenous inputs. Considering inverter-type air conditioners as the TCL, the approach is validated using a practical signal corresponding to the Australian Energy Market Operator. The results demonstrate that accurate tracking of the load set-point signal can be achieved under a considerable range of uncertainties while preserving thermal comfort for end-users. Furthermore, the proposed DR scheme is computationally tractable and robust for real-world implementation. [ABSTRACT FROM AUTHOR]

In this paper, for strict-feedback nonlinear systems with positive odd rational powers, the problem of adaptive fixed-time tracking control (FTTC) is considered. With the support of fixed-time theorem and adaptive backstepping method, this paper proposes a new globally adaptive FTTC strategy, which can overcome the singular problems caused by the derivation of virtual control signal. In addition, the proposed control scheme is a universal approach that can be applied to other types of nonlinear systems. Furthermore, the designed adaptive fixed-time tracking controller ensures the boundedness of all signals in the controlled system, and it guarantees the tracking error converges to a small neighbourhood near equilibrium in fixed-time. Finally, the simulation result further verifies the feasibility of the presented control scheme. [ABSTRACT FROM AUTHOR]

This paper deals with a new design problem of adaptive gain robust model-following/tracking controllers for a class of systems with matched and unmatched uncertainties via piecewise Lyapunov functions. In the proposed design approach, compensation inputs for matched and mismatched uncertainties for the system are introduced and the proposed adaptive gain model-following/tracking robust controller can achieve that the tracking error decreases asymptotically to zero in spite of uncertainties. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show linear matrix inequality-based sufficient conditions for the existence of the proposed controller. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, some less conservative sufficient conditions for uniform exponential stability, local uniform exponential stability and uniform practical exponential stability of nonlinear time-varying systems on time scales are proposed. Compared with the traditional exponential stability results, the negative definiteness of the time derivatives of Lyapunov functions is weakened, that is, the time derivatives of related Lyapunov functions in this paper are allowed to be indefinite. The main tools used are some Gronwall's inequalities on time scales. Two examples are also included to verify the effectiveness of the results obtained. [ABSTRACT FROM AUTHOR]

To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

This paper studies the problem of scheduling control data transmissions from embedded processors to physical systems. For this problem, we propose novel state feedback and output feedback control architectures that are predicated on energy function-based and norm-free event-triggering conditions, where the embedded processor broadcasts a sampled data of its control signal value through a zero-order-hold operator to the physical system when the left side of the event-triggering condition equals to its right side. In this context, the energy function-based feature means that the right sides of the proposed event-triggering conditions involve an energy function as well as its time-derivative to make the selection of these right sides user-adjustable. Furthermore, the norm-free feature means that the left sides of the proposed event-triggering conditions do not depend on signal norms to allow for better control data transmission reduction. System-theoretical analyses of our event-triggered state feedback and output feedback control architectures are shown using the same energy functions and their time-derivatives used in the proposed event-triggering conditions, where illustrative numerical examples are also presented to demonstrate the efficacy of our contributions. To the best of our knowledge, the results given in this paper explore how event-triggering conditions are linked not only to energy functions but also to their time-derivatives for the first time. [ABSTRACT FROM AUTHOR]

This paper studies the $ {H_\infty } $ H ∞ filtering problem for a class of discrete-time semi-Markov switching repeated scalar nonlinear systems with an event-triggered scheme. Considering the limitation of bandwidth, the mode-dependent event-triggered mechanism is introduced to determine whether the currently sampled sensor data is transmitted to the filter, in which the parameters of the event generator depend on the system mode. By means of a constructed time-varying Lyapunov function, the two stages of the systems jump instant and mode residence are analysed, and a linear matrix inequality technique is used to ensure the mean-square stability and $ {H_\infty } $ H ∞ performance of the filter error system. Accordingly, the co-design method of the mode-dependent time-varying filter and the event-triggered mechanism is derived for semi-Markov switching systems. Finally, a numerical simulation is given to illustrate the effectiveness and feasibility of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, an optimisation problem for the monotone mean-variance (MMV) criterion is considered from the perspective of the insurance company. The MMV criterion is an amended version of the classical mean-variance (MV) criterion which guarantees the monotonicity of the utility function. With this criterion we study the optimal investment and reinsurance problem which is formulated as a zero-sum game between the insurance company and an imaginary player. We apply the dynamic programming principle to obtain the corresponding Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. As the main conclusion of this paper, by solving the HJBI equation explicitly, the closed forms of the optimal strategy and the value function are obtained. Moreover, the MMV efficient frontier is also provided. At the end of the paper, a numerical example is presented. [ABSTRACT FROM AUTHOR]

