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This paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete‐time nonlinear systems subject to nonlinear (maybe non‐convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination‐flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence‐guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution; (ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time; and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed‐loop system. We conduct simulation experiments on multi‐agent formation control with non‐convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we develop an online learning algorithm for solving the Bellman equation for affine in the control discrete‐time nonlinear uncertain dynamical systems. To ensure accelerated learning of our algorithm in generating optimal control policies, we use an actor‐critic structure predicated on higher‐order tuner laws. More specifically, we construct a Nesterov‐like architecture involving momentum‐based learning laws leading to an accelerated convergence of the optimal control policy. The proposed online learning‐based optimal control framework guarantees uniform ultimate boundedness of the closed‐loop system under the assumption that the system is persistently excited. Finally, two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

Data-driven learning of the fractional discrete-time unified system is studied in this paper. A neural network method is suggested in the parameter estimation of fractional discrete-time chaotic systems. An optimization problem is obtained and the famous Adam algorithm is employed to train the neural network's weights and parameters. The parameter estimation result is compared with that of the stepwise response sensitivity approach (SRSA). This paper provides a high accuracy method for parameter inverse problems. The method also can be applied to data-driven learning of other fractional chaotic systems. [ABSTRACT FROM AUTHOR]

Summary: This study proposes a novel iterative learning control scheme for discrete‐time linear systems based on the Broyden‐class optimization method. To overcome the difficulty of lacking system information, a cost function is introduced for the performance index by constructing a positive‐definite matrix with little system information. An optimization‐based learning control algorithm is proposed using a Hessian matrix approximation and the generated input sequence is demonstrated to exhibit a superlinear convergence rate. The proposed scheme is extended to address the point‐to‐point tracking problem. Numerical simulations are provided to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article develops a novel framework for iterative learning control (ILC) design of discrete‐time systems with non‐uniform trial lengths by using the method of alternating projections. In contrast to existing results for the non‐uniform trial length problem, this article uses the Hilbert space setting and hence the linear discrete‐time system dynamics with non‐uniform trial lengths can be represented by multiple affine subspaces (or linear varieties). Motivated by the successive projection design between two closed convex sets, the considered ILC problem can be transformed into alternating projections between multiple sets, then the Hilbert space setting is used to establish key systems theoretic properties. Moreover, an optimal ILC design is developed for systems with non‐uniform trial lengths, which is also extended to the case of input constraints. A numerical case study is given to illustrate the applicability of the new design. [ABSTRACT FROM AUTHOR]

In this work, we propose the construction of discrete‐time systems with two time scales in which infectious diseases dynamics are involved. We deal with two general situations. In the first, we consider that individuals affected by the disease move between generalized sites on a faster time scale than the dynamics of the disease itself. The second situation includes the dynamics of the disease acting faster together with another slower general process. Once the models have been built, conditions are established so that the analysis of the asymptotic behavior of their solutions can be carried out through reduced models. This is done using known reduction results for discrete‐time systems with two time scales. These results are applied in the analysis of two new models. The first of them illustrates the first proposed situation, being the local dynamics of the SIS‐type disease. Conditions are found for the eradication or global endemicity of the disease. In the second model, a case of co‐infection with a primary disease and an opportunistic disease is treated, the latter acting faster than the former. Conditions for eradication and endemicity of co‐infection are proposed. [ABSTRACT FROM AUTHOR]

In this work, a novel adaptive event‐trigered iterative learning control (ILC) scheme is designed for discrete‐time nonlinear systems with time‐varying parameters and random initial states. The reference trajectory can be iteration‐invariant or iteration‐varying. The control input is updated when the event‐triggering condition is satisfied, which reduces the action time of controller and consequently the unnecessary waste of communication resource. An adaptive event‐triggering condition parameter is designed to improve the efficiency of the event generator. Moreover, the parameter updating law of adaptive iterative learning controller is designed based on the recursive least squares algorithm. With the proposed adaptive ILC with event‐triggered mechanism, the learning convergence along the iteration axis is guaranteed and communication burden is reduced. Finally, rigorous theoretical analysis under Lyapunov theory and illustrative examples are given to demonstrate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on an iterative learning fault-tolerant control strategy for discrete-time affine nonlinear systems where actuator faults arbitrarily occur. First of all, the actuator fault is decomposed into multiplicative model and additive one. Then, the behaviors of both the faults-corrupted control signals from the actuator to the systems and the faults-free ones from the iterative learning controller to the actuator are analyzed from the statistical point of view. Meanwhile, sufficient conditions of convergence are derived by resorting to norm. Last, in order to verify the effectiveness and reliability of the proposed results, numerical experiments are carried out. Both theoretical analysis and simulations illustrate that the developed strategy is satisfactory in maintaining decent tracking accuracy of the controlled systems, even though faults randomly occur in actuator [ABSTRACT FROM AUTHOR]

