P-type iterative learning control algorithm for a class of linear singular impulsive systems

This paper is focused on the iterative learning control problem for linear singular impulsive systems. For the purpose of tracking the desired output trajectory, a P-type iterative learning control algorithm is investigated for such system. Based on the fundamental property of singular impulsive systems and the restricted equivalent transformation theory of singular systems, the convergence conditions of the tracking errors for the system are obtained in the sense of λ norm. Finally, the validation of the algorithm is confirmed by a numerical example.     

Event-triggered control for nonlinear systems involving hybrid impulses

In this paper, we apply event-triggered control to nonlinear systems with impulses, and investigate the problem of ensuring globally exponential stability (GES) of the systems, where events and impulses may occur at different time. Moreover, two types of impulses (i.e., stabilizing and destabilizing) can coexist. On the basis of Lyapunov method and impulsive control theory, some sufficient conditions ensuring GES are derived, and the Zeno behaviour can be excluded. These conditions are presented in the form of linear matrix inequalities (LMI). In particular, inspired by average dwell-time methods, conditions for restriction of impulses are proposed, which guarantee GES of nonlinear systems involving single stabilizing and destabilizing or multiple impulses, respectively. Furthermore, the problem of designing event-triggered mechanism and control gains are solved by using LMI method. Lastly, two numerical simulation examples are given to represent the effectiveness of our results.     

Discrete Razumikhin-type stability theorems for stochastic discrete-time delay systems

By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined.     

GIMC architecture for linear systems with a single I/O delay

A new feedback controller architecture is presented for linear systems with a single I/O delay in the generalized internal model control (GIMC) framework. According to the doubly coprime factorization of these systems, traditional GIMC strategy is extended to linear systems with a single I/O delay. The distinguished feature of the control system architecture is that high tracking performance and good external disturbance rejection could be done separately by a nominal Smith predictor part and a finite dimensional conditional controller. First, a nominal Smith predictor part could be designed to deal with command tracking performance. Second, according to the left coprime factorization of the nominal controller, a finite dimensional conditional controller could be considered for external disturbance rejection, when the controlled plant should be assumed to be a square one. Finally, a simple design example is illustrated the effectiveness of the presented method.Finally, a simple design example is illustrated the effectiveness of the presented method.     

Data-driven ILC algorithms using AFD in frequency domain for unknown linear discrete-time systems

In conventional PID-type iterative learning control (ILC) designs, to determine the learning control gains involved, relevant model knowledge on the controlled systems is often dependent. In this paper, two completely data-driven ILC laws, the extended PD-type ILC law and the extended P-type ILC law, are designed in frequency domain for linear discrete-time (LDT) single-input single-output (SISO) systems. The designs of the proposed ILC laws are based on the approximation/identification to unknown transfer function with a novel adaptive Fourier decomposition (AFD) technique. As a result, the strictly monotonic convergence of ILC tracking error is guaranteed in a deterministic way. A numerical example on a four-axis robot arm is performed to illustrate the effectiveness of the proposed data-driven ILC algorithms     

Kernel recursive generalized mixed norm algorithm

This work studies the problem of kernel adaptive filtering (KAF) for nonlinear signal processing under non-Gaussian noise environments. A new KAF algorithm, called kernel recursive generalized mixed norm (KRGMN), is derived by minimizing the generalized mixed norm (GMN) cost instead of the well-known mean square error (MSE). A single error norm such as l_p error norm can be used as a cost function in KAF to deal with non-Gaussian noises but it may exhibit slow convergence speed and poor misadjustments in some situations. To improve the convergence performance, the GMN cost is formed as a convex mixture of l_p and l_q norms to increase the convergence rate and substantially reduce the steady-state errors. The proposed KRGMN algorithm can solve efficiently the problems such as nonlinear channel equalization and system identification in non-Gaussian noises. Simulation results confirm the desirable performance of the new algorithm.     