This paper considers modeling and state estimation of timed discrete-event systems (TDESs) with communication delays and losses. In the previous framework, the specified closed-loop system language may contain physically impossible strings, i.e. strings never occur in practice. To exclude these physically impossible strings, this paper presents a new modeling framework for supervisory control of networked TDESs. Specifically, we first analyse how to model and update the observation channel and the control channel under communication delays and losses. We then construct an automaton that explicitly describes the interaction process between the plant and the supervisor over the observation channel and the control channel so that the language of the closed-loop system can be specified. Compared with the existing work, the proposed framework can model the 'dynamics' of the closed-loop system more accurately. Under the proposed framework, we further estimate states of the closed-loop system under communication delays and losses. The state estimation is implemented on-the-fly and bases on only the information of observations and controls in history. As an application of the proposed modeling and state estimation approaches, we finally extend the existing approaches to find all the admissible and safe supervisors of networked TDESs. [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 addresses the vibration reduction and disturbance attenuation problems of a flexible arm, which is modelled as a fourth-order partial differential equation. The main control objectives lie in reducing the influence of the disturbance, steering the flexible arm to the desired angular position and suppressing the vibration, simultaneously. To achieve the objectives, firstly, two different disturbance observers are designed. Secondly, we construct boundary controllers based on the two designed disturbance observers and boundary measurable signals. Then, with the two disturbance observers, the boundary disturbance compensation is achieved, and with the designed boundary controllers, the uniform boundedness of the flexible arm is guaranteed. Moreover, the well-posedness of the closed-loop system under the designed boundary controllers is discussed by means of the operator semigroup theory. Finally, the effectiveness and advantages of the proposed controllers are demonstrated through simulations and physical experiments. [ABSTRACT FROM AUTHOR]

In this paper, an $ H_{\infty } $ H ∞ negative imaginary static output feedback (SOF) controller is designed for a low frequency (LF) networked control system (NCS) with time-delays. A difference operator is introduced to deal with the time-delays in a feedback configuration via integral quadratic constraints (IQCs). Both $ H_{\infty } $ H ∞ performance and negative imaginariness are analysed via LF IQCs and a generalised Kalman–Yakubovich–Popov (GKYP) lemma. A two-stage algorithm is presented to obtain the $ H_{\infty } $ H ∞ negative imaginary SOF controller for the LF NCS with time-delays. Simulation results are given to show the effectiveness and superiority of the $ H_{\infty } $ H ∞ negative imaginary SOF controller. [ABSTRACT FROM AUTHOR]

In this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation, which we show is equivalent to interval excitation of the regressor vector. An extension to – separable and monotonic – nonlinear parameterisations is also given. The estimators are shown to be robust to additive measurement noise and – not necessarily slow-parameter variations. Moreover, a version of the estimator that is robust with respect to sinusoidal disturbances with unknown internal model is given. Simulation results that illustrate the performance of the estimator compared with other algorithms are given. [ABSTRACT FROM AUTHOR]

The AIMD algorithm, which underpins the Transmission Control Protocol (TCP) for transporting data packets in communication networks, is perhaps the most successful control algorithm ever deployed. Recently, its use has been extended beyond communication networks, and successful applications of the AIMD algorithm have been reported in transportation, energy, and mathematical biology. A very recent development in the use of AIMD is its application in solving large-scale optimisation and distributed control problems without the need for inter-agent communication. In this context, an interesting problem arises when multiple AIMD networks are coupled in some sense (usually through a nonlinearity). The purpose of this note is to prove that such systems in certain settings inherit the ergodic properties of individual AIMD networks. This result has important consequences for the convergence of the aforementioned optimisation algorithms. The arguments in the paper also correct conceptual and technical errors in Alam et al. (2020, The convergence of finite-averaging of AIMD for distributed heterogeneous resource allocations. arXiv:2001.08083 [math.OC].). [ABSTRACT FROM AUTHOR]

