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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]

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]

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]

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]

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]

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]

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 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]

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]

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]

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 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]

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]

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]

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]

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 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, 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]

This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modelled in the linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and is used to generate scenarios that ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance the performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance. [ABSTRACT FROM AUTHOR]

This paper proposes a novel stable economic model predictive control (EMPC) strategy for constrained nonlinear systems with changing economic criteria. The traditional EMPC may lead to infeasibility and even instability of the closed-loop system when the criterion has been changed. Firstly, a generalised terminal constraint is introduced to ensure the recursive feasibility of the economic optimisation problem, which enforces the terminal states to converge to an arbitrary equilibrium state rather than a predetermined fixed one at the initial time. Then the stability constraint is constructed by solving an auxiliary optimisation problem online, which is the key to guaranteeing the asymptotic stability of the closed-loop system. Finally, sufficient conditions for feasibility and asymptotic stability are derived in the context of changing economic criteria. The main feature of the proposed strategy is that it does not need to know the changes of economic criterion in advance, and its properties and effectiveness are exemplified by simulations on a nonlinear chemical process example. [ABSTRACT FROM AUTHOR]

This paper copes with a matter of event-triggered fast finite-time prescribed tracking control for non-affine stochastic nonlinear systems, in which deception attacks are taken into consideration. The main objective of the proposed controller is that all the closed-loop variables are bounded in probability, and the tracking error is constrained to the predefined funnel functions by choosing suitable parameters. Primarily, the mean value theorem is utilised to transform the considered systems into the equivalent systems with affine structures. Next, based on the backstepping algorithm, a modified event-triggered scheme is developed to save the network resources. Meanwhile, the unknown parts in the designed systems are approximated by neural networks. Finally, an actual simulation is conducted to verify the validity of the theorem. [ABSTRACT FROM AUTHOR]

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

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

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

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

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

This paper investigates the stabilization problem for upper-triangular nonlinear systems subject to timedelay by using sampled-data control. In order to make the design process more feasible, the coordinate transformation is introduced to generate a scaling gain. Then the linear observer is constructed and the sampled-data controller is obtained based on the estimated states. Under the upper-triangular linear growth assumption and Lyapunov method, the suitable parameters can be selected to make the system achieve globally stable. It can be proved that the proposed method can also be extended to the system with multiple time delays. Finally, the effectiveness of the designed controller is demonstrated by using numerical and practical examples. [ABSTRACT FROM AUTHOR]

For most nonlinear systems, it is in general a difficult task to obtain algebraic controllability criteria. In this paper, we consider small-controllability of discrete-time state-affine nonlinear systems. We first focus on the systems in dimension two with single-input and improve a previous controllability criterion. That is, we derive a sufficient algebraic criterion for small-controllability of the systems, which is easier to apply than the previous one. We then show that if the state-affine nonlinear systems are bilinear, a necessary and sufficient algebraic criterion for small-controllability can be obtained using invariant sets. We also extend the derived controllability criteria to continuous-time state-affine nonlinear systems and to discrete-time multi-input state-affine nonlinear systems. Examples are given to illustrate the derived controllability criteria of this paper. [ABSTRACT FROM AUTHOR]

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

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

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

In this paper, $ \mathcal {H}_{\infty } $ H ∞ observer-based consensus for a class of nonlinear multiagent systems (MASs) with actuator saturation and input delays are estimated. A new delay-dependent region partitioning approach has been introduced in multiagent systems. The state information of the leader can be obtained by designing a distributed observer for each follower. Based on the state information of the follower and the estimated state information of the neighbouring agents, a distributed controller has been developed. With the help of a novel Lyapunov–Krasovakii functional (LKF), using a region partitioning approach combined with Wirtinger inequalities, a sufficient condition is established in terms of Linear Matrix Inequality (LMI). Finally, simulation examples are presented to the applicability of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the output feedback problem is studied for a class of nonlinear cascade systems with integral input to state stability (iISS) inverse dynamics and an unknown control direction. The tan-type barrier Lyapunov function (UBLF) is introduced for an asymmetric time-varying output constraint, which can be equal to the standard Lyapunov function of an unconstrained system, thereby solving the requirement for the asymmetric time-varying output constraint. A design strategy based on backstepping is proposed to construct a dynamic output feedback control law, and an output feedback controller is designed using the barrier function. The proposed strategy satisfies the constraint condition while keeping all other closed-loop signals bounded. Finally, the effectiveness of the proposed strategy is proven by the simulation results. [ABSTRACT FROM AUTHOR]