In this paper, a high-order model-free adaptive iterative learning control (HOMFAILC) scheme is proposed for nonlinear non-affine discrete-time systems. The main feature of the proposed HOMFAILC is that not only the control input iterative learning law is designed with higher-order algorithms but also the parameter iterative adaptive updating law has the similar forms. Using additional control knowledge in both the iterative learning control law and the parameter estimation law, the control performance of the proposed HOMFAILC can be improved consequently. Furthermore, the similar structure in the control law and parameter updating law can also help to achieve a better control performance. The convergence is proved with rigorous mathematical analysis. Simulation study shows the effectiveness of the proposed HOMFAILC. [ABSTRACT FROM AUTHOR]

In this work, the problems of predictive compensation, unknown nonlinearity, and nonaffine structure are considered simultaneously for a quantized iterative learning control (QILC) design and analysis under a data‐driven framework. The compensation strategy can avoid deteriorated data transmission quality owing to limited channel capacities. First, a dynamic linearization methodology is employed to transform the nonlinear plant into a virtual iterative linear data model (iLDM) which includes all the input signals over a time‐window from the initial time instant to the current one. The iLDM is also used as a predictive model to estimate the unavailable information caused by the encoding–decoding mechanism. Then, a predictive compensation‐based QILC is proposed by optimizing quadratic functions, which includes an output prediction mechanism, a quantized iterative learning updating law, a quantized iterative parameter estimation law, and a resetting algorithm. The result is also extended to a class of MIMO nonlinear nonaffine discrete‐time systems. The developed control laws are data‐driven and independent of any system information. The theoretical results are proved by the use of contraction mapping principle and induction method. Examples are provided to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The second-order ILC algorithm is studied for a class of linear discrete-time switched systems with model uncertainties, external noises and the time-delay for tracking reference trajectory by taking advantage of super-vector representation. This study is based on the assumption that the systems operate under finite intervals. A sufficient condition for convergence of the algorithms is deduced when the model uncertainties and external noises are absent. Then the convergence is analysed, when the model uncertainties are present but the external noises are absent and the robustness against the bounded external noises is discussed. The analysis manifests that the second-order ILC algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily present switching rules when they are imposed on the system. We have presented a simulation example to illustrate effectiveness of the proposed second-order ILC algorithm in the study of robustness of the considered SISO linear discrete time-invariant time delay switched system. [ABSTRACT FROM AUTHOR]

This article proposes a dynamic time warping (DTW)‐based iterative learning control (ILC) scheme for discrete‐time nonlinear systems to tackle the path learning problem with varying trial lengths and terminus constraint. By incorporating the improved DTW algorithm, the varying trial lengths are aligned as a desired length. Meanwhile, this algorithm can find the most similar waypoints between the output and the desired paths, which can be used to design an updating law and facilitate the convergence of path learning. Different from the existing ILC methods based on the probability distribution function for learning trajectory in the time domain, the method in this article can be applied to learn the spatial path corresponding to the desired trajectory. Furthermore, the learning property in the presence of variable initial states is discussed under the proposed method. Several illustrative examples manifest the validity of the proposed DTW‐based ILC algorithm. [ABSTRACT FROM AUTHOR]

This paper considers the learning-ability for discrete-time iterative learning control (ILC) systems with feedforward. More specifically, the relation between the output realizability and the feedforward matrix is first established. Then, the learning-ability of four ILC systems is considered. It is shown that the proportional type (P-type) update law can only ensure the fully asymptotic learning-ability. By only using the feedforward matrix, a more efficient point-wise P-type update law is developed, which can ensure the fully (T +2)-step learning-ability, where T is the trial length. In the case that the state is measurable and controllable, it is proven that the update law with current state feedback can ensure the fully monotone learning-ability and the fully 2-step learningability, respectively. In addition, by only using the output data at the previous trial, a full output feedback update law is proposed, which can respectively ensure the fully 2-step learning-ability and the fully monotonic learning-ability. [ABSTRACT FROM AUTHOR]

This paper considers a linear discrete-time system operating in a repetitive mode to track a reference trajectory with a required accuracy. The control variable has a delay along the sample trajectory, and saturation-type constraints are imposed. We introduce a new method for designing an iterative learning control law that depends on the delay and ensures the required accuracy of tracking. A numerical example demonstrates the effectiveness of this method. [ABSTRACT FROM AUTHOR]