In this paper, the fixed-/preassigned-time anti-synchronisation problem is studied for delayed memristive neural networks (DMNNs) with discontinuous activation functions and external disturbance. First of all, several simple controllers are structured for the fixed-time anti-synchronisation (FTAS) of DMNNs with discontinuous activation functions. Moreover, an effective and convenient control scheme for preassigned-time anti-synchronisation (PTAS) is presented by modifying the controller parameters. The proposed control scheme is also available for DMNNs with continuous activation functions or without time delays. In addition, sufficient conditions for FTAS and PTAS of DMNNs are derived and the accurate estimation for settling-time is given. Finally, simulation examples are presented to verify the validity of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of large-scale stochastic reaction-diffusion systems. To prove the exponential stability of the system, we introduce the corresponding isolated subsystems. We show that the exponential stability of the isolated systems implies the exponential stability of the large-scale stochastic reaction-diffusion system under some conditions. Furthermore, we discuss a special case where the large-scale stochastic reaction-diffusion system is described in a hierarchical form. In this case, we prove that the original system is exponentially stable if and only if the corresponding subsystems are exponentially stable. [ABSTRACT FROM AUTHOR]

This paper studies the trajectory behavior evaluation for generalised Persidskii systems with an essentially bounded input on a finite time interval. Also, the notions of annular settling and output annular settling for general nonlinear systems are introduced. We propose conditions for annular short-time stability, short-time boundedness with a nonzero initial state, annular settling, and output annular settling for a class of Persidskii systems. These conditions are based on the verification of linear matrix inequalities. An application to recurrent neural networks illustrates the usefulness of the proposed notions and conditions. [ABSTRACT FROM AUTHOR]

The paper considers the problem of nonparametric estimation of nonlinear characteristic in the FIR Wiener system. Methods proposed so far have suffered from the so-called 'curse of dimensionality' and their practical applications have been limited to the very short impulse responses of the linear component. In the proposed approach, the class of (stochastically initialised) repeated exponential input excitations is introduced, and a modified kernel-based estimator is presented. It is shown that the rate of convergence to the genuine system characteristic is significantly improved and does not depend on the length of the impulse response of the linear dynamic block. [ABSTRACT FROM AUTHOR]

Transient performance is a highly valued factor in real control systems. Having a suitable transient performance not only guarantees the safety of the system but also makes the response more desirable by reducing transient factors like the overshoot and the settling time. This paper is the first attempt to design a novel controller to improve the transient performance of switched singular time-delay systems. The proposed controller comprises a combination of linear and nonlinear parts. First, a linear part is designed to fulfill the stabilisation. Then a nonlinear part is added to it to improve the transient response. The admissibility of the closed-loop system is investigated through some given theorems based on the Lyapunov-Krasovskii approach. The closed-loop system's regularity and impulse freeness are also guaranteed in the given theorems. Computer simulation of some numerical and practical examples will endorse the theoretical achievements afterward. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive stabilisation of output-constrained high-order nonlinear systems with more general high-order and low-order nonlinearities. By skilfully introducing nonlinear mappings, a key coordinate transformation, integral Lyapunov functions and the sign function into the adding a power integrator technique, and combining a novel analysis method, a continuous adaptive state-feedback controller is constructed. When the initial value of system states lies in the constrained set, it is rigorously proved that all the closed-loop signals are uniformly bounded, the asymmetric output constraint isn't transgressed, and the equilibrium point of the closed-loop system is uniformly asymptotically stable. A simulation example shows the effectiveness of this control scheme. [ABSTRACT FROM AUTHOR]

