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This paper investigates the problem of robust output feedback control tracking for a class of nonlinear dual-rate sample-data systems subject to time-varying disturbances. These dual-rate systems, known as slow measurement fast control (SMFC) systems, are characterised by a slow sampling rate of the sensor and a fast updating rate of the controller. To facilitate high-frequency signal tracking, this paper introduces an alternating predictive generalised proportional integral observer (APGPIO). The proposed control method not only effectively restores the system state and captures disturbance changes between samples but also enhances the control bandwidth and anti-disturbance ability, enabling effective tracking of high-frequency reference outputs. By combining it with a fast updating sample-data feedback controller, APGPIO utilises predictive methods to increase the sampling rate of the system's sensors, matching the update frequency of the controller. Stability analysis demonstrates that the tracking error of this hybrid nonlinear system converges to a bounded region centred at the origin. Finally, the designed method's high control bandwidth and anti-disturbance ability are demonstrated through multiple sets of simulations using a real system. [ABSTRACT FROM AUTHOR]

This paper gives a fault-tolerant control scheme concerning with the optimal and near-optimal system performance for a class of nonlinear systems with time-varying actuator faults, time-varying disturbances, and identification errors of the neural network-based identifier. In this paper, the adaptive dynamic programming method is directly used to design the optimal sliding surface, so that the designer can design the target dynamics of the sliding mode in advance. In addition, the barrier function-based sliding-mode control is used to cope with the bounded but boundary-unknown estimation errors of the identifier, and the method ensures that the sliding-mode variable converges to the designer's predefined neighborhood of zero in finite time and the control gain is not overestimated. Specifically, first, by adaptive dynamic programming, near-optimal sliding surface is designed in the sense of the quadratic optimal criterion. Second, a neural network identifier is designed to model the lumped uncertainties including actuator faults and disturbances. Third, a barrier function-based adaptive sliding-mode control is used to cope with the identification errors of the neural network identifier and has no control gain overestimation, which can guarantee to confine the sliding variable to a predefined vicinity of the proposed sliding surface. For this system with faults and disturbances, it is shown that near-optimal property is achieved by this scheme, the chattering phenomenon is effectively suppressed, and the reconstruction error of the neural network identifier with unknown boundary is effectively handled by the adaptive sliding-mode control based on the barrier function. The proof of stability is given by Lyapunov's direct method and the effectiveness of this control scheme is verified by applying it to the spacecraft attitude system. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive tracking control strategy based on neural networks (NNs) is proposed for the stochastic nonlinear strict-feedback system with a time-varying input delay and unmeasurable states. A state observer is constructed to solve the problem of unmeasurable state and the effect of the time-varying input delay is compensated by using an auxiliary signal. All the virtual controllers and the actual controller are designed as the optimised solution of the corresponding subsystems to ensure the entire obtained controllers are optimised. To ensure that the states of the system are constrained within some given compact sets, the barrier Lyapunov function (BLF) is used to design the controller and perform stability analysis. Meanwhile, this paper adds a self-triggered mechanism to reduce the communication burden of the data transfer. Thus, the proposed control strategy can achieve optimised control and all system states can be constrained within the given ranges. On the other hand, all closed-loop signals of system are bounded in probability. Finally, it is demonstrated that the proposed control strategy can achieve the expected system performance by a simulation experiment. [ABSTRACT FROM AUTHOR]

This paper studies the global regulation problem by a non-predictor event-triggered controller for high-order feedforward nonlinear systems with unknown time-varying delays in the states and input. We propose a non-predictor-based event-triggered controller with a dynamic gain-scaling factor, in which any information on the delays is not required in controller design. The dynamic gain-scaling factor is utilised to deal with high-order terms so that the considered class of systems are generalised over the previous results. The simulation results effectively demonstrate the validity of our proposed control method. [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]

