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This research paper focuses on the design of a boundary optimal controller with output feedback for a tubular catalytic cracking reactor. The process is represented by a set of non-linear parabolic partial differential equations (PDEs). The approach involves utilising the linearised infinite-dimensional version of the model, taking advantage of the system generator being a Riesz spectral operator. A stabilising compensator is designed by leveraging the eigenvalues and eigenvectors of the system generator. This paper also includes numerical simulations to demonstrate the performance of the developed algorithm. [ABSTRACT FROM AUTHOR]

Ever since Brockett, Clark and Mitter introduced the estimation algebra method, it becomes a powerful tool to classify the finite-dimensional filtering system. In this paper, we investigate finite-dimensional estimation algebra with non-maximal rank. The structure of Wong matrix Ω will be focused on since it plays a critical role in the classification of finite-dimensional estimation algebras. In this paper, we first consider general estimation algebra with non-maximal rank and determine the linear structure of the submatrix of Ω by using rank condition and property of Euler operator. In the second part, we proceed to consider the case of linear rank n−1 and prove the linear structure of Ω. Finally, we give the structure of finite-dimensional filters which implies the drift term must be a quadratic function plus a gradient of a smooth function. [ABSTRACT FROM AUTHOR]

This paper investigates the examination of global asymptotic stability pertaining to uncertain complex-valued stochastic neural networks (UCVSNNs) with multiple time delays. This paper employs the real-imaginary separated activation function to establish an equivalence between complex-valued neural networks (CVNNs) and two real-valued activation functions, representing the real and imaginary parts respectively. This equivalence is utilised to analyse the original UCVSNNs model in a comprehensive manner. The global asymptotic stability of the studied UCVSNNs model is ensured by constructing an appropriate Lyapunov-Krasovskii generalised function and applying the $ It\hat {o} $ It o ˆ formula, linear matrix inequality (LMI) and other analytical techniques to derive the system stability and other sufficient conditions. In the meanwhile, we provide two numerical examples to demonstrate the reliability and benefit of the discovered results. [ABSTRACT FROM AUTHOR]

This paper explores a reinsurance and asset liability management problem in a factor model with dependent risks, considering economic factors as non-Markovian processes impacting the appreciation rate, volatility, and value of liabilities. It encompasses various stochastic volatility (SV) models like Hull-White, Heston, 3/2, and 4/2 models as special cases. The model addresses dependent risks through a common shock in claim number processes. The insurer's aim is to minimize variance in terminal net wealth while achieving a certain expected terminal net wealth, balancing reinsurance, new business, and asset allocation. The paper employs linear-quadratic (LQ) control and backward stochastic differential equation (BSDE) theory to derive both the efficient strategy and the efficient frontier. To illustrate our results, numerical examples are provided in two special cases, the 3/2 and 4/2 SV models. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive tracking control strategy based on multi-dimensional Taylor network (MTN) is proposed for a class of stochastic nonlinear state-constrained systems with input delay. Firstly, to avoid constraint violation, the adaptive backstepping approach and barrier Lyapunov function (BLF) are combined in a unified framework. Then, a suitable auxiliary system with the same order as the considered system is constructed to deal with the effect of input delay. In addition, MTN is used to estimate unknown nonlinear functions during the design of the controller. Furthermore, with the help of the Lyapunov stability theorem, the controller presented in this paper can guarantee that all the closed-loop signals are bounded in probability, the system states remain in the defined compact sets, the output signal can track the reference signal successfully, and the tracking error is bounded by the expected bound. Finally, two examples are given to verify the effectiveness of the designed scheme. [ABSTRACT FROM AUTHOR]

The simultaneous fault detection and control (SFDC) has emerged as a reliable scheme. However, what happens when the designed structure undergoes changes? Such variations have the potential to cause instability and misdiagnosis. This paper delves into a cutting-edge SFDC structure that surpasses conventional designs in terms of reliability. The proposed Resilient Simultaneous Fault Detection and Control (RSFDC) structure considers variations in the designed parameters and provides a more robust and fault-tolerant approach to SFDC, with important implications for the design of reliable and resilient control systems in a broad range of applications. This scheme is formulated as a multi-objective optimisation problem, encompassing control and diagnosis objectives. Specifically, it aims to minimise the impact of faults and disturbances on the controlled output while reducing residual sensitivity to all changes and maximising the fault effects on the residual. Through simulation comparisons, this paper showcases the merits of the RSFDC structure in two examples, highlighting its superiority over other designs. [ABSTRACT FROM AUTHOR]

