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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]

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 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]

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 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 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]

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]

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]

A multirotor unmanned aerial vehicle (UAV) slung load system (SLS) is a nonlinear dynamics with eight degrees of freedom and four inputs that can be used for load transportation. The suspended payload can be modelled as a two degree-of-freedom pendulum attached to the UAV. This paper presents a path-following control (PFC) for an SLS. The PFC renders motions along any smooth Jordan curve in $ {\mathbb R}^3 $ R 3 for payload position controlled-invariant. This property has practical benefits over traditional time-based trajectory tracking. Furthermore, the PFC prescribes UAV yaw and a desired payload speed profiles along the path. The PFC adopts dynamic extension and input-output state feedback linearisation. The closed-loop has a 1-dimensional zero-dynamics which is shown to be bounded. Hence, the PFC error dynamics is exponentially stable. Simulations are provided to validate the design. [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]

In this paper, we explore a stabilisation problem for two different class of memductance functions for memristive bidirectional associative memory neural networks (MBAMNNs) with time-varying delay. A new Lyapunov-Krasovskii function (LKF) with double and triple integral terms is derived with some sufficient conditions to guarantee the global asymptotic stability criteria using the Lyapunov stability theory. The controller gain matrix for sampled-data controller is obtained for the state-dependent switched system and state-dependent continuous system in terms of linear matrix inequalities (LMIs). Finally, we stabilise the considered model by visualising the simulation part using standard MATLAB software which demonstrates the validness of the theoretical results. [ABSTRACT FROM AUTHOR]

The safety monitoring for nonlinear dynamical systems with embedded neural network components is addressed in this paper. The interval-observer-based safety monitor is developed consisting of two auxiliary neural networks derived from the neural network components of the dynamical system. Due to the presence of nonlinear activation functions in neural networks, we use quadratic constraints on the global sector to abstract the nonlinear activation functions in neural networks. By combining a quadratic constraint approach for the activation function with Lyapunov theory, the interval observer design problem is transformed into a series of quadratic and linear programming feasibility problems to make the interval observer operate with the ability to correctly estimate the system state with estimation errors within acceptable limits. The applicability of the proposed method is verified by simulation of the lateral vehicle control system. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of transforming a single-input single-output discrete-time system into the extended observer form which comprises a linear observable component and a nonlinear injection term depending on the input, output and their forward shifts up to a finite order. The necessary and sufficient conditions for the existence of the extended observer form are provided in terms of vector fields. The algorithm is presented to find a parametrised state transformation necessary to transform the system into the extended observer form. The obtained results are applicable also in case of non-reversible systems. [ABSTRACT FROM AUTHOR]

This paper deals with the converse problems about the robust stability of finite dimensional negative imaginary systems. Various converse negative imaginary theorems are established for linear time-invariant systems. It is shown that the feedback interconnection stability of a specific system with an arbitrary strictly negative imaginary system implies the negative imaginary property of the specific. [ABSTRACT FROM AUTHOR]

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the exponential bipartite synchronisation in mean square (EBS-MS) of stochastic signed networks (SSNs) via periodically intermittent pinning control. It is important to note that intermittent control is an extension of existing literature, which depends on discrete observations instead of continuous observations during the work period. Additionally, only a small percentage of the network nodes are controlled by intermittent control. Several sufficient conditions are established by the Lyapunov method and graph theory. Especially, when the duration τ between two consecutive observations tends to zero, our control will degenerate into common periodically intermittent pinning control. Meanwhile, a corollary about the EBS-MS of SSNs is presented. Besides, theoretical results are applied to a single-link robot arm system and an oscillator system. Finally, numerical simulations are presented to show the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a predetermined performance controller is proposed for a modular charging system for electric vehicles to solve the problem that the entering and leaving of electric vehicles will cause large voltage fluctuation, which will affect the service life of the battery. A barrier Lyapunov function is introduced and combined with the backstepping method to design the controller to ensure that the output voltage of the system can be limited to a set range. The entering and leaving of electric vehicles will result in changes in the system's load, however, this change is unknown, so a finite-time load estimator is designed to estimate the load variation. Then the estimated load is introduced into the controller to improve the adaptive ability of the controller. [ABSTRACT FROM AUTHOR]