Single-link flexible-joint manipulator (FJM) is a kind of time-varying nonlinear system with underactuated characteristics. This paper takes the uncertain single-link FJM (USLFJM) as the object, and presents a novel robust control approach based on equivalent input disturbance (EID) method for motion control (i.e., position control and trajectory tracking control) of the USLFJM. Based on the uncertain dynamic model and desired target of this system, an error system is constructed. The error system is considered as a linear system with a nonlinear virtual disturbance. The motion control objective of the USLFJM can be realized by globally asymptotically stabilizing this linear system and compensating the influence of the nonlinear virtual disturbance. Then, an EID-based control system is designed to realize this control objective. Only position measurements are utilized in this paper, and the stability of the control system is proved. The simulation results are presented to illustrate the validity and the robustness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of the estimation of non-uniformly nonlinear systems with time-varying delays in the state and input. In addition, the problem of the sampled output measurement is also been addressed. Thus, an observer design for a class of uncertain, non-uniformly nonlinear systems in the presence of time-varying delay is proposed. A continuous–discrete observer based on a high-gain approach is designed to achieve undelayed estimation. Thus, sufficient conditions to ensure the convergence of the observer are obtained. The analysis is based on a Lyapunov–Krasovskii functional, which shows that the bounded observation error depends on the sizes of the known upper delay and the upper sampling rate. The performance of the proposed algorithm is evaluated by considering a control-based observer for a two-degrees-of-freedom helicopter system with a known time-varying delay and sampled output measurements. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of stabilization of nonlinear fractional order time-delay systems in the presence of fault. A general class of nonlinear fractional order systems is considered in which fault causes variations in the system dynamic and actuators. Besides, time-varying delay is noticed in the system equations that is of high importance in control of real-life systems. In order to facilitate the problem of controller design for such systems, a precise method for modeling complex nonlinear systems, namely, Takagi–Sugeno fuzzy model, is adopted. Regarding a Caputo derivative–based Lyapunov–Krasovskii functional, new delay-dependent stabilization conditions are established in the form of linear matrix inequalities. Eventually, two examples including a truck–trailer and Lorenz system are simulated in order to evaluate the results of this research work. [ABSTRACT FROM AUTHOR]

The adaptive predefined settling time performance tracking control for a class of uncertain nonlinear network systems with fast time-varying or even abrupt reference signals is studied. In this paper, an improved performance function with time-varying boundary (following the change of reference signal) is designed to overcome the problem that the traditional prescribed performance control (PPC) can only converge to a constant in steady state. Compared with the existing adaptive finite time prescribed performance congestion control for tracking fixed value reference signals, an adaptive predefined settling time prescribed performance congestion control strategy is proposed by means of some new recursive construction (introducing nonautonomous differential equations (NDE)) and analysis innovation. In addition, the network system considered in this paper is more general. Under the framework of backstepping, NDE is used iteratively to control the approximation error with boundary inequality. It is proved theoretically that all signals of the closed-loop system are predefined settling time bounded. Finally, the effectiveness of the proposed control strategy is verified by simulations. [ABSTRACT FROM AUTHOR]

To promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, nonlinear model predictive control (MPC) is applied to realize trajectory tracking of mobile robots. Specifically, to alleviate the online computational complexity of nonlinear MPC, this paper devises a lattice piecewise affine (PWA) approximation method that can approximate both the nonlinear system and control law of explicit nonlinear MPC. The kinematic model of the mobile robot is successively linearized along the trajectory to obtain a linear time‐varying description of the system, which is then expressed using a lattice PWA model. Subsequently, the nonlinear MPC problem can be transformed into a series of linear MPC problems. Furthermore, to reduce the complexity of online calculation of multiple linear MPC problems, the optimal solution of the linear MPCs is approximated by using the lattice PWA models. That is, for different sampling states, the optimal control inputs are obtained offline, and lattice PWA approximations are constructed for the state control pairs. Simulations are performed to evaluate the performance of the method in comparison with the state‐of‐the‐art methods, and the results show that the method has a higher online computing speed and can decrease the offline computing time without significantly increasing the tracking error. [ABSTRACT FROM AUTHOR]

This paper examines the boundary stabilisation results for time fractional-order reaction-diffusion systems involving with time-varying delays. The main goal is to design the boundary control for the system by proving the well-posedness of the kernel function using the backstepping method. An invertible Volterra integral transformation is used to convert the considered system into a stable target system. Different from the existing results, the stability results for fractional RDEs are discussed in the sense of the Lyapunov–Krasovskii theory and sufficient conditions are derived with the help of the linear matrix inequality (LMI) approach. Finally, to show the application of the results, the proposed conditions are numerically validated over a time fractional-order reaction-diffusion cellular neural network model. [ABSTRACT FROM AUTHOR]