This paper discusses the output-feedback-based model-free optimal output tracking control problem of discrete-time systems with completely unknown system models under mild assumptions. The only information that allows utilisation is the system output and the reference output. To overcome these challenges, the paper aims to solve a model-free optimal output regulation problem for achieving optimal output tracking control; solving an optimal output regulation problem is equivalent to solving a linear quadratic regulation (LQR) problem and a constrained static optimisation problem. The state reconstruction is first given to represent the system state in terms of the input and output sequences. A data-driven value iteration (VI) algorithm is then proposed to iteratively approximate the solution to the discrete-time algebraic Riccati equation (ARE) of the corresponding LQR problem on the basis of input and output data. Next, based on the iterative solutions with respect to the ARE, a model-free solution is provided for the corresponding constrained static optimisation problem. Finally, an alternative reference system equivalent to the original reference system is established to avoid the requirement of having the knowledge of the reference system dynamics and the reference state. A numerical example is employed to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The article proposes an intelligent controller for output regulation of nonlinear non-autonomous continuous-time systems with mismatched uncertainties and matched disturbances. This controller is established by firstly converting the original system into an input-to-state stable one via learning-based compensation of lumped system disturbances and then applying the standard P-type iterative learning control. The learning-based disturbance compensator is basically created with the numerical backward differentiation in iterative mode. The control performance of the obtained sampled data system using the proposed controller has been verified throughout both in theory and comparison with the existing method via numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, an iterative learning approach is proposed for the formation control of discrete‐time multi‐agent systems, where the trial length of each learning iteration is randomly varying. In particular, a modified state error related to the prescribed formation is defined by taking into account the nonuniform actual trial length that could be different from the desired one. Then, a P‐type iterative learning protocol is established for switching networks of agents subject to nonuniform trial lengths, and the convergence analyses are given for the fixed and the iteration‐varying initial conditions respectively. It shows that through iterative learning, the given formation will be maintained among multiple agents in the entire time interval of one trial. In the end, simulations are done to demonstrate the correctness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Complex dynamical networks with time-varying connections have characteristics that allow a better representation of real-world complex systems, especially interest in their not static behavior and topology. Their applications reach areas such as communication systems, electrical systems, medicine, robotic, and more. Both continuous and discrete-time complex dynamical networks and the pinning control technique have been studied. However, even with interest in the research on complex networks combining characteristics of discrete-time, time-varying connections, pinning control, and impulsive control, there are few studies reported in the literature. There are some previous studies dealing with impulsively pin-controlling a discrete-time complex network. Nevertheless, they neglect to deal with time-varying connections; they deal with these systems by experimentally using continuous-time methods or linearizing the node dynamics. In this manner, this paper presents a control scheme that not only deals with pin control on discrete-time complex networks but also includes time-varying connections. This paper proposes an impulsive pin control to a zero state using passivity degrees considering a discrete-time complex network with undirected, linear, and diffusive couplings. Additionally, a corresponding mathematical analysis, which allows the representation of the dynamics as a set of symmetric matrices, is presented. With this, certain kinds of time-varying connections can be integrated into the analysis. Moreover, a particular criterion for selecting nodes to pin is also presented. The behavior of the controller for the non-varying and time-varying coupling cases is shown via numeric simulations. [ABSTRACT FROM AUTHOR]

In this paper, the optimal tracking problem for discrete-time linear systems with multiple delays is studied without system dynamics. It is known that the total state of a system without specific dynamic characteristics is hard to be measured, unless such a system is equipped with massive sensors, which, however, may lead to an increase in cost and complexity for analysing. To deal with this problem and avoid adverse effects caused by using system state information, a new data-driven value iteration (DDVI) algorithm is proposed by considering three factors: past control inputs, system outputs, and external reference trajectories. Before the algorithm is proposed, a transformation is made to the original system according to the characteristics of the time-delay system, so that the time-delay number can be reduced or become a delay-free system. A novel data-driven state equation is derived from the historical data of the three factors, and then, it is adopted to solve the optimal control of multi-delay systems. Further results show that the proposed DDVI algorithm is convergent and the tracking error is asymptotically stable. Finally, simulations are provided to show the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

An adaptive fuzzy iterative learning control (ILC) algorithm is designed for the iterative variable reference trajectory problem of nonlinear discrete-time systems with input saturations and unknown control directions. Firstly, an adaptive fuzzy iterative learning controller is constructed by combining with the fuzzy logic system (FLS), which can compensate the loss caused by input saturation. Then, the discrete Nussbaum gain technique is adopted along the iteration axis, which can be embedded to the learning control method to identify the control direction of the system. Finally, based on the nonincreasing Lyapunov-like function, it is proven that the adaptive iterative learning controller can converge asymptotically when the number of iterations tends to infinity, and the system signals always remain bounded in the learning process. A simulation example verifies the feasibility and effectiveness of the learning control method. [ABSTRACT FROM AUTHOR]