This paper studies the approximate optimal event-triggered tracking control problem for a class of second-order nonlinear systems with prescribed performances. By employing a prescribed performances function, restrictions on tracking errors are removed for prescribed performances including convergence rate, maximum overshoot, and steady-state error. On this basis, a complex optimal tracking control problem can be transformed into an optimal stabilising control problem by constructing an augmented system. Subsequently, an event-triggered mechanism is introduced to reduce communication resources. Then, an adaptive critic learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation, where the weights in the critic networks are tuned through the gradient descent approach and experience replay technology. Through the developed learning method, the persistence of excitation condition is released, and the data efficiency is improved. The Lyapunov stability theory is introduced to verify the stability of the close-loop system and the tracking errors are uniformly ultimately bounded. Finally, simulation results are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper studies a partially observed stochastic Stackelberg game with two followers, where state satisfies a linear stochastic differential equation of mean-field type, and cost functionals are quadratic. Using decomposition technique and backward separation approach, we derive the followers' optimal strategy. The leader focuses on an optimal control problem driven by a fully coupled mean-field forward–backward stochastic differential equation with conditional expectation. By layer-by-layer decomposition technique, some inequalities and Riccati equations, we not only get the existence and uniqueness of solution to the corresponding Hamiltonian system but also give a feedback form of Stackelberg solution. Finally, we tackle a government debt problem by the above theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of sampled-data adaptive tracking control for a class of switched nonlinear systems with prescribed performance is considered. In order to guarantee the system is stable and achieves the prescribed performance in sampled-data control, a coordinate transformation satisfying the prescribed performance is introduced. In addition, the neural networks (NNs) used to approximate the unknown nonlinear functions and the backstepping technique are applied to design the sampled-data controller and the adaptive laws. An upper bound on the sampling period is obtained to maintain the stability of the systems. It is confirmed that the designed sampled-data scheme ensures that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is limited to the prescribed performance function. The effectiveness of the designed control scheme is demonstrated by two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, we propose an event-triggered dual-mode predictive control strategy to deal with two-channel packet dropouts for discrete-time constrained nonlinear networked control systems. The main focus is on the construction of network compensation mechanisms and control algorithms. Firstly, two types of novel event generators are set, respectively, in sensor node and controller node to reduce resource consumption while preserving the desired system performance. In order to establish corresponding event-triggering conditions, two special states, successful transmitted states and reconstructed states, are introduced. Subsequently, a dual-mode control scheme, where the switch of modes depends on reconstructed states, is designed. The recursive feasibility of optimization problems is ensured by determining relationships between actual states and reconstructed states. By constructing actual control laws under two system modes, the stability property of closed-loop systems is guaranteed. Furthermore, effects of packet dropouts and disturbances on system performance are analyzed. At last, the efficiency of the proposed control strategy is illustrated by a cart-damper-spring simulation example. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability analysis of the stochastic strict-feedback nonlinear systems with time-varying delays on networks (SSNSTDN) via pinning control. Different from the previous literature, the new model we studied owns the non-strongly connected topology. The actual controllers are realised by back-stepping and designing virtual controllers. In particular, a novel method for constructing global Lyapunov functions is proposed,which exploits the Lyapunov function of each stochastic strict-feedback nonlinear systems with time-varying delays (SSNSTD) to construct the global Lyapunov function of SSNSTDN. Meanwhile, combining the Lyapunov method with graph theory, several sufficient conditions to guarantee the exponential stability in mean square of SSNSTDN are obtained in the form of coefficients-type criterion. Furthermore, we apply our main results to investigating the stabilisation of stochastic coupled oscillators with time-varying delays on networks and the effectiveness of proposed theories is illustrated by some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the joint state and fault estimation problem for a class of discrete-time complex networks with time delays is investigated. The information on the dynamics of the fault is not required with an appropriate structure of the proposed fault estimator. Unbiased state and fault estimation can be obtained simultaneously at each node only with locally available information, thereby avoiding the requirement of a centre node which collects information from every node. Considering the effects of time delays and the interconnections between different nodes, an upper bound of the estimation error covariance is calculated, and the desired filter parameters are obtained in a recursive manner such that the trace of the bound is minimised. The existence conditions of the developed filter are provided explicitly as well. Finally, a simulation example is employed to demonstrate the state estimation and fault diagnosis performances of the given strategy. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of marking constraints in a class of partially controllable timed Petri nets. Specifically, these are Timed Event Graphs (TEGs) which include disturbed input transitions and which are subject to token capacity constraints in some paths. Using the Min-Plus algebra formalism, formal approaches are proposed to design causal control laws to guarantee compliance with marking constraints in TEGs. Sufficient conditions are defined to show the existence and synthesis of these controllers. The developed methodologies are illustrated in a case study of a disassembly system with a limited stock of components. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the instability issues of stochastic differential systems with impulsive effects. Definitions of instability including almost sure exponential instability, pth moment exponential instability and pth moment instability are given. By using the Lyapunov functions, the comparison theorem and the average impulsive interval condition, several instability criteria are established. Three examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The focus of this paper is the design of open-loop control profiles for linear differentially flat systems whose model parameters are uncertain and are represented probabilistically. To account for the time-invariant model parameter uncertainties, polynomial chaos is used to derive a surrogate model which permits easy evaluation of the mean and variance of the uncertain states. A chance constrained optimisation problem is posed to minimise the terminal error of the stochastic states for a prescribed risk of not satisfying the terminal state bounds. To permit posing a convex optimisation problem, the cost function which is the residual energy is approximated by a hypercube circumscribing the hypersphere which bounds the terminal residual error. This relaxation permits posing a convex optimisation problem to arrive at the robust control profile. The proposed technique is illustrated on two examples including the benchmark spring-mass-dashpot system undergoing a rest-to-rest maneuver and a UAV undergoing a translation in a prescribed time. Parametric studies are conducted where the impact of varying the order of the polynomial chaos expansion and the degree of the parameterised control profiles are used to conclude that a 2–3 degree polynomial chaos expansion is sufficient to capture the time evolution of the mean and variance of the states which are required for the chance constrained optimisation problems. As expected, the design results in improved performance as the number of free variables used to parameterise the control profiles increases. [ABSTRACT FROM AUTHOR]