This paper discusses the multi-player non-cooperative game of nonlinear stochastic time-varying systems described by Itô-type differential equations in a finite time interval. Multi-player non-cooperative game problems are represented by multi-objective Pareto (MOP) control problems to describe the fact that each player has their own goals. By applying Hamilton–Jacobi inequalities (HJIs), the criterion of upper bounds of the MOP boundary is obtained for nonlinear stochastic systems, and the corresponding strategies are designed for such games, so the MOP problem is transformed into a HJI-constrained MOP problem. In order to overcome the difficulty of solving HJIs, a global linearization method is proposed to approximate the nonlinear systems. By the proposed global linearization method, multi-player non-cooperative game problems are transformed into Riccati equation-constrained MOP problems, and the approximate solutions of HJI-constrained MOP problems are obtained. Finally, a practical example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Purpose: Considering the unmeasurable states of the systems and the previewed reference signal, a novel fuzzy observer-based preview controller, which is a mixed controller of the fuzzy observer-based controller, fuzzy integrator and preview controller, is considered to address the tracking control problem. Design/methodology/approach: The authors employ an augmentation technique to construct an augmented error system for uncertain T-S fuzzy discrete-time systems with time-varying uncertainties. Additionally, the authors obtain the corresponding linear matrix inequality (LMI) conditions for designing the preview controller. Findings: This paper discusses the preview tracking problem for nonlinear systems. First, considering the unmeasurable states of the systems and the previewed reference signal, a novel fuzzy observer-based preview controller, which is a mixed controller of the fuzzy observer-based controller, fuzzy integrator, and preview controller, is considered to address the tracking control problem. Then, using the fuzzy Lyapunov functional with the linear matrix inequality (LMI) technique, new sufficient conditions for the asymptotic stability of the augmented system are derived by applying the LMI technique. The preview controller and fuzzy observer can be designed in one step. Finally, a numerical example is used to illustrate the effectiveness of the results. Originality/value: An augmented error system is successfully constructed by the state augmentation approach. A novel preview controller is designed to address the tracking control problem. The preview controller and fuzzy observer can be designed in one step. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive robust control problem based on reinforcement learning for an affine nonlinear system with unknown time‐varying uncertainty. Inspired by the ability to estimate uncertainty of neural network, a novel policy iteration algorithm is proposed which alternates between the value evaluation, uncertainty estimation, and policy update steps until the adaptive robust control law is obtained. Especially during the step of uncertainty estimation, the unknown time‐varying uncertainty is approximated by a radial basis function neural network and introduce it into the reinforcement learning framework. By designing an appropriate utility function, the algorithm improves both convergence rate and final approximate error comparing with existing reinforcement learning algorithm. The Lyapunov stability theorem provides theoretical demonstrations of the stability and convergence. Furthermore, the uniformly ultimately bounded stability of the affine nonlinear system is demonstrated with unknown time‐varying uncertainty. Finally, the performance of the proposed algorithm is demonstrated through a torsion pendulum system. [ABSTRACT FROM AUTHOR]

Summary: In control engineering, the disturbance is a major problem that deteriorates system robustness. To address this problem, a disturbance observer (DOB) has been proposed and developed. In particular, a general method of estimating high‐order disturbance, expressed as a time series expansion, was studied (H‐DOB). However, systems to which H‐DOB are applicable are limited to those in which disturbance gain is constant. This constraint degrades the generality of H‐DOB because applicable systems are limited. Therefore, by expanding to a system with a time‐varying disturbance gain, we propose a more general H‐DOB. The DOB proposed in this paper redesigns the dynamics of the observer based on the structure of the H‐DOB. The proposed DOB is applicable even if the system is highly nonlinear. This paper verifies the convergence of the proposed DOB through proof. Using this proof, the same characteristic error dynamics can be obtained, so the same design method can be applied. The simulation for the verification of the proposed method performs disturbance estimation of the extension system. This simulation proves that, compared to H‐DOB, the proposed DOB has good disturbance estimation performance. [ABSTRACT FROM AUTHOR]

This paper studies the input-to-state stability (ISS) and the finite-time input-to-state stability issues for the discrete-time stochastic switched nonlinear systems with time-varying delay. Based on the improved vector-version comparison principle and by employing the stochastic analysis method, sufficient conditions are first derived to guarantee the discrete-time stochastic switched system to be finite-time input-to-state stable in mean and finite-time stochastic input-to-state stable. Then, the comparison principle is further utilised to establish the p-th moment ISS result. As an application, the mean-square ISS is analysed for the linear discrete-time stochastic switched system. At the end of the paper, two numerical examples are provided to illustrate the feasibility/effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed cubature Kalman filtering (DCKF) for a class of discrete time‐varying nonlinear systems subject to stochastic communication protocol (SCP). In order to avoid the data collisions, the SCP is introduced to randomly schedule each sensor node information from one of the neighboring nodes to the filter which is presented via not only the information of itself sensor but also the information of neighboring sensors. The considered scheduling probability of the selected node is unknown. Therefore, the exact filtering error covariance is not available. The purpose of this paper is to design a DCKF under the spherical–radial cubature rule such that an upper bound of the filtering error covariance is guaranteed by utilizing fundamental inequality. Such an upper bound is dependent on known upper and lower bounds of the scheduling probabilities. Subsequently, the desired filter matrices are given by minimizing the upper bound of the filtering error. A sufficient condition is derived by using Riccati‐like difference equations method. Besides, a recursive form of filter algorithm is designed for online computation. Finally, the usefulness of the DCKF is verified by utilizing a simulation example on the induction machines. [ABSTRACT FROM AUTHOR]