This paper presents a new robust convergence condition of iterative learning control with initial state learning (ILC-ISL) for linear multivariable discrete-time systems in the presence of iteration-varying uncertainty. This method is based on linear matrix inequality (LMI) and provides fixed learning gains during time and iteration. Since the convergence of the ILC algorithm may change due to uncertainty in the parameters of a system, and the ILC algorithm is incapable of dealing with iteration-related challenges, it is a major challenge to reject the effect of iteration varying uncertainty. Besides, in the basic ILC algorithm, the initial state is constant in each iteration and consequently always leads to a tracking error. In this paper, first, a convergence condition of the ILC-ISL algorithm is designed based on closed-loop system stability in the iteration domain, and second, a new robust convergence condition is achieved by the LMI approach. Finally, the effectiveness of the proposed robust convergence scheme is evaluated through a numerical example and a mechanical system, respectively. [ABSTRACT FROM AUTHOR]

This paper considers a linear discrete-time system operating in a repetitive mode to track a reference trajectory with a given accuracy. The system parameters are incompletely known and are described by the affine uncertainty model. In addition, the system is subjected to random disturbances, and measurements are carried out with noise. During system operation, the reference trajectory changes after a given number of repetitions. The resulting transient error may cause a temporary loss of accuracy. We propose a new iterative learning control design method to compensate the transient error. An example illustrates the effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this article a novel data-driven iterative learning control (ILC) approach is proposed for unknown nonlinear nonaffine repetitive discrete-time systems, where the dynamic linearization (DL) technique in the iteration domain is applied both on the controlled nonlinear system and on the unknown nonlinear ideal learning controller. Through updating the weight matrix of a radial basis function neural network (RBFNN), the learning control gain of the obtained iterative learning law is automatically tuned in reaching the optimal learning controller using only the input-output data of the nonlinear system. The uniformly ultimately bounded property is established for the tracking error of the proposed ILC scheme in the iteration domain through rigorous theoretical analysis. The effectiveness and applicability are validated by a simulation example and further demonstrated by simulation on a high-speed train model. [ABSTRACT FROM AUTHOR]

In this article, an output‐feedback Q‐learning algorithm is proposed for the discrete‐time linear system to deal with the H∞$$ {H}_{\infty } $$ tracking control problem. The problem is formulated as a zero‐sum game in the Stackelberg game framework with a discount factor to make the value function bounded. According to the principle of optimality, the game algebraic Riccati equation (GARE) is derived and solved by the Q‐learning algorithm to get the optimal solution of the Stackelberg game without requiring the knowledge of system dynamics and state. It is proved that the solution of the algorithm converges to the optimal control input and the worst‐case disturbance with excitation noises during training, and the Stackelberg strategy can achieve a lower L2$$ {L}_2 $$ disturbance attenuation level than the Nash one. Moreover, the impacts of the discount factor on the stability of the closed‐loop system and solvability of the GARE are analyzed to provide some criteria for the choice of the discount factor. Simulation examples are provided to validate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This work provides a framework for data-driven control of discrete-time systems with unknown dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control such that a feasible output trajectory can be tracked. This is made possible by Hölder-continuous real-time stable learning schemes that act as discrete-time stable uncertainty observers. These observers learn from prior input-output history and ensure finite-time stable convergence of estimation errors to a bounded neighborhood of the zero vector if the system is Lipschitz-continuous with respect to time, outputs, inputs, internal parameters and states. In combination with nonlinearly stable controllers, this makes the proposed framework nonlinearly stable and robust to disturbances, model uncertainties, and unknown measurement noise. Nonlinear stability and robustness analyses of the observer and controller designs are carried out using discrete Lyapunov analysis. A numerical experiment on a second-order system demonstrates the performance of this nonlinear model-free control framework. [ABSTRACT FROM AUTHOR]

This manuscript deals with the qualitative study of certain properties of an immunogenic tumors model. Mainly, we obtain a dynamically consistent discrete-time immunogenic tumors model using a nonstandard difference scheme. The existence of fixed points and their stability are discussed. It is shown that a continuous system experiences Hopf bifurcation at one and only one positive fixed point, whereas its discrete-time counterpart experiences Neimark–Sacker bifurcation at one and only one positive fixed point. It is shown that there is no chance of period-doubling bifurcation in our discrete-time system. Additionally, numerical simulations are carried out in support of our theoretical discussion. [ABSTRACT FROM AUTHOR]

This paper is concerned with an iterative learning fault-tolerant control strategy for discrete-time nonlinear systems where actuator faults arbitrarily occur. First, the stochastic faults occurring in multiplicative and additive manner are considered. Then, statistical behaviors of both faults-corrupted control signals from the actuator to the plant and faults-free ones from the iterative learning controller to the actuator are analyzed. Meanwhile, sufficient conditions of convergence for the proposed strategy are established by resorting to the time-weighted norm technique. Finally, two numerical examples are provided to illustrate the effectiveness and reliability of the proposed results. Both theoretical analysis and simulations indicate that the developed strategy is satisfactory in preserving decent tracking accuracy of the addressed systems subject to actuator faults. [ABSTRACT FROM AUTHOR]