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]

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, 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]

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 mainly investigates the fixed-time almost disturbance decoupling (ADD) stabilisation problem for a class of nonlinear systems in the p-normal form. Under suitable assumptions, a novel fixed-time ADD feedback controller is designed to ensure all states in the underlying system are not affected by disturbances. By constructing an appropriate Lyapunov function, it is shown that the corresponding closed-loop system is fixed-time stable which means the upper bound of the settling time depends on the control design parameters only. To testify the effectiveness of the proposal, two simulation examples are presented. [ABSTRACT FROM AUTHOR]

This paper presents an observer-based event-triggered boundary control strategy for the one-phase Stefan problem, utilising the position and velocity measurements of the moving interface. The design of the observer and controller is founded on the infinite-dimensional backstepping approach. To implement the continuous-time observer-based controller in an event-triggered framework, we propose a dynamic event triggering condition. This condition specifies the instances when the control input must be updated. Between events, the control input is maintained constant in a Zero-Order-Hold manner. We demonstrate that the dwell-time between successive triggering moments is uniformly bounded from below, thereby precluding Zeno behaviour. The proposed event-triggered boundary control strategy ensures the well-posedness of the closed-loop system and the satisfaction of certain model validity conditions. Additionally, the global exponential convergence of the closed-loop system to the setpoint is established using Lyapunov approach. A simulation example is provided to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

Real-time numerical differentiation plays a crucial role in many digital control algorithms, such as PID control, which requires numerical differentiation to implement derivative action. This paper proposes an algorithm for estimating the numerical derivative of a signal from noisy sampled data measurements. The method uses adaptive input estimation with adaptive state estimation (AIE/ASE), and thus it requires only minimal prior information about the signal and noise statistics. Furthermore, since the estimates of the derivative at step k provided by AIE/ASE depend only on data available up to step k, AIE/ASE is thus implementable in real time. The accuracy of AIE/ASE is compared numerically to several conventional numerical differentiation methods. Finally, AIE/ASE is applied to simulated vehicle position data, generated in the CarSim simulator software. [ABSTRACT FROM AUTHOR]

In this paper, we consider cyber physical systems security control problems under DoS attacks via the tracking-removed autoencoder. The DoS attack model is described by the switch signal, which occurs in the controller-actuator transmission channel. Then, the linear matrix inequality theory is used to solve the average dwell time of the attack mode that the system can tolerate. Moreover, when the attack dwell time exceeds the tolerance range, a tracking-removed autoencoder is chosen to train to get the control signal. And it can be proved that the closed-loop system with the controller based on the tracking-removed autoencoder is asymptotically stable with $ H_\infty $ H ∞ performance index. Finally, the correctness and advancement of the theory are proved by an example. [ABSTRACT FROM AUTHOR]

'Co-design' problems try to simultaneously design the physical and control components to improve the overall system performance. However, existing co-design paradigms cannot deal with complex frequency temporal domain specifications. In this paper, we investigate the co-design problem for a class of linear parameter-varying (LPV) systems with frequency temporal domain specifications. Firstly, the frequency temporal domain specifications are written in a formal language called spectral temporal logic (STL). Secondly, the satisfaction conditions of the spectral temporal logic specifications have been transformed into non-linear matrices inequality forms with necessary and sufficient conditions. Thirdly, the co-design problem is transformed into a non-convex optimisation problem with mixed-integer linear matrix inequalities (MILMIs) constraints, and then an iterative algorithm is proposed to solve the co-design problem with semidefinite programming (SDP). Finally, the performance of the algorithm and the expressiveness of spectral temporal logic are illustrated with the applications to micro-electromechanical systems (MEMS). [ABSTRACT FROM AUTHOR]