In this paper, input-to-state stability (ISS) is investigated for a class of nonlinear switched systems with time-varying switching delay, in which both ISS and non-ISS subsystems are considered simultaneously. By means of the Lyapunov function method, we show that ISS can be ensured for switched systems with time-varying switching delay if the activation time of ISS subsystems is sufficiently large and switching delays satisfy certain conditions. Moreover, inspired by (Zhang et al. 2020), a time-dependent multiple Lyapunov function is considered for linear switched systems with switching delay to obtain less conservative results, where the conservativeness can be reduced by explicitly providing the lower and upper bounds of switching intervals. Finally, simulations including an example of coordination of multiagent systems are offered to verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper discusses an Event-Triggered (ET) control of nonlinear system with time-varying parameters. Based on the modeling technology, polynomial Takagi–Sugeno (T–S) fuzzy model is applied to represent the nonlinearity. By virtue of Linear Parameter Variation (LPV) model, the parameter depended on time can be modeled by combining the weighting function and linear systems. With the modeling technology and LPV description, the polynomial T–S fuzzy model is built to interpret the considered system. For the stabilization problem, fuzzy controller is constructed via the polynomial gains with time-varying parameters. Moreover, the ET scheme is applied for building a fuzzy controller saving the control cost. For the stabilization problem, a criterion is proposed and Sum of Squares (SOS) algorithm is utilized to find solutions. Finally, some simulations are provided for show the applicability of this paper. [ABSTRACT FROM AUTHOR]

Based on a new constructive solution of a couple of matrix inequalities containing an unknown time-varying parameter, this paper proposes a novel dual-gain scaling approach including a dynamic-gain observer and an output feedback controller with static and dynamic gains. In particular, our control approach is applicable to a class of nonlinear time-delay systems with nonlinear growth constraint and large unknown measurement sensitivity that may be non-differentiable. With the help of the Razuminkhin theorem, it is shown that the global adaptive stability of the resulting closed-loop system is achieved and our controller is robust to arbitrary bounded time-varying delay. In addition, the control approach proposed is non-backstepping and has low computing complexity. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of adaptive tracking control for a class of stochastic nonlinear systems with time-varying input delays, and the nonlinear functions of the systems are with not only the unknown parameters but also the unknown state time-varying delays, which is different from the previous work. In this paper, through a state transformation, the system can be easily transformed into a system without the time-varying input delay; the appropriate Lyapunov–Krasovskii functionals are used to compensate the unknown time-varying delay terms, and the quadratic functions instead of the quartic functions often utilized in the existing results are used as Lyapunov functions to analyze the stability of systems and the hyperbolic tangent functions are introduced to deal with the Hessian terms. Fuzzy logic systems (FLSs) in Mamdani type are used to approximate the unknown nonlinear functions. Then, based on the backstepping technique, the adaptive fuzzy controller is designed. The three main advantages of the developed scheme are that (i) unlike the existing results which deal with the nonlinearly parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS; (ii) the number of the adjusted parameters only depend on the order of the investigated systems, which can reduce the computational burden greatly; and (iii) the existence of the time-varying input delay such that the controller design becomes much more difficult, and in this paper, it can be dealt with by using an appropriate state transformation. It is proven that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded in probability, whereas the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The problem of observer‐based finite‐time event‐triggered H∞ control for nonlinear uncertain switched systems is investigated in this paper. An observer‐based event‐triggered controller is constructed using a state observer. The event‐triggering updating strategies for the control law are designed. The multiple Lyapunov–Krasovskii functional and average dwell time technique are utilized to derive some sufficient conditions that guarantee the switched system is observer‐based event‐triggered H∞ finite‐time stabilizable. We give the observer gain and controller gain. At the end of this paper is a numerical example that illustrates the effectiveness and advantages of the proposed approaches. [ABSTRACT FROM AUTHOR]