This paper investigates the fault estimation problem for a class of nonlinear nonrepetitive systems subject to iteration-dependent references. Firstly, based on the high-order internal model strategy, iterative learning fault estimation scheme is proposed to track the fault signals that varies with iteration index increasing. Then, the convergence of the presented method is achieved by the norm-based approach. Further, the proposed method is also extended to the uncertain systems with varying parameter matrices, discrete-time systems with Lipschitz perturbation and time-variant coefficients. Finally, the effectiveness of the proposed iterative learning fault estimation scheme is verified by numerical simulation studies. [ABSTRACT FROM AUTHOR]

Summary: Initial condition problem is crucial to a conventional iterative learning control (ILC) scheme, which steers the tracking error from arbitrary initial value to zero in the time steps equaling to the relative degree of the system undertaken. The implementation may be difficult, due to the practical limitation for the control amplitude. This paper presents an error‐tracking approach to discrete‐time adaptive ILC designs for tracking nonidentical tasks in the presence of initial repositioning errors, which may be quite large. A prototype iterative learning algorithm is derived for estimating the time‐varying unknowns, and the saturation is introduced for assuring the estimates to keep away from zero. A key technical lemma, tailored for the analysis purpose in the iteration domain, is presented and applied to analysis of the ILC scheme. The tracking performance of the closed‐loop system is evaluated and explored in detail. It is shown that the perfect tracking for the error between the tracking error and the desired error is achieved at every time instant, while the input and output signals remain bounded. By the simulation example, the proposed scheme is verified to be applicable to tracking tasks without restriction on initial repositioning. [ABSTRACT FROM AUTHOR]

We consider tracking control of an underactuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, S E (3) . We formulate a finite-time stable (FTS) tracking control scheme for this underactuated system in discrete time. This scheme is based on our recently developed theory for finite-time stability for discrete-time systems using discrete Lyapunov analysis. The proposed scheme here is developed in discrete time as it is more convenient for onboard computer implementation and ensures stability irrespective of the sampling period. This scheme guarantees a stable convergence of translational and rotational tracking errors to the desired trajectory in finite time. Furthermore, the advantages of finite-time stabilisation in discrete-time over finite-time stabilisation of a sampled continuous-time tracking control system is addressed here through a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned aerial vehicle model. [ABSTRACT FROM AUTHOR]

In this work, based on the robust iterative learning control (ILC) scheme, the finite‐iteration tracking control is investigated for discrete‐time linear systems in repetitive process setting with external disturbances. First, the concept of finite‐iteration tracking is defined. Then by utilizing the lifted‐vector‐matrix technique, the discrete‐time linear system can be reformulated as an input–output transmission equation. Moreover, a P‐type ILC scheme is employed, and then the finite‐iteration tracking of the resultant system is guaranteed with the designed iterative learning controller. Meanwhile, the settling iteration can be explicitly obtained. Particularly, the case of data loss occurred during information transmission is also studied, and sufficient conditions are presented such that the finite‐iteration tracking can be achieved in a finite interval. Lastly, the effectiveness and applicability of the presented method are validated via a numerical simulation. [ABSTRACT FROM AUTHOR]

This article considers the equivalence and convergence of two iterative learning control (ILC) schemes with state feedback for a class of multi‐input‐multi‐output discrete‐time nonlinear systems in which each desired trajectory corresponds to a unique desired input or an infinite number of desired inputs. First, we strictly prove that the two ILC schemes are equivalent if they have the identical initial system inputs. Moreover, by the input space transformation method and mathematical induction we establish the necessary and sufficient criterion for the convergence of system output, input and state sequences. It is shown that the (locally Lipschitz) continuity is enough to guarantee the (exponential) convergence. Generally, the learned desired input depends on the values of the initial signals, the learning gain matrix and the state feedback item. By designing them with appropriate structures, the dependence is disappeared. Third, we show how to leverage the available information of system dynamics to design the learning gain matrix and state feedback for better tracking performance. Finally, we provide an example to illustrate the usefulness of our findings, in which we introduce the energy of learnable desired input to evaluate the learning performance. [ABSTRACT FROM AUTHOR]

We consider the problem of optimal control of a linear time-invariant discrete-time system by inaccurate measurements of its output signals subject to guaranteed satisfaction of geometric constraints on the output signals. We study the case in which a minimal realization of the system in the state space is known and the case where the parametric model of the system is not known. A novel method is proposed for solving the problem in the case of an unknown model. The method is based on a single observed trajectory of the input and output signals of the system and allows omitting the stage of parametric identification of the system. [ABSTRACT FROM AUTHOR]