In this paper, an observer-based tracking control problem is considered for a polynomial system with parameter uncertainties and external disturbances. Noting that some states are difficult to measure in practice, a polynomial state observer is employed to obtain the unknown states. Then a robust observer-based tracking controller is designed to force the states of the polynomial uncertain system to follow the ones of the reference model and satisfy $ H_\infty $ H ∞ performance. By using a full-state-dependent homogeneous polynomial function, the solvability condition is derived for the observer-based tracking control strategy, which reduces conservatism. Sum of squares technique is utilised to calculate the corresponding observer and controller, effectively dealing with the calculation problem in polynomial systems. Simulation examples are given to illustrate the effectiveness of the presented control strategy. [ABSTRACT FROM AUTHOR]

The looped-functional approach has been extensively used for stability analysis of sampled-data systems. For this approach, this paper introduces two new functionals to minimise the conservatism of stability conditions. The first one is called a non-negative integral functional (NIF) that is added to the derivative of a common Lyapunov functional. The second one is a general looped-functional (GLF), whose values at sampling instants are traditionally not well-defined, and are defined here in terms of their limits. Leveraging further affine canonical Bessel-Legendre inequalities expressed by simplified polynomials, a polynomial-based NIF, a polynomial-based GLF, and a polynomial-based zero equality are tailored for obtaining hierarchical types of stability conditions in the form of linear matrix inequalities. Finally, numerical examples show that: (i) the proposed functionals lead to less conservatism when compared with several state-of-the-art methods; and, (ii) the resulting stability conditions exhibit a hierarchical characteristic in the sense that the higher level of hierarchy, the less conservatism of the criteria. [ABSTRACT FROM AUTHOR]

We consider a class of forced continuous-time Lur'e systems obtained by applying nonlinear feedback to a higher-order linear differential equation which defines an input-output system in the sense of behavioural systems theory. This linear system directly relates the input and output signals and does not involve any internal, latent or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability and strong integral input-to-output stability, concepts which are very much reminiscent of input-to-state stability and strong integral input-to-state stability, respectively. The methods used in the paper combine ideas from the behavioural approach to systems and control, absolute stability theory and input-to-state stability theory. [ABSTRACT FROM AUTHOR]