The paper concentrates on the issue of distributed disturbance observer-based nonfragile bipartite consensus within nonlinear delayed multiagent systems, encompassing both leaderless and leader-following structures. The delays under consideration are nonuniform, manifesting in the state, the nonlinearity, and the communication processes. To suppress the external disturbances and the observer gain perturbations, distributed nonfragile disturbance observers pertaining to relative output and communication delays are developed to estimate the external disturbances for each agent. Employing the developed disturbance observer, distributed control protocols for nonfragile bipartite consensus are constructed incorporating states, estimated disturbances, and communication delays. These protocols can ensure bipartite consensus, compensate for external disturbances, and tolerate uncertainties in control gain. New augmented Lyapunov-Krasovskii functions are formulated by introducing the triple integral term and the augmented vector. The new bipartite consensus criteria for the studied multiagent systems are established with less conservatism by employing the techniques on second-order Bessel-Legendre integral inequality, reciprocally convex combination, and free weight matrix. Finally, numerical simulations and comparisons are performed for both leaderless and leader-following scenarios, thereby validating and enhancing the theoretical outcomes. • Multiagent systems with nonlinearity, disturbance and multiple delay, is considered. • Both cooperative and antagonistic relationships are all considered in consensus. • The perturbations in both observer and bipartite consensus protocol. • New Lyapunov-Krasovskii functions, and Bessel-Legendre inequality are employed. [ABSTRACT FROM AUTHOR]

This paper investigates a tracking control issue for a class of time-varying output constrained nonlinear systems subject to non-affine nonlinear faults and virtual control coefficients. In the controller design process, the nonlinear function is approximated by fuzzy logic systems. Utilizing a feasible function to convert the system, a new transformation strategy is proposed to handle the system with time-varying output constraints or without output constraints. The mean value theorem is applied to split non-affine faults, and the Nussbaum-type function is used to eliminate the effect of the unknown directional affine variable gain of input resulted from non-affine faults. Combined with adaptive fuzzy backstepping technology and the error transformation function, a new control strategy is presented, which not only deals with the time-varying output constraint but also handles non-affine faults, effectively. Finally, all closed-loop system signals are bounded, and the tracking error can converge to a small preset set. Two simulations are performed to confirm the validity of the presented strategy. • Nonlinear transformation functions are adapted to systems with or without output constraints. • Tracking error can converge to a small adjustable set and maintain within a prescribed range. • Updating estimates of virtual control coefficient online reduces system limitations. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive fuzzy tracking controller for uncertain strict-feedback nonlinear systems suffering from asymmetric time-varying state constraints, unmeasured states, and unknown external disturbances. Firstly, a state observer with a simplified structure is constructed to approximate the unavailable system states based on fuzzy logic systems. The difficulties caused by time-varying state constraints are effectively addressed in a direct approach via the nonlinear state-dependent functions. Compared to the classical barrier Lyapunov functions-based (BLFs-based) method, the strict condition imposed on the virtual controller is eliminated, which significantly enhances the applicability of the controller in practical systems. Meanwhile, to handle the issue of "explosion of complexity," a novel adaptive fuzzy tracking control technique is proposed by using the sliding-mode differentiator. Finally, rigorous stability analysis is employed to verify that the error between the system output signal and the reference signal can converge to an arbitrarily small set around the origin, and all closed-loop signals are bounded without time-varying state constraints violation. The effectiveness of the theoretical result is further illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, fixed-time stability (FxTS) of time-varying (TV) hybrid systems with time-delay (TD) is investigated. Starting with TV nonlinear systems with TD, some sufficient conditions are given to verify the FxTS of systems by using TV Lyapunov–Krasovskii functional and integral technique. Then, the obtained results are extended to the case of hybrid systems, several FxTS conditions are provided by using the multiple TV Lyapunov–Krasovskii functional and the function-dependent minimum dwell time technique. Comparing with the existing results, the obtained results can provide the more accurate estimation of the convergence time of systems, and can be applied to a wider class of systems. Finally, two numerical examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates variable‐gain PD‐type iterative learning control (ILC) for a class of nonlinear time‐varying systems to well balance high‐gain convergence rate and low‐gain noise transmission. Different from the classic PD‐type ILC, the control gains of the proposed method are variable. Each variable‐gain consists of an amplitude‐dependent term and an iteration‐varying term. The amplitude‐dependent terms vary with the amplitudes of tracking error and derivative of tracking error, and the iteration‐varying terms are increasing along the iteration axis. The proposed ILC achieves a faster convergence rate than low‐gain ILC and higher tracking accuracy with limited noise amplification than high‐gain ILC. Moreover, the convergence condition of the proposed method in the presence of external noise is provided. Simulation and experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite‐time stability (FTS) and H∞$$ {H}_{\infty } $$ control of nonlinear Hamiltonian systems with time‐varying state delays and output delays subject to input saturation. By introducing a new class of Lyapunov–Krasovskii (L‐K) functionals and the assumption about the Hamiltonian function, we present a delay‐dependent FTS criterion. Then, a finite‐time H∞$$ {H}_{\infty } $$ feedback control is designed for the nonlinear Hamiltonian systems. Finally, the validity of the proposed results is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper presents an alternative adaptive parameter estimation framework for nonlinear systems with time-varying parameters. Unlike existing techniques that rely on the polynomial approximation of time-varying parameters, the proposed method can directly estimate the unknown time-varying parameters. Moreover, this paper proposes several new adaptive laws driven by the derived information of parameter estimation errors, which achieve faster convergence rate than conventional gradient descent algorithms. In particular, the exponential error convergence can be rigorously proved under the well-recognized persistent excitation condition. The robustness of the developed adaptive estimation schemes against bounded disturbances is also studied. Comparative simulation results reveal that the proposed approaches can achieve better estimation performance than several other estimation algorithms. Finally, the proposed parameter estimation methods are verified by conducting experiments based on a roto-magnet plant. [ABSTRACT FROM AUTHOR]