In this paper, the problem of actuator fault detection and isolation is investigated for a class of nonlinear interconnected large-scale systems with modelling uncertainty and measurement noise, where each subsystem can have multiple inputs and multiple outputs (MIMO). The main contribution of this work is the derivation of a scheme that is able to diagnose single or multiple actuator faults in one or multiple subsystems. Each subsystem is monitored by a local diagnosis agent which contains the actuator fault detection module and the isolation module. The detection threshold in the fault detection module is generated through the use of a novel filtering technique, while the fault isolation module is realised by applying a reasoning-based decision logic based on a fault signature matrix. Fault propagation among subsystems is investigated and the results obtained allow for the identification of the subsystems that contain the faulty actuators. Finally, the effectiveness of the proposed actuator fault diagnosis method is demonstrated through a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, a min–max adaptive dynamic programming approach is studied for a zero-sum differential game problem with unknown nonlinear dynamics. The unknown nonlinear dynamics is learned through the online Recurrent Neural Network (RNN). The error between the learned RNN model and the dynamics of the system is proved to converge to zero. The policy iteration algorithm is utilised to solve the Hamilton–Jacobi–Isaacs (HJI) equation associated with the differential game. Furthermore, the value function in the HJI equation is approximated through a critical Neural Network with its weights and activation functions updated online iteratively. The Uniform Ultimate Bounded stability of the closed-loop system is proved based on the Lyapunov theory. Finally, the effectiveness of the proposed solution method is demonstrated by applying it to three examples. [ABSTRACT FROM AUTHOR]

This paper considers the sliding-mode consensus control problem of the multi-agent systems (MASs), in which an event-triggering weighted try-once-discard (ET-WTOD) protocol is proposed to schedule the transmission of each agent's state information. The key feature of the ET-WTOD protocol is to flexibly adjust the number of transmitted state components at each triggering instant based on the variation of each component and the set thresholds. Then, a token-dependent sliding-mode controller under the ET-WTOD protocol is designed to achieve the desirable consensus of MASs, meanwhile, an iterative optimisation algorithm is used to search the sliding matrix and reduce the sliding domain. Eventually, a numerical simulation example demonstrates the efficacy of the proposed sliding-mode control approach. [ABSTRACT FROM AUTHOR]

This paper considers the stability robustness and $ H_2 $ H 2 performance robustness of continuous-time Markovian jump linear systems with uncertain transition rates. Based on the Kronecker product, the robustness problems are transformed into problems of judging whether a class of uncertain matrices can maintain nonsingularity. For the robust stability problem, the method for computing the robust upper and lower bounds of transition rates is given first and then the necessary and sufficient condition for the investigated system to maintain robust stochastic stability is given when considering interval uncertainty. For the robust $ H_2 $ H 2 performance problem, the robustness bounds and sufficient and necessary conditions guaranteeing the robust $ H_2 $ H 2 performance are similarly given. The robustness bounds for analysing the tolerance of continuous-time Markovian jump linear systems to parameter uncertainties can be conveniently computed by utilising the proposed results. Numerical examples illustrate that the results are less conservative than existing results. [ABSTRACT FROM AUTHOR]

This paper considers the optimal control of a second-order nonlinear system with unknown dynamics. A new reinforcement learning based approach is proposed with the aid of direct adaptive control. By the new approach, actor-critic reinforcement learning algorithms are proposed with neural network approximation. Simulation results are presented to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper studies an event-triggered fault-tolerant tracking control strategy design of multiple quadrotor UAVs (MQUAVs) formation subject to the composite influence of external disturbance, tracking error constraints and actuator faults. A prescribed time prescribed performance function is employed to solve tracking error constraints and it ensures the tracking error enters into the constraint boundary in the prescribed time. A first-order filter is designed to solve the problem of computational explosion caused by reference trajectory and unknown external disturbance. The adaptive method is used to deal with the unknown parameters and the comprehensive uncertainty which contains actuator faults and external disturbance. Furthermore, the event-triggered controller is designed to achieve the formation tracking with the reduction of update number of controller to save resources. The bounded stability of the tracking error is proved via the Lyapunov theory. At last, the effectiveness of the control strategy is verified by simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the interval consensus problem of second-order multi-agent systems over a directed graph, where each agent is allowed to propose an interval constraint on the achievable consensus value. In order to reduce the communication among agents, a distributed impulsive controller is given. The impulsive control is implemented only at impulsive instants. Moreover, each agent has its own impulsive instants independently and the impulsive intervals are aperiodic. Sufficient conditions are established to guarantee the achievement of interval consensus for the considered systems. Finally, a numerical example is presented to demonstrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global uniform practical asymptotic and exponential stability for a large class of time-varying systems by using the concept of practical scalar functions. A new converse stability theorem is established which is used to give some sufficient conditions that guarantee the global uniform practical asymptotic and exponential stability of a class of perturbed systems. Furthermore, some examples are presented. [ABSTRACT FROM AUTHOR]