Robust H∞ control of an observer-based repetitive-control system

This paper concerns the problem of designing a robust observer-based modified repetitive-control system with a prescribed H_∞ disturbance rejection level for a class of strictly proper linear plants with unknown aperiodic disturbances and time-varying structural uncertainties. A correction to the amount of the delay in the repetitive controller is introduced that leads to a significant improvement in tracking performance. An integrated performance index is defined to quantify the overall effect of rejecting the aperiodic disturbances and tracking the periodic reference input. A Lyapunov functional with two tuning parameters is used to derive a linear-matrix-inequality based robust stability condition for the system with a prescribed disturbance-rejection bound. Combining the performance indices, an optimization algorithm that searches for the best combination of state-observer gain and the feedback control gains is developed. A numerical example illustrates the design procedure and demonstrates the effectiveness of the method.     

Adaptive iterative learning control for MIMO nonlinear systems performing iteration-varying tasks

The present work aims to develop a novel adaptive iterative learning control(AILC) method for nonlinear multiple input multiple output (MIMO) systems that execute various control missions with iteration-varying magnitude-time scales. In order to reduce the variations of the systems, this work proposes a series of time scaling transformations to normalize the iteration-varying trial lengths. An AILC scheme is then developed for the transformed control systems on a uniform trial length, which is shown to be capable of ensuring the asymptotic convergence of the tracking error. In other words, the proposed AILC algorithm is able to relax the constraint in conventional ILC where the control task must remain the same in the iteration domain. Additionally, the basic assumption in classic ILC that the control system must repeat on a fixed finite period is also removed. The convergence analysis of the AILC is derived rigorously according to the composite energy function (CEF) methodology. It is shown that the newly developed learning control strategy works well for control plants with either time-invariant or time-varying parametric uncertainties. To show the effectiveness of the AILC, three examples are illustrated in the end. Meanwhile, the proposed learning method is also implemented to a traditional X–Y table system.     

Tracking policies for a class of dynamic production-inventory systems

In this paper, new results are established for generating tracking policies in aggregated production-inventory systems. A dynamic model is developed to characterize the evolution of targeted production, inventory and demand over time and incorporates the inventory, production and demand tracking errors as additional variables. The control variables are managerial decision variables on rate of production and advertisement. The developed model takes the form of linear system with time-varying delay. Tracking policies are then formulated and determined to ensure that the production-inventory tracking model achieves a desirable performance in terms of H_∞-measure. Numerical simulation is performed to illustrate the theoretical developments.     

pth Moment exponential stability of impulsive stochastic functional differential equations and application to control problems of NNs

This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained.     

Fixed-time stability of dynamical systems with impulsive effects

The present article is concerned with the fixed-time stability(FxTS) analysis of the nonlinear dynamical systems with impulsive effects. The novel criteria have been derived to achieve stability of the non-autonomous dynamical system in fixed-time under the effects of stabilizing and destabilizing impulses. The fixed time stability analysis due to the presence of destabilizing impulses in dynamical system, that leads to behavior of perturbing the systems’ stability, have not been addressed much in the existing literature. Therefore, two theorems are constructed here, for stabilizing and destabilizing impulses separately, to estimate the fixed-time convergence precisely by using the concept of Lyapunov functional and average impulsive interval. The theoretical derivation shows that the estimated fixed-time in this study is less conservative and more accurate as compared to the existing FxTS theorems. Further, the theoretical results are applied to the impulsive control of general neural network systems. Finally, two numerical examples are given to validate the effectiveness of the theoretical results.     

Adaptive unit-vector control of an uncertain heat diffusion process

This paper deals with the distributed tracking control of a heat process having uncertain diffusivity and subject to a distributed disturbance whose L₂ norm is bounded by a constant which is not known a priori. Under certain regularity assumptions on the disturbance and on the chosen reference profile, a distributed unit-vector control, with an adaptive magnitude, is designed which provides the asymptotic tracking of the reference. The logic governing the gain adaptation is gradient-based and monodirectional, i.e. the gain cannot decrease over time. Lyapunov arguments are invoked to support the convergence properties of the proposed scheme, whose performance are also investigated by means of computer simulations.     