This paper is concerned with the output tracking control problem for random nonlinear systems with time-varying powers. A distinct feature of this paper is that we consider time-varying powers and the second-order moment process simultaneously, which is more practical in real applications than the existing results where only one factor is considered. We propose a new design scheme, which ensures that the fourth moment of the tracking error can be adjusted to be arbitrarily small and all the states of the closed-loop system are bounded in probability. Finally, a numerical simulation is given to demonstrate the feasibility of the control idea. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive control of a class of time-varying nonlinear systems. Under the framework of Immersion and Invariance (I&I) adaptive control, a set of sufficient conditions is obtained to stabilize the concerned time-varying nonlinear systems. It is shown that the presented controller can also be utilized to complete tracking control for a class of nonholonomic constraint systems if the desired trajectories satisfy certain conditions. The effectiveness of the new adaptive controller is demonstrated by some numerical simulations on a nonholonomic mobile robot. [ABSTRACT FROM AUTHOR]

In this paper, two iterative learning control (ILC) approaches based on a neural iterative learning identifier (NILI) are proposed for a class of unknown time‐varying nonlinear systems. Since both control and identification processes are done at the common iteration domain, so both tracking performance and identification performance are improved at each iteration simultaneously. A class of neural networks is proposed as iterative learning identifier. The proposed NILI is time varying because the system is time varying. An auxiliary error function is used in new iterative updating laws of the proposed NILI. First, P‐type ILC with iteration‐varying learning gain based on the NILI is proposed and applied to the system. Then, a new ILC based on the NILI is proposed and applied to the system. In comparison with other ILC algorithms proposed for similar systems, the proposed algorithm in this paper has more accurate performance and takes less amount of time and memory. Also, the new proposed NILI‐based ILC can be successfully applied to the system with iteration‐varying initial condition. Theoretical analysis of the trajectory convergence both tracking and identification errors is fully done. Finally, the effectiveness of the proposed algorithms is verified through some simulation case studies. [ABSTRACT FROM AUTHOR]

For a class of stochastic nonlinear systems in pure-feedback form with dead-zone input and multiple time-varying delays, a novel neural network (NN)-based adaptive control approach is presented in this paper through the use of backstepping approach and dynamic surface technique. By choosing proper Lyapunov–Krasovskii functionals, utilizing the characteristic of hyperbolic tangent functions and adopting the function separation technique, difficulties of controller design that introduced by the time-varying delays can be dealt with properly. Moreover, all unknown nonlinear functions are lumped together and approximated by the NN. Additionally, any information over the boundedness of dead-zone parameters is not needed in the process of controller design. The control scheme proposed in this paper ensures the boundedness in probability of all signals in the closed-loop system, besides, excellent performance of arbitrarily small tracking error will be achieved by selecting control parameters appropriately. At last, two numerical simulation examples are provided to verify the validity of the designed algorithm. [ABSTRACT FROM AUTHOR]