This paper proposes a novel control methodology to achieve fixed-time stabilisation for a class of three-order nonlinear systems based on fast nonsingular terminal sliding mode control. In this research, based on the combination of integral fast nonsingular terminal sliding mode (IFNTSM) surface and fixed-time control theory, a novel backstepping fast nonsingular terminal sliding mode (FNTSM) controller is being studied. The interests of this method are that the presented controller can not only maintain the characteristics of integral fast nonsingular terminal sliding mode control (IFNTSMC) but also has the advantages of fixed time convergence and fast transient response. Piecewise function is introduced to solve the singularity problem caused by negative exponential term. Our control strategy achieves the stabilisation performance within finite convergent time being independent of initial condition. The control scheme is applied to the gyros system with chaotic state and suppress its chaotic phenomenon. The theoretical results are supported by simulation results. [ABSTRACT FROM AUTHOR]

This paper introduces a feedforward control method for physical systems that can be described with linear parameter-varying (LPV) models. The proposed feedforward controller structure is consequently derived from a generic LPV representation and is shown to be identifiable directly from noisy measurement data. The identified structure is advantageous for feedforward control, as using a simple least squares algorithm allows to parameterise basis functions representing the required input trajectory to follow a given output trajectory. Also, with the proposed regularisation, the input trajectory remains bounded even when the physical system exhibits non-minimum phase behaviour. Additionally, the proposed controller structure does not possess states but only considers the inputs and outputs signals and their derivatives, leading to a unique physical interpretation of each controller's parameter. Multiple feedforward controllers identified at various operating points can therefore be directly merged to create a parameter-varying controller. A nonlinear and locally non-minimum phase system is considered in this study, i.e. an engine air path, to evaluate the performances of the proposed feedforward strategy. The controller parameters are first identified from noisy measurement data, and then the proposed feedforward controller is implemented with a feedback controller to track the exhaust pressure and $ \mathrm {NO}_{\mathrm {x}} $ NO x concentration. Using a detailed physical simulation of the engine air path, the proposed feedforward strategy showed encouraging output tracking performances compared to state-of-the-art control methods. The presented feedforward method is shown to be straightforward to identify and calibrate while guaranteeing a contained computational complexity and being applicable to many physical systems thanks to its modularity. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time adaptive practical tracking control for a class of high-order nonlinear systems with full-state constraints and input saturation. The state constraints are handled by applying nonlinear transformed functions (NTFs) and the input saturation is estimated by an auxiliary hyperbolic tangent function. On the basis of adding a power integrator technique and adaptive control method, an adaptive state feedback controller is designed for the closed-loop system. With the aid of finite-time stability theory, the tracking error converges to a bounded neighbourhood of the origin in a finite time, and all the signals in the closed-loop system are bounded. At last, a simulation example and a practical example are presented to show the effectiveness of the proposed control procedure. [ABSTRACT FROM AUTHOR]

In this paper, the quantisation synchronisation control problem of bilateral teleoperation systems with communication delays is investigated. The inaccurate modelling problem including the system uncertainties and the unknown disturbances are compensated by using the radial basis function networks (RBFN). By introducing the hysteretic quantiser, the control signals are quantised to a set of discrete values to ease the accuracy requirement for actual physical systems and the requirement for communication rate. The position synchronisation of joint variables between the master and slave manipulators is achieved by using the designed control signals and adaptive parameters. Simulation results verify that the synchronisation tracking errors gradually converge to a small neighbourhood around zero. [ABSTRACT FROM AUTHOR]

This paper designs a novel coordinated control scheme to improve the control performance of voltage source converters (VSC) based multi-terminal high voltage direct current (MTDC) transmission network by merging the benefits of adaptive drooping and voltage margin controllers. In this proposed scheme, the droop coefficient is used to manage the DC voltage and maintain power sharing by shifting the control modes of the rectifiers and inverters in the presence of considerable power disturbances. The droop coefficient is planned based on the stability limit of DC voltage. The performance of the designed control scheme is compared to that of existing coordinated control and voltage margin droop control approaches. A ±400 kV five-terminal VSC-MTDC network is developed in PSCAD to verify the planned control method. The simulation results indicate that the proposed control scheme can achieve good performance for controlling the DC voltage and maintaining active power in the MTDC system. [ABSTRACT FROM AUTHOR]