In this article, a model-free compensation learning control scheme is presented for asymmetric hysteretic systems to achieve high-precision output tracking, where the effects of asymmetric input hysteresis nonlinearities are denoted by the asymmetric Prandtl–Ishlinskii model (APIM). In the presented control scheme, the feedforward iterative learning technique is generalized to the control design of asymmetric hysteretic systems. To improve the robustness and dynamic performance of the existing feedforward learning control for hysteretic systems, both the feedback action and the differential term are utilized to design a discrete-time PD-P open-closed-loop learning control law for simultaneously compensating the asymmetric input hysteresis nonlinearities and the linear dynamics effects without constructing compensators based on their models. The initial state error of such a system is also considered, a modified initial state learning strategy is proposed to ensure the initial state error tends to a prescribed level with the increasing of iterations. By fully analyzing the properties of the APIM, the convergence conditions with respect to the input error, the state error, and the tracking error along the iteration domain are given. The simulation and experimental results are provided to demonstrate strong robustness and excellent tracking accuracy with the proposed model-free compensation learning control scheme. • The asymmetric hysteretic property analysis for the ILC design. • A modified initial state learning scheme for the reduction of initial state errors. • The convergence analysis of the tracking error for the hysteretic control system. • Successful real-time implementations and excellent tracking accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a novel neural-network iterative learning control (IL, ILC) protocol for generalized regression neural networks (GRNN) based on global space–time is proposed for a class of unknown nonlinear discrete-time systems. The proposed controller is an ideal controller with multidimensional gain based on the global space–time in the iteration domain. The control gain is automatically learned by updating the matrix of the GRNN with correction factors based on the accumulation of global system input and output (I/O) data along the iteration axis. By a rigorous theoretical analysis, properties that can drive the tracking error to be uniformly bounded in the iteration axis are established for the proposed control protocol with the goal of achieving optimal control. The effectiveness and adaptability of the proposed control protocol have been validated through numerical simulations and two comparative examples on general high-frequency signal tracking. • A novel ILC protocol for nonlinear non-affine systems is proposed via GRNN. • The proposed ILC directly constructs the input and control objectives through GRNN. • The controller is designed by the accumulation of global system I/O data along the iteration axis. • The control gain is automatically learned by updating GRNN matrix with correction factors. [ABSTRACT FROM AUTHOR]

The research objective of this paper is to address the tracking control problem of high-order discrete-time nonlinear systems in the presence of completely unknown internal uncertainties, unknown external disturbances, and unknown control input gain. To address this challenge, the paper proposes a high-order discrete-time model-free anti-disturbance tracking control method without relying on prior knowledge of system parameters. The core of the approach is the development of a data-driven concurrent learning extended state observer. The uniqueness of this observer lies in its ability to estimate unknown control input gains without the persistent excitation and ensure the convergence of the estimates. Based on the concurrent learning extended state observer, a high-order discrete-time tracking control law is designed to precisely track the reference signal, ensuring the stability of the nonlinear closed-loop system. The effectiveness of this method was verified by applying simulation verification to the heading tracking control of surface automatic vehicles. [ABSTRACT FROM AUTHOR]

This article investigates two On-policy and Off-policy Q-learning algorithms for time-varying linear discrete-time systems (DTSs) in the presence of complete dynamic uncertainties. To handle the challenge of time-varying description, the lifting method is employed to transform the original time-varying linear DTS into time-invariant linear DTS in the absence of the conventional controllability condition, which affects to the convergence of traditional Q-learning algorithms. Based on theoretical analysis of the structure in the obtained time-invariant linear DTS, On-policy and Off-policy algorithms are proposed to guarantee the convergence of Q-learning algorithms. Both On-policy and Off-policy Q-learning algorithms guarantee model-free consideration under the data collection. Especially, the Off-policy technique is able to develop the algorithm with high data efficiency because the collected data can be utilized again after each iteration. Finally, the simulation results of two-dimensional systems and spacecraft control systems are presented to validate the effectiveness of the two proposed control schemes. [ABSTRACT FROM AUTHOR]

Toward the aim of zero tracking error and user-specified convergence rate, a data-driven output tracking design for unknown linear discrete-time systems is investigated in this work. For policy learning, we customize a virtual auxiliary system, based on which an enhanced Bellman equation with the user-specified convergence rate is derived. This allows us not to explicitly measure the time for the system evolution, while only the input–output data are sufficient in our design. By utilizing the robust output regulation technique, we can learn an optimal tracker for such an auxiliary system via policy iteration and value iteration. It is proved that the output tracking error of the original discrete-time system converges to zero at the specified convergence rate. The effectiveness of the proposed algorithms is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

In this work, an adaptive iterative learning control (AILC) method is designed for a class of parametric discrete‐time nonlinear systems with random initial condition, unknown time‐varying input gain and multiple time‐iteration‐varying factors including multiple unknown time‐iteration‐varying parameters and unknown time‐iteration‐varying external disturbance. The iteration‐varying factors can be generated by virtue of multiple iteration‐varying high‐order internal models, respectively, where iteration‐varying high‐order internal model means it has iteration‐varying order or coefficients. Moreover, the parameter updating law is designed based on the recursive least squares algorithm. Using the designed AILC based on iteration‐varying high‐order internal model, the learning convergence in the iteration domain is guaranteed through rigorous theoretical analysis under Lyapunov theory. Finally, two simulation examples are given to demonstrate that the proposed scheme is effective. [ABSTRACT FROM AUTHOR]