In networked control systems, the communication load is a main concern for implementing model predictive control (MPC). This paper introduces a self-triggered MPC algorithm under network environments to reduce communication load, for discrete-time linear systems with bounded state and output disturbances, when only the system output can be measured at triggering instants. The proposed algorithm mainly based on a state estimator whose estimation error is bounded by an invariant set, and on the self-triggered model predictive control of a nominal system. Moreover, the new cost function explicitly adopts communication load is in consideration. The proposed algorithm is proved to drive the system to an invariant set with respect to the bounded disturbances. Finally, simulation results is provided to verify the effectiveness of the proposed robust output feedback MPC algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the spacecraft formation control problem is investigated under the undirected tree communication topology subjected to connectivity preserving and collision avoidance constraint. To implement the connectivity preservation and collision prevention of initially connected spacecrafts without employing any potential functions, a novel appointed-time performance function is developed to impose restrictions on the relative orbit distance of the adjacent spacecrafts. Moreover, this function can also characterise the upper boundary of the convergence time and steady-state error explicitly. Then a reinforcement-learning-based relative orbit-attitude control scheme is proposed to propel the formation error to the vicinity of the origin. An actor-critic neural network architecture is utilised to online compensate the system uncertainties, in which the critic neural network is introduced to improve the approximate performance of the actor neural network for the unknown uncertainties by evaluating the consensus performance of the formation system. In addition, an auxiliary system is devised to cope with the input saturation constraint. By using the Lyapunov stability theory, the stability and convergence of the closed-loop system are analysed. Finally numerical simulations are conducted to illustrate the feasibility and effectiveness of the proposed formation control scheme. [ABSTRACT FROM AUTHOR]

In this paper, a novel data-driven invariant-based safe control scheme for control of a nonlinear vehicle is developed. First, a novel incremental finite-time Koopman representation-based identifier is introduced to learn approximated lifted-states linear system model of system from a limited budget of incrementally sampled data points which not only minimises the instantaneous Koopman representation's identification errors but also the identification errors for a batch of past samples collected in a history stack. A great advantage of the presented identifier is that the uncertainty of the identified system is also quantified and updated over time on a slower time scale. Using set-theoretic tools, then, the quantified uncertainty will be leveraged in conjunction with the learned model in order to impose robust contractivity on the safe set, which guarantees its safety and stability. The proposed approach significantly reduces conservativeness through quantifying and updating the uncertainty level of the learned model over time. [ABSTRACT FROM AUTHOR]

This paper considers a class of distributed aggregative games for first-order and second-order integrator-type multi-cluster systems, respectively. Two Nash equilibrium seeking algorithms are designed based on a distributed aggregation observer which is used to estimate the aggregations of the clusters. The convergence is proved by the input-to-state stable method. Moreover, the algorithms are applied to a class of location control problems, that is, distributed nonlinear placement problems for multi-cluster systems. Finally, some simulations are presented to illustrate the effectiveness of the designed algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a systematic deterministic learning-based rapid sensor fault detection, isolation and accommodation (SFDIA) scheme for a class of nonlinear systems with unmodeled output dynamics. First, locally accurate approximations of sensor faults and unmodeled output dynamics are achieved by using a deterministic learning-based neural network observer. Second, a sensor fault pattern bank which stores the knowledge of sensor faults and unmodeled output dynamics is established. A set of observers utilising the learned knowledge are constructed to generate residuals for rapid SFDIA. The contributions are: (1) the fault detectability and isolability conditions are rigorously analysed and verified in the simulation; (2) using the proposed fault accommodation approach, compared with online parameter adaptation techniques, better tracking performance can be achieved in the presence of sensor faults. Simulation results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we examine the problems of existence and computation of proper and stable stabilising compensators in the feedback path of a special class of linear time-invariant multivariable systems characterised by a strictly proper transfer function matrix. For the class of systems that are 'square', i.e. have the same number of inputs and outputs and have no zeros in the closed right half complex plane and the class of 'non-square' systems that include a 'square' subsystem that has no zeros in the closed right half complex plane we present a sufficient condition for the existence and computation of proper stabilising (pole placing) compensators which in certain cases that depend on the transfer function matrix of the system can be chosen to be stable. [ABSTRACT FROM AUTHOR]

This paper proposes an integrated cooperative guidance strategy for multiple unmanned aerial vehicles to simultaneously attack multiple targets. To solve the challenging cooperative attack problem coupled with the target assignment problem simultaneously in a unified one-phase framework, a novel auxiliary index denoted as the integrated relative distance is designed and analysed from two opposite perspectives. Because of its special properties, the proposed integrated relative distance plays a crucial role in evaluating dynamic engagement situations between attackers and targets, and it further provides a criterion for whether the cooperative attack mission is completed. Then all integrated relative distances are minimised to directly derive a cooperative guidance law for attackers based on optimal control theory. The simultaneous minimisation of integrated relative distances from both forward and backward perspectives ensures that each target is destroyed by at least one attacker and all attackers are fully exploited to obtain optimal attack performance. By this means, the target assignment problem is automatically solved and the cooperative simultaneous attack is achieved. Several simulation cases are presented to illustrate the effectiveness of the proposed integrated cooperative guidance strategy. [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 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]

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]

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 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 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]

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]

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]

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]

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]

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]