This paper explores the adaptive output feedback event-triggered consensus control of a network of parabolic systems modelled by partial differential equations (PDEs). An infinite-dimensional state observer is established to estimate the state based on the relative output information. On the basis of the adaptive state observer, two novel distributed event-triggered controllers are proposed to address the leaderless consensus and leader-follower consensus problem. Based on the Lyapunov method and PDE theory, it is shown that the asymptotic consensus control can be achieved. Compared to the related works, a distinctive feature of the designed event-triggered consensus protocols is fully distributed which does not demand any global information of the graph. In addition, the absence of Zeno behaviour is demonstrated. Lastly, the obtained results are demonstrated using two simulations. [ABSTRACT FROM AUTHOR]

Due to the discrepancy between an individual's expressed opinion and private opinion in many social situations, this paper aims to study the convergence and bipartite consensus of expressed and private opinion (EPO) model on signed directed network $ \mathcal {G}(W) $ G (W) without satisfying common strong connectivity. First, by constructing an enlarged network $ \mathcal {G}(P) $ G (P) of $ \mathcal {G}(W) $ G (W) and studying the properties of CSCCs in $ \mathcal {G}(P) $ G (P) , we establish some general convergence criteria for the EPO model. Second, we explore the relationship between the final private opinion, final expressed opinion and initial opinion of an individual and prove that the self-confidence of an individual can influence the gap between his final expressed opinion and group pressure. Third, by structural balance theory, we establish the bipartite consensus criterion of the EPO model. Finally, numerical simulations are presented to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

The Lyapunov approach is one of the most effective and efficient means of studying the partial stability of stochastic systems. A number of authors have analysed the partial practical stability of stochastic differential equations using Lyapunov techniques. Nevertheless, no results are concerned with the partial stability of stochastic systems based on the knowledge of the solution of the system explicitly. This paper has been concerned with the problem of partial practical stability for linear time-varying stochastic perturbed systems. Necessary and sufficient conditions for partial practical uniform exponential stability are given based on generalised Gronwall inequalities, in particular of Gamidov's type. An example is developed to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This paper studies the optimal investment and benefit payment strategies for target benefit (TB) pension plans. The pension fund receives contributions from active members and pays benefits to retirees. Meanwhile, the accumulated wealth is invested in financial market consisting of one risk-free asset and one risky asset, in which the risk-free interest rate is described by the Vasicek model. The general hyperbolic absolute risk aversion (HARA) utility is adopted to describe pension fund managers' risk preferences. Using the dynamic programming approach, we construct the Hamilton–Jacobi–Bellman (HJB) equation and obtain explicit expressions for optimal investment and benefit payment strategies using the Legendre transform-dual technique. Finally, numerical analysis is presented to illustrate the sensitivity of the optimal strategies to model parameters. [ABSTRACT FROM AUTHOR]

This paper is concerned with prescribed-time control for spacecraft formation flying. Firstly, based on Lie group SE(3), the coupled 6-degrees-of-freedom kinematics and dynamics for leader and followers are modelled. Then, by using exponential coordinates of SE(3), the relative configuration between leader and followers is expressed and its linearised model is also given. Finally, by constructing a finite-time escape function and using the properties of parametric Lyapunov function, a novel time-varying high-gain controller is developed such that the spacecraft formation flying can be achieved within a finite time that can be explicitly prescribed. As a further result, the observer-based controller is also proposed for the same problem. Numerical simulations verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper develops a methodology for designing a control system composed of a linear time-invariant system interconnecting with multiple decoupled time-invariant memoryless nonlinearities. The design problem is to determine parameters of the system such that its outputs and the nonlinearity inputs always remain within prescribed bounds for all exogenous inputs whose magnitude and slope satisfy certain bounding conditions. By using Schauder fixed point theorem, we show that a design associated with a linear system is also a solution of the problem. Based on this, we further develop surrogate design criteria in the form of the inequalities that can readily be solved in practice. Sufficient conditions for the solvability of such inequalities are given for deadzone and saturation. To show the usefulness and the effectiveness of the methodology, a design example of a load frequency control system with time delay is carried out where deadzone and saturation are taken into account. [ABSTRACT FROM AUTHOR]

In this paper, we consider the cooperative robust output regulation problem for a class of nonlinear multi-agent systems over jointly connected switching networks. First, by attaching each subsystem with an input driven filter, we obtain an extended system. Second, by integrating the distributed observer approach and the distributed internal model approach, we convert the cooperative output regulation problem of the original system into a distributed robust stabilisation problem of an augmented error system which is also a multi-agent system. Finally, we solve the original problem by stabilising the augmented error system via a distributed output feedback control law. [ABSTRACT FROM AUTHOR]

