Iteration Axis Research Articles

Iterative Learning Consensus Control for Nonlinear Partial Difference Multiagent Systems with Time Delay

This paper considers the consensus control problem of nonlinear spatial-temporal hyperbolic partial difference multiagent systems and parabolic partial difference multiagent systems with time delay. Based on the system’s own fixed topology and the method of generating the desired trajectory by introducing virtual leader, using the consensus tracking error between the agent and the virtual leader agent and neighbor agents in the last iteration, an iterative learning algorithm is proposed. The sufficient condition for the system consensus error to converge along the iterative axis is given. When the iterative learning number k approaches infinity, the consensus error in the sense of the L 2 norm between all agents in the system will converge to zero. Furthermore, simulation results illustrate the effectiveness of the algorithm.

Adaptive boundary iterative learning vibration control using disturbance observers for a rigid–flexible manipulator system with distributed disturbances and input constraints

In this article, an adaptive boundary iterative learning vibration control is developed for a class of the rigid–flexible manipulator system under distributed disturbances and input constraints. With the help of the virtual work principle, the dynamics of the rigid–flexible manipulator are modeled and described by coupled ordinary differential equations and partial differential equations. Based on the original infinite dimension system model, three compounded adaptive boundary iterative learning vibration control laws are constructed with disturbance observers and adaptive vibration laws, aiming to track the desired joint angular positions and achieve vibration suppression simultaneously. Three disturbance observers are proposed to determine the upper bounded approximation of the unknown external disturbances. Hyperbolic tangent and saturation functions are incorporated into adaptive vibration laws to handle input constraints. It is proved by Lyapunov–Krasovskii-like composite energy functions that elastic vibrations and tracking errors can asymptotically converge to zero along the iteration axis. Finally, the efficacy of the developed adaptive boundary iterative learning vibration control approach is illustrated by the simulation results under distributed disturbances and input constraints.

Open-loop and closed-loop Dα-type iterative learning control for fractional-order linear multi-agent systems with state-delays

This study focuses on implementing consensus tracking using both open-loop and closed-loop Dα-type iterative learning control (ILC) schemes, for fractional-order multi-agent systems (FOMASs) with state-delays. The desired trajectory is constructed by introducing a virtual leader, and the fixed communication topology is considered and only a subset of followers can access the desired trajectory. For each control scheme, one controller is designed for one agent individually. According to the tracking error between the agent and the virtual leader, and the tracking errors between the agent and neighboring agents during the last iteration (for open-loop scheme) or the current running (for closed-loop scheme), each controller continuously corrects the last control law by a combination of communication weights in the topology to obtain the ideal control law. Through the rigorous analysis, sufficient conditions for both control schemes are established to ensure that all agents can achieve the asymptotically consistent output along the iteration axis within a finite-time interval. Sufficient numerical simulation results demonstrate the effectiveness of the control schemes, and provide some meaningful comparison results.

Iterative Learning Consensus Tracking for Multi-Agent Systems With Output Constraints and Data Losses

In this paper, the consensus tracking problem for nonlinear multi-agent systems subjected to the output constraint, data loss and switching topologies is considered. Firstly, a consensus term is defined based on the communication information in present of the nonlinear output saturation and time-varying switching topologies. Since the random data loss is taken into consideration, the consensus term is redesigned by an introducing stochastic variable, which obeys the Bernoulli sequence with known probability. Then, a novel distributed ILC algorithm is designed by using the incomplete communication data of agents, which is more universal than the results without considered nonlinear constraint and random factors simultaneously. Through the contraction mapping method, an obtained convergence condition can also guarantee the asymptotic convergence of the agent along the iteration axis under nonlinear saturation factor and random factors. It is verified that the proposed algorithm can handle more complex situations in the consensus control of multi-