This paper investigates the secure optimal tracking control problem for cyber-physical systems, in which the controller-actuator channel is jammed by denial-of-service attacks. Without leveraging model knowledge, learning-based tracking control algorithms are proposed by utilizing the measured input-output data. The impact of malicious attacks on tracking performance is discussed. More specifically, an augmented system consisted of the system model and the reference model is derived. Then the states of the augmented system are rewritten by utilizing the input, output, and reference trajectory, following which both the Bellman equation and algebraic Riccati equation are given. The conditions of existence and uniqueness of the solution to the algebraic Riccati equation are derived. Furthermore, both policy iteration and value iteration learning-based tracking control algorithms are provided for cyber-physical systems against denial-of-service attacks, and the convergence of the algorithms is also proved. Finally, a DC motor system and a numerical example are given to illustrate the effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we have analysed the influence of viscoelastic and frictional damping on the decay rate of solutions for a Kirchhoff-type viscoelastic wave equation with a distributed delay acting on nonlinear internal damping. Taking the relaxation function of a fairly large class and using the method of energy in which we introduce an adapted Lyapunov functional and by exploiting certain properties of convex functions, under certain assumptions on the constants of system, we obtain the optimal decay rate of energy in the sense that it is compatible with the decay rate of the relaxation function. [ABSTRACT FROM AUTHOR]

In this paper we present and provide a proof for a set of non-recursive formulae arising in the computation of the largest output-nulling and the smallest input-containing subspaces which have been used in a variety of contexts in the framework of the geometric approach. These expressions have been used in the literature both in the strictly proper and in the non-strictly proper case, but, to the best of our knowledge, a proof is still missing. These formulae are established here in the general possibly non-strictly proper case. Some ancillary side results of independent interest are also proposed. [ABSTRACT FROM AUTHOR]

In this paper, we mainly concern the fixed-time consensus control problem for nonlinear leader-following multi-agent systems(MASs). An edge-based adaptive control protocol is presented with part of parameters updated by relative information of system state. Compared with the common node-based adaptive protocols, the proposed edge-based adaptive control protocol assigning different time-varying weights to different communication edges is more accurate. By selecting special Lyapunov functions and theoretical analysis, the obtained conclusions indicate that both sufficient conditions and the settling time of the fixed-time consensus are independent of the system's global information such as the spectrum of Laplacian matrix, which implies that the given protocol is fully distributed. Finally, numerical simulation is illustrated to support the correctness of the main theoretical results. [ABSTRACT FROM AUTHOR]

This paper aims at adaptive event-triggered output-feedback stabilisation in the presence of intractable non-parametric uncertainties. Typically, double-side (i.e. sensor-to-controller and controller-to-actuator) event-triggered communication is pursued for efficient resource utilisation, unlike in related works only reducing single-side communication. This renders more constrained information transmitted via network, challenging the co-design of the compensation and event-triggering mechanisms. By incorporating a switching-varying mechanism, a distinctive adaptive event-triggered output-feedback scheme is established based on a switching filter reconstructing the unmeasurable states. Crucially, a convergence-preserving event-triggering mechanism is proposed with the adaptiveness for uncertainty compensation, by suitably exploiting the switching-varying gain. As such, a desired event-triggered output-feedback control is designed with linearity (with respect to the system output and the filter states) rendered for the controller signal. Just owing to the linearity, the controller signal is subtly kept from entering the event-triggering mechanism, so as to match the double-side event-triggered architecture. Furthermore, it is achieved that the system and filter states converge to zero while a positive minimum inter-execution time is ensured. [ABSTRACT FROM AUTHOR]

We investigate the robustness, disturbance attenuation and performance capabilities of a Proportional-Integral-Retarded (PIR) controller when controlling a class of uncertain second-order systems with input disturbances. The purpose of this paper is to provide insight into the trade-offs between these conflicting requirements. This is accomplished by introducing simple delay-dependent stability conditions, expressed in linear matrix inequality form, which are used to establish the trade-offs in PIR control. In light of the obtained stability conditions, we show that improving performance comes at the cost of reduced robustness and disturbance attenuation. To our knowledge, this problem has not been addressed before and these new results provide valuable insights and systematic guidelines for designing these controllers with trade-offs in mind, thereby completing our current understanding of the tuning mechanisms in PIR control. Inspired by the application field of fuel-cell systems, experiments are carried out on a proof-of-concept switching converter prototype to demonstrate the relevance of the obtained results. [ABSTRACT FROM AUTHOR]