Summary: The finite‐time input‐to‐state stability (FTISS) of stochastic impulsive time‐varying nonlinear systems is investigated in this paper. Different from the previous works concerning FTISS, we allow the coefficients of the estimated upper bound for the diffusion operator of a Lyapunov function to be time‐varying. Moreover, a relaxed relation between the impulsive frequency is provided. Leveraging the Lyapunov method along with Lambert W function and average impulsive interval (AII) method, the input‐to‐state (ISS) property is obtained within finite time. Furthermore, two examples are provided to verify the validity of the conclusion. [ABSTRACT FROM AUTHOR]

This paper addresses the H ∞ filters design problem for delayed nonlinear systems subject to L 2 − norm disturbances via Takagi-Sugeno (T-S) fuzzy approach with interval time-varying delay. An appropriate Lyapunov-Krasovskii functional (LKF) is established in the framework of augmented system. Then, on the basis of the free-weighting matrix technique and convex method, some improved integral inequality are employed and combined with a decoupling approach without ignoring any useful terms. Therefore, less conservative delay dependent conditions are obtained in terms of linear matrix inequality (LMIs), wish can be solved by using the Matlab LMI toolbox, to achieve the desired H ∞ performance. Finally, three numerical examples are given to demonstrate the advantages and the effectiveness of the obtained results, compared with some previous method in the literature. [ABSTRACT FROM AUTHOR]

This paper is devoted to work out a stabilized controller by state feedback for a class of nonlinear systems. In this paper, we not only extend the existing results that system has a single power term to the case with multiple coupling power terms, but also consider that the power is time varying, which makes the system studied in this paper more general than that in other literature. By the backstepping method, a linear easy-to-implement controller is designed, which not only ensures the stability of the system but also has a good convergence speed. Finally, with a representative numerical example, by calculating all the parameters in the design procedure, the simulation shows that all the responses of the states and the controller are asymptotically stable at the equilibrium zero, which verifies the effectiveness of the control design scheme of this paper. [ABSTRACT FROM AUTHOR]

The double-holding water tank system is a common non-linear control system that plays a crucial role in process control in the chemical industry. It consists of two cylindrical glass containers: the preset tank and the main tank. The main challenge in controlling this system is adjusting the main control valve to ensure that the actual liquid level of the main tank tracks the desired liquid level. This paper explores the zeroing dynamics (ZD) method and its application in tracking control. A non-linear model is developed for the double-holding water tank system, and the ZD method is used to design an effective controller (called the ZD controller) for tracking control. Additionally, the robustness of the double-holding water tank system in the presence of time-varying perturbations is investigated. In order to substantiate the effectiveness and robustness of the ZD controller, simulation experiments on four different tracking trajectories corresponding to four different practical situations, as well as an extra simulation experiment considering time-varying perturbations, are conducted. Furthermore, a comparative simulation experiment based on the backstepping method is conducted. The presented results successfully illustrate the feasibility and effectiveness of the ZD method for the tracking control of double-holding water tank systems. [ABSTRACT FROM AUTHOR]

In a thermal plant, the combustion system of the coal-fired boiler is a nonlinear time-varying system, which leads to undesired responses, if traditional proportional-integral-derivative controllers are utilized. Internal process delay is an important characteristic of the steam pressure in the boiler of coal-fired power plants, which affects the closed-loop dynamics. To compensate for this significant delay and reach the desired performance, a novel control strategy based on a combination of an optimal fractional-order proportional-integral-derivative (OFOPID) controller with a Smith predictor (SP) structure is suggested in this paper that achieves the desired control performance required for the optimal operation of the boiler. The simulation results of a coal-fired power plant boiler with the power of 300 MW show that the performance is improved considerably by having lower overshoot and lower rise and settling times, as well as a lower mean square error during the operation of the power plant Boiler. [ABSTRACT FROM AUTHOR]