This paper reconsiders the iterative learning control (ILC) problem for variable trial lengths via compensating output data by using an auxiliary predictive model when the controlled process does not reach the desired trial length. Moreover, this paper aims to propose a general and data-driven ILC method without requiring any explicit mechanistic model information. Specifically, an iterative difference with state transition expression is performed at first over the desired trial length in iteration domain to build an auxiliary predictive model for the iterative input–output dynamics of the linear discrete-time system. Then, an auxiliary predictive compensation-based ILC (APC-ILC) method is presented by defining an expanded output variable in which the predictive output is incorporated to compensate the unavailable output data due to the shorter operation length. The learning gain is iteration-time-varying and is updated using real-time data to adapt to system changes. Furthermore, the proposed learning control law contains additional input information to further improve the control performance. Theoretical analysis and simulations further verify the effectiveness of the proposed APC-ILC. [ABSTRACT FROM AUTHOR]

In this article, a robust networked iterative learning control (ILC) method is presented for switched nonlinear discrete-time systems (NDTS) subject to non-repetitive uncertainties and random data dropouts. In the proposed robust networked ILC scheme, the switching law, iterative initial state, and disturbances, all of which vary with iterations, are well addressed. Corresponding to the actuator side and the measurement side of the networked switched NDTS, the random data dropouts occurred are compensated by the input signals at last iteration and the reference outputs, respectively. As a result, it is theoretically proved that under the non-repetitive uncertainties of the switched NDTS, the mathematical expectation of ILC tracking error remains bounded during the ILC process. While the non-repetitive uncertainties are progressively convergent in iteration domain, a precise tracking to the reference trajectory in mathematical expectation sense can be achieved. The effectiveness of the proposed networked ILC design is validated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of asynchronous communications on stationary solutions for discrete-time multiagent systems with a fixed topology. The asynchrony in this context implies that there is no global clock to synchronize the update time in each distributed agent and also each agent updates its own state asynchronously without waiting for values received from neighboring agents. It has been noted without much attention that asynchronous stationary solutions may not be unique and disagree with a synchronous stationary value. In some applications, this discrepancy may cause serious consequences, and thus it is critical to analyze the effect of asynchrony on stationary solutions. In this paper, we develop necessary and sufficient conditions for the uniqueness of stationary solutions for discrete-time multiagent systems. In the case of nonunique stationary solutions, the normalized expected error between synchronous and asynchronous stationary solutions is also analyzed. To validate the proposed methods, we provide three example problems: 1) containment control; 2) fixed-point iteration; and 3) distributed averaging formulated in a discrete-time setting. [ABSTRACT FROM AUTHOR]

The macro traffic flow model of expressway is transformed into a general discrete-time nonlinear system model including this model by using the repeatability of the macro traffic flow model, and then a parameter identification algorithm based on iterative learning is designed for this general discrete-time nonlinear system model. The convergence of this parameter identification scheme is proved by strict theoretical derivation and robustness. Simulation results verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an extended state observer-based data-driven iterative learning control [extended state observer (ESO)-based DDILC] is developed for a permanent magnet linear motor (PMLM). The PMLM is formulated mathematically by using a general nonlinear discrete-time system with consideration of exogenous disturbances. Then, a new iterative dynamic linearization (IDL) is proposed to equivalently reformulate the nonlinear PMLM system with a linear input–output incremental form involving iteration-varying initial states and disturbances. The concept of ESO is introduced into iteration direction to iteratively estimate the random initial states and disturbances as well as their corresponding partial derivatives by considering all of them as a whole extended state. The proposed ESO-based DDILC scheme contains a learning control algorithm and a gradient parameter updating algorithm obtained from two distinct objective functions, respectively. Moreover, the proposed method is data-driven and no explicit model is involved. Theoretical analysis shows the robustness of the proposed method in the presence of iteration-varying initial shifts and disturbances. The simulation on PMLM is conducted to confirm the validity and applicability of the ESO-based DDILC. [ABSTRACT FROM AUTHOR]

This paper investigates the convergence characteristics of the conventional P-type iterative learning control (ILC) scheme and exploits a gain-adaptive iterative learning control mechanism for a class of linear discrete-time singular systems. Based on the lifted vector technique, the paper reforms the discrete-time singular system as a kind of algebraic input-output transmission. For the conventional P-type ILC scheme, the asymptotical convergence in terms of the tracking-error vector is achieved and the monotonic convergence in the sense of 2-norm of the tracking-error vector is derived. Further, in order to improve the learning performance, a gain-adaptive iterative learning control (GAILC) strategy is developed, which argues the iteration-time-variable gain vector while minimising the increment of quadratic tracking-error vectors of two adjacent iterations. The existence of the optimal gain vector is explored through the optimisation criterion and the algebraic approach of the columns/ rows exchanging transformation of matrix. Then the non-conditionally strictly monotonic convergence of the GAILC is made by studying the eigenvalues of the quadratic function. Finally, the validity and the effectiveness of the P-type ILC are numerically demonstrated and the remarkable outcomes of the GAILC are illustrated. [ABSTRACT FROM AUTHOR]