Fraction dynamic-surface-based adaptive neural finite-time control for stochastic nonlinear systems subject to unknown control directions,time-varying input delay and state delay

In this paper, an adaptive neural finite-time tracking control is studied for a category of stochastic nonlinearly parameterized systems with multiple unknown control directions, time-varying input delay, and time-varying state delay. To this end, a novel criterion of semi-globally finite-time stability in probability (SGFSP) is proposed, in the sense of Lyapunov, for stochastic nonlinear systems with multiple unknown control directions. Secondly, a novel auxiliary system with finite-time convergence is presented to cope with the time-varying input delay, the appropriate Lyapunov Krasovskii functionals are utilized to compensate for the time-varying state delay, Nussbaum functions are exploited to identify multiple unknown control directions, and the neural networks (NNs) are applied to approximate the unknown functions of nonlinear parameters. Thirdly, the fraction dynamic surface control (FDSC) technique is embedded in the process of designing the controller, which not only the “explosion of complexity” problems are successfully avoided in traditional backstepping methods but also the command filter convergence can be obtained within a finite time to lead greatly improved for the response speed of command filter. Meanwhile, the error compensation mechanism is established to eliminate the errors of the command filter. Then, based on the proposed novel criterion, all closed-loop signals of the considered systems are SGPFS under the designed controller, and the tracking error can drive to a small neighborhood of the origin in a finite time. In the end, three simulation examples are applied to demonstrate the validity of the control method.     

Adaptive iterative learning control for nonlinear pure-feedback systems with initial state error based on fuzzy approximation

In this paper, an iterative learning control strategy is presented for a class of nonlinear pure-feedback systems with initial state error using fuzzy logic system. The proposed control scheme utilizes fuzzy logic systems to learn the behavior of the unknown plant dynamics. Filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the existing controllers. Backstepping design technique is applied to deal with system dynamics. Based on the Lyapunov-like synthesis, we show that all signals in the closed-loop system remain bounded over a pre-specified time interval [0,T]. There even exist initial state errors, the norm of tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity and the learning speed can be easily improved if the learning gain is large enough. A time-varying boundary layer is introduced to solve the problem of initial state error. A typical series is introduced in order to deal with the unknown bound of the approximation errors. Finally, two simulation examples show the feasibility and effectiveness of the approach.     

Robust stability and stabilization of fractional order interval systems with coupling relationships: The 0<α<1 case

In this paper we consider a class of fractional order linear time invariant (FO-LTI) interval systems with linear coupling relationships among the fractional order, the system matrix and the input matrix. We present the sufficient conditions for the robust stability and stabilization of such coupling FO-LTI interval systems with the fractional order α satisfying 0<α<1. All the results are proposed in terms of linear matrix inequalities (LMI). Two numerical examples show that our results are effective for checking the robust asymptotical stability and designing the stabilizing controller for FO-LTI interval systems.     

Iterative learning control for fractional-order multi-agent systems

In this paper, we apply iterative learning control to both linear and nonlinear fractional-order multi-agent systems to solve consensus tacking problem. Both fixed and iteration-varying communicating graphs are addressed in this paper. For linear systems, a PD^α-type update law with initial state learning mechanism is introduced by virtue of the memory property of fractional-order derivative. For nonlinear systems, a D^α-type update law with forgetting factor and initial state learning is designed. Sufficient conditions for both linear and nonlinear systems are established to guarantee all agents achieving the asymptotic output consensus. Simulation examples are provided to verify the proposed schemes.     

Stability and L2-gain analysis of switched input delay systems with unstable modes under asynchronous switching

We consider the stability and L₂-gain analysis problem for a class of switched linear systems. We study the effects of the presences of input delay and switched delay in the feedback channels of the switched linear systems with an external disturbance. By contrast with the most of the contributions available in literatures, we do not require that all the modes of the switched system are stable when input delay appears in the feedback input. By reaching a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and permitting the increasing of the multiple Lyapunov functionals on all the switching times, the solvable conditions of exponential stability and weighted L₂-gain are developed for the switched system under mode-dependent average dwell time scheme (MDADT). Finally, numerical examples are given to illustrate the effectiveness of the proposed theory.     

Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays

This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results.