This paper is concerned with the adaptive tracking control problem of nonlinear time-varying systems. Based on the backstepping technology, an event-based prescribed performance control scheme is developed. And the time-varying uncertainties of the system are handled by utilising bound estimation method. The proposed controller not only ensures the prescribed tracking performance, but also reduces the communication burden. By using Lyapunov stability analysis, it is proven that all of the closed-loop signals are bounded, and the tracking error can converge to zero. Simultaneously, Zeno behaviour is excluded. Finally, the simulation results are utilised to illustrate the effectiveness of the proposed adaptive control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the networked set-membership state estimation is discussed for a class of nonlinear discrete time-varying systems subject to cyber attacks and time delays. Two forms of malicious attacks (i.e. Denial-of-Service (DoS) attack and bias injection attack) are taken into account to describe the adversary's attempt to destroy/deteriorate the system performance via communication network. It is the aim of the investigated issue to propose a set-membership state estimator ensuring the required estimation performance despite the existence of both the external mixed attacks and internal time delays. By resorting to the feasibility of a series of matrix inequalities, sufficient conditions are provided for the solvability of the addressed state estimator design problem. Furthermore, an optimisation strategy is developed with the purpose of seeking the local optimal estimator parameters. At last, a numerical simulation example is presented to demonstrate the effectiveness of the proposed theoretical algorithm. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of event-triggered control for a class of nonlinear systems with unknown control coefficients, time-varying delays, full state constraints and external disturbances, simultaneously. Firstly, based on integral Barrier-Lyapunov Functionals, an adaptive event-triggered controller is designed to account for the impacts of complete state constraints, unknown time-varying delays and external disturbances. Using fuzzy logic systems, the unknown functions of systems are then roughly estimated. The system redundancy can be significantly reduced by implementing the event-triggered control technique in the meanwhile. By introducing the separation technique and Lyapunov–Krasovskii functionals, it is shown that the strategy can ensure tracking performance greatly and all the closed-loop signals of the system are bounded. Compared with the existing results, the proposed design scheme is less conservative and has a wilder application range. Finally, the simulation results show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates adaptive finite-time stabilisation for a class of output-constrained low-order nonlinear systems with unknown time-varying powers, parametric and dynamic uncertainties. Due to low-order nonlinear systems being merely continuous but not smooth, and the presence of time-varying powers and multiple unknowns, all the existing control methods of output-constrained nonlinear systems are inapplicable. By characterising unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), applying finite-time stability theory and introducing the tan-type barrier Lyapunov function, low-power and high-power terms into control design, a unified adaptive state-feedback controller, which can deal with both constrained and unconstrained systems, is constructed. It is proved that all the closed-loop signals are uniformly bounded, the output constraint is not violated, and system states converge to zero in a finite time. Finally, a simulation example is given to illustrate the effectiveness of this control scheme. [ABSTRACT FROM AUTHOR]

This paper integrates extended state observer into sliding mode controller for better transient and steady-state performance and robustness against nonlinearity, uncertainty, and time-varying disturbance. The design process of the proposed controller is composed of two main stages. Firstly, all the nonlinearity, uncertainty, and time-varying disturbance of the system are considered as the total disturbance, which is estimated by a designed high-order extended state observer (HESO). Secondly, by integrating the sliding mode control into the HESO, the composite controller is formed. Benefits from HESO's disturbance estimation and online compensation, the problem of chattering is substantially alleviated. Thanks to the sliding mode term, the closed-loop system will converge to the reference even under severe disturbances. The numerical and experimental results for a calibration-free robotic hand-eye coordination system indicate the effectiveness and robustness of the proposed approach. [ABSTRACT FROM AUTHOR]

In terms of system modeling, random differential equations (RDEs) with colored noise are demonstrated to be more appropriate than stochastic differential equations (SDEs) relating to white noise in most practical situations. This paper discusses a category of nonlinear random systems involving time‐varying delay and exogenous disturbances. The definitions for noise‐to‐state practically stable (NSPS) and noise‐to‐state practically exponentially mean‐square stable (NSPEMS) are first given. An event‐based controller is then constructed to render the closed‐loop system NSPEMS and circumvents the Zeno behavior at the same time. Since the introduction of event‐triggered mechanism endows the closed‐loop system with hybrid behaviors, event‐based control for RDE systems still remains difficult to deal with. Within our cognitive scope, this paper serves as a pioneering attempt for event‐based control of RDE systems. And the validity of the results is corroborated by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust $H_{\infty }$ control for a class of nonlinear systems with state and input time-varying delays. The nonlinearity is presented by a continuous-time Takagi-Sugeno (T-S) fuzzy model with parameter uncertainties. A sufficient asymptotic stability condition is first proposed by constructing a delay-product-type augmented Lyapunov–Krasovskii functional and utilizing an extended reciprocally convex matrix inequality together with a Wirtinger-based integral inequality. Then, a state feedback controller is derived that guarantees the closed-loop fuzzy system being asymptotically stable with an $H_{\infty }$ performance index. Finally, four numerical examples are given to reveal the effectiveness and merits of the developed new design techniques. [ABSTRACT FROM AUTHOR]

This paper studies the global stabilisation of a class of partial-state feedback nonlinear systems with time-varying delay. By adopting the dynamic gain-based design method and backstepping technique, a state-feedback controller is constructed with the help of appropriate Lyapunov–Krasovskii functional. It is proved that all the measurable states of the closed-loop systems converge to the origin, and a simulation example is given to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]