This paper proposes a neural network-based (NN-based) data-driven iterative learning control (ILC) algorithm for the tracking problem of nonlinear single-input single-output (SISO) discrete-time systems with unknown models and repetitive tasks. The control objective is to make the output of the system track the reference trajectory in each iteration process. Therefore, at each relative time during every iteration process, a generalized regression neural network (GRNN) is used as the estimator to solve the key parameters of the system, and a radial basis function neural network (RBFNN) is used as the controller to solve the control input. Compared with the traditional ILC algorithm, the two complex solving processes, i.e., dynamic linearization and criterion function minimization, are replaced and simplified into the iterative training of GRNNs and RBFNNs. The proposed algorithm is out-of-the-box and uses a point-to-point method to calculate the control input for each relative time of the system iteration, driving the tracking error of the system to approach zero. In addition, it is proved that the tracking error of the system under the proposed control algorithm is uniformly ultimately bounded. Finally, a numerical example shows the effectiveness and superiority of the control algorithm, and a path tracking experiment of an unmanned vehicle further verifies its practicability. • A novel neural network-based iterative learning control algorithm is proposed. • GRNNs are designed as the estimators to solve the key parameters of the system. • RBFNNs are developed as the controllers to solve the control input. • The convergence of tracking error under the proposed algorithm is proved. [ABSTRACT FROM AUTHOR]

This note considers the problem whether we can design a time-varying learning gain to ensure the monotone convergence of system output tracking errors (SOTEs) in the sense of unweighted 1/2/ ∞ -norm for iterative learning control systems. Firstly, it points that the iterative learning control update law with the exponentially decaying learning factor considered in Moore et al. (2005) cannot ensure the monotonic convergence of SOTEs in the sense of unweighted 1-norm, 2-norm or ∞ -norm. Secondly, it is strictly proven that there exists a time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted ∞ -norm and there is no time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted 1-norm. Finally, this paper presents a sufficient condition under which there exists a time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted 2-norm. [ABSTRACT FROM AUTHOR]

The existing frequency-domain-based iterative learning control (ILC) methods are highly dependent on the mathematical models of the controlled systems. For linear discrete-time single-input single-output (SISO) systems with unknown mathematical models, this paper tries to present fully data-driven ILC designs in frequency domain. With the help of support vector machine (SVM), the input-output data of the linear discrete-time SISO system at the first repetition is utilised to constitute an adaptive Fourier decomposition (AFD) model. Then, based on the AFD model, a P-type ILC law and an extended D-type ILC law with data-driven determining techniques for learning gains are presented. It is noted that comparing with the conventional D-type ILC law, the newly proposed extended D-type ILC law exhibits superior tracking characteristic due to involving the frequency information during the ILC process. A numerical example is utilised to illustrate the effectiveness of the proposed ILC algorithms with the data-driven determining techniques for learning gains. [ABSTRACT FROM AUTHOR]

Discrete-time linear systems with switching in the repetitive mode are considered. The systems are subjected to random disturbances, and the measurements are corrupted by additive noises. Two iterative learning control design methods are proposed. Both of the methods involve an auxiliary 2D model in the form of a discrete repetitive process. The first method is based on the dissipativity conditions established for the auxiliary model with a special choice of the supply rate and storage function. This choice allows finding a control law (in the general case, nonlinear) that ensures the convergence of the learning process. The second method adopts a linear iterative learning control update law of a given form, while the convergence of the learning process is ensured by the stability conditions of the auxiliary 2D model. The structure of both control laws includes a stationary Kalman filter. The stability conditions are obtained using the divergent method of vector Lyapunov functions. An example is given to demonstrate the capabilities and features of the new method. [ABSTRACT FROM AUTHOR]

For systems that can only be locally stabilized, control laws and their effective regions are both important. In this paper, invariant policy iteration is proposed to solve the optimal control of discrete-time systems. At each iteration, a given policy is evaluated in its invariantly admissible region, and a new policy and a new region are updated for the next iteration. Theoretical analysis shows the method is regionally convergent to the optimal value and the optimal policy. Combined with sum-of-squares polynomials, the method is able to achieve the near-optimal control of a class of discrete-time systems. An invariant adaptive dynamic programming algorithm is developed to extend the method to scenarios where system dynamics is not available. Online data are utilized to learn the near-optimal policy and the invariantly admissible region. Simulated experiments verify the effectiveness of our method. [ABSTRACT FROM AUTHOR]