The paper presents output feedback control of a class of two-time-scale nonlinear systems. State feedback control for two-time-scale system is converted into output feedback via two high-gain observers. The high-gain observers are designed for reduced-order, quasi-steady-state, and boundary layer models of the two-time-scale system. Analyses reveal three-time-scale structure of the closed-loop system. Convergence of the closed-loop system is guaranteed under sufficient conditions. Simulation results of control of inverted pendulum on a cart illustrate the application of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper discusses a class of delayed Clifford-valued shunting inhibitory cellular neural networks. Firstly, we obtain several sufficient conditions for the existence of weighted pseudo almost periodic solutions for Clifford-valued shunting inhibitory cellular neural networks with delays by applying the non-decomposition method and Banach fixed point theorem. Secondly, we get the finite-time stability for Clifford-valued shunting inhibitory cellular neural networks with delays by using inequality techniques. Finally, we give one illustrative example to illustrate the feasibility and effectiveness of the main results. [ABSTRACT FROM AUTHOR]

This paper studies the analysis and synthesis of distributed adaptive control architectures for uncertain multiagent systems with coupled dynamics in a leader-follower setting, where overall closed-loop system stability is established, and sufficient stability conditions are defined. Specifically, we first analyse a standard distributed adaptive control law and reveal local stability conditions that guarantee the boundedness of the closed-loop system trajectories. We next synthesise fixed and adaptive robustifying terms to show relaxed local stability conditions. We also show that the fixed robustifying term can yield high-gain parameters in the resulting control signals, where the adaptive robustifying term removes this high-gain requirement. Finally, an illustrative numerical example is further presented to compare the proposed methods and demonstrate our theoretical contributions. [ABSTRACT FROM AUTHOR]

This paper investigates the secure synchronisation for multiple coupled complex networks with time-varying delays under Denial-of-Service attacks, in which the attacks are considered in the controller-to-actuator channel. A synchronisation criterion is established to ensure the secure synchronisation of the presented networks based on the designed adaptive topology observer, controller and Lyapunov function. Furthermore, the result adapts to study the synchronisation of complex networks without and with multiple time-varying delays. Finally, two numerical examples are provided to illustrate the availability of the derived theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a numerical approach to solve the estimator-based filtering problem of a linear system with multiple and distributed delays. We consider the problem of finding a filter or estimator that suppresses the $ \mathcal {H}_2 $ H 2 filtering cost on the transfer matrix from a given noise input to the filtering error. By solving an optimisation problem associated with the $ \mathcal {H}_2 $ H 2 performance, the gain matrices of the filter are obtained. The effectiveness of the presented approach is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies the finite-time output tracking problem for a class of nonlinear sandwich systems with sandwiched dead-zone function and input actuator saturation constraint. To achieve the goal, a systematic adaptive backstepping controller is proposed based on the practical finite-time stability criterion which guarantees the output tracking even if the dead zone and saturation constraints occur, simultaneously. In the control approach to confine the system output to a predefined set, the barrier Lyapunov function is utilised. To cope with the problem of 'explosion of complexity', a finite-time command filter is also employed. Furthermore, the values of the unknown parameters are estimated by appropriate adaptive laws. The finite-time stability of the closed-loop system is proved based on the Lyapunov approach which ensures the boundedness of all signals. Finally, the efficiency and applicability of the proposed method are confirmed by providing the simulation results for the hydraulic servo press system. [ABSTRACT FROM AUTHOR]

Motivated by rational expectations theory, this paper studies a class of stochastic linear-quadratic dynamic optimisation problems involving a large number of weakly-coupled heterogeneous agents. Different from well-studied mean field games, these agents formalise a team with cooperation to minimise some social cost functional. Moreover, the state here evolves by some anticipated backward stochastic differential equation in which the terminal instead initial condition is specified and the anticipated terms are involved. Applying a so-called anticipated person-by-person optimality principle, we construct an auxiliary control problem for each agent based on decentralised information. The decentralised social strategy is derived by a class of new consistency condition systems, which are mean-field-type anticipated forward–backward stochastic differential delay equations (AFBSDDEs). The well-posedness of such consistency condition system is obtained via discounting method. The corresponding asymptotic social optimality is also verified as the population size goes to infinity. [ABSTRACT FROM AUTHOR]