A self-excited system is a nonlinear system with the property that a constant input yields a bounded, nonconvergent response. Nonlinear identification of self-excited systems is considered using a Lur'e model structure, where a linear model is connected in feedback with a nonlinear feedback function. To facilitate identification, the nonlinear feedback function is assumed to be continuous and piecewise affine (CPA). The present paper uses least-squares optimisation to estimate the coefficients of the linear dynamics and the slope vector of the CPA nonlinearity, as well as mixed-integer optimisation to estimate the order of the linear dynamics and the breakpoints of the CPA function. The proposed identification technique requires only output data, and thus no measurement of the constant input is required. This technique is illustrated on a diverse collection of low-dimensional numerical examples as well as data from a gas-turbine combustor. [ABSTRACT FROM AUTHOR]

Controller design for finite-time attractive and energy consumption of stochastic nonlinear systems is investigated in this paper. By constructing appropriate controller and using inequality techniques, sufficient conditions for finite-time attractiveness of stochastic nonlinear systems are addressed. To estimate the control energy consumption, this paper first gives the definition of expected energy consumption for stochastic system. Furthermore, the upper bounds of control time and energy consumption are given. Afterwards, the trade-off analysis between control time and energy consumption is carried out to find a optimal control intensity choice. Finally, two numerical examples are presented to verify the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an approximation-based adaptive multi-dimensional Taylor network (MTN) control approach is proposed for a class of nonlinear systems with unknown dead-zone output. Firstly, MTNs are utilised to approximate the unknown nonlinearity of the system. Secondly, the relation of the unknown function f 1 ( x 1 ) and the output y is establish. Thirdly, integrating adaptive control method and MTNs into the backstepping design process, a novel MTN-based adaptive controller is constructed by introducing a Nussbaum function. The proposed control scheme has the advantages of simple structure and small calculation. Finally, two simulation examples are given to illustrate the effectiveness of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a redesigned approximate dynamic inversion (RADI) method is developed for a class of pure-feedback nonaffine-in-control nonlinear systems (PFNNSs). Recently, the approximate dynamic inversion (ADI)-based algorithms have been widely implemented for nonaffine-in-control nonlinear systems. To employ ADI-based methods, a fast dynamic subsystem has to be established to derive the explicit inversion of the nonaffine equation. However, the previous research on ADI rarely considers that the amplitude of actual input derived from the fast augmented subsystem can be extremely high, which maybe intolerable for practical systems. In this paper, we set up input saturation and view the difference between input with and without saturation as a perturbation. Then, an intermediate subsystem is constructed to compensate the influence of this perturbation by approximating its inversion. The exponential stability of the overall closed-loop system is ensured via singular perturbation theorem. Numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a new distributed optimal control strategy for continuous-time nonaffine nonlinear systems with unknown dynamics is presented. We exploit a paradigm based on an Extended Adaptive Dynamic Programming (EADP), which will be fully stated in the paper, to provide a distributed optimal control strategy in the presence of subsystem interactions. A proper design of optimal control law is further fully investigated through the framework of Hamilton–Jacobi–Bellman (HJB). The proposed EADP algorithm can now be employed in order to solve iteratively the HJB equation associated with each subsystem. The proposed distributed optimal control system mainly consisting of three weighted basis functions for each subsystem is fully developed to handle the issue associated with the availability of unknown dynamics. The convergence analysis of the proposed algorithms is also established. Finally, two numerical examples are given to confirm the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, exponential synchronisation of nonlinear multi-agent systems with K agents by distributed self-triggered hybrid control and virtual link mechanism is investigated. Based on the Lyapunov function and linear matrix inequalities, some synchronisation conditions are provided. Because of using the virtual link, the system can be divided into two subsystems, real link subsystem and virtual link subsystem. They can be synchronised with the desired dynamical behaviours by using the same self-triggered hybrid control. Hence, the original dimension (K) of synchronisation conditions can be reduced to ⌈ K 2 ⌉ ( K 2 round up). Finally, a simulation example is given to demonstrate the performance of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time stability of nonautonomous systems is studied by using Lyapunov Krasovskii method and Gronwall inequality. Firstly, a new lemma for the finite-time stability for nonautonomous systems is given by using Gronwall inequality. which make the derivative of Lyapunov function not to be negative all the time. Then, based on the new lemma and Lyapunov Krasovskii method, some finite-time stability criteria about nonautonomous linear systems and nonlinear systems are proposed. Based on this, by designing controllers, the finite-time stabilizable theorem is obtained. In addition, it is pointed out that the conclusion of this paper is more general than the existing literature in the remarks. Finally, several examples are simulated with MATLAB to verify the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper deals with novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do not maintain recursive feasibility for a piecewise constant control parameterisation. The key idea in this paper is to introduce uniform grids with variable discretisation. A shrinking-horizon grid adaptation scheme ensures convergence to a specific region around the target state and recursive feasibility. The size of the region is configurable by design parameters. This facilitates the systematic dual-mode design for quasi-time-optimal control to restore asymptotic stability and establish a smooth stabilisation. Two nonlinear programme formulations with different sparsity patterns are introduced to realise and implement the underlying optimal control problem. For a class of numerical integration schemes, even nominal asymptotic stability and true time-optimality are achieved without dual-mode. A comparative analysis as well as experimental results demonstrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper provides a procedure for designing a sliding mode observer for a nonlinear system in the presence of Gaussian input disturbances and sensor noises. The paper first proposes a novel candidate for Lyapunov stability, termed a Time-averaged Lyapunov (TAL) function. The TAL averages the Lyapunov analysis over a small finite time interval, allowing for intuitive analysis of noises and disturbance. The paper then provides the necessary and sufficient condition for the design of the sliding observer gainsusing the TAL in the form of Linear Matrix Inequality (LMI). The LMIs can then be explicitly solved offline using commercial LMI solvers. The paper compares the LMIs for the two observer designs to demonstrate the design of the sliding mode observer using TAL can greatly enhance the scope of observer design for nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, the problems of the stochastic input-to-state stability (SISS) properties are investigated for impulsive stochastic nonlinear systems with delayed impulses. By employing Lyapunov method together with average impulsive interval approach, the sufficient conditions are established to ensure properties for impulsive stochastic systems with all stable subsystems. Moreover, the ISS properties are also derived for the stochastic systems when the system is with both stable and unstable subsystems. Then, we also study impulsive systems with multiple jumps, i.e. there exist different impulses in a system. By now, there has been no papers to consider multiple jumps for stochastic cases. Finally, two examples are provided to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper proposes a finite-time dynamic surface control (FTDSC) scheme using a novel nonlinear filter for nonlinear systems with input saturation and output constraint. The FTDSC scheme featured by nonlinear filter is presented to overcome the drawback of the traditional DSC scheme using first-order linear filter. The barrier Lyapunov function (BLF) is used to handling output constraint and the disadvantage of conventional input saturation problem is solved through introducing a nonlinear smooth function. In order to deal with the impact of external disturbance, the nonlinear disturbance observer (NDO) is introduced to estimate the disturbance. It is proved that All signals are semi-globally uniformly ultimately bounded (SGUUB) in the closed loop system. Moreover, the tracking error can convergences to a neighborhood of zero through the proper designed parameters. Comparison studies are conducted to verify that the proposed FTDSC scheme comparing with the traditional DSC scheme has the more accurate tracking capability. [ABSTRACT FROM AUTHOR]

Recent years, there has been an increasing interest in the application of reinforcement learning (RL) to nonlinear system control. And many published studies have shown that reusing historical data can improve the learning efficiency of intelligent agents. However, reusing historical data leads to a large increase in the data to be processed. This paper proposes a novel adaptive law for the critic network in the RL framework to address this problem. The innovation of the proposed method is the introduction of an auxiliary matrix containing information about the historical estimation errors instead of the historical data itself. Moreover, the addition of the auxiliary matrix allows the persistent excitation (PE) conditions to be checked online. As a validation, the proposed approach is applied to a motor servo system containing unknown dynamics. Simulation and experimental results demonstrate the effectiveness of the proposed controller in the end. [ABSTRACT FROM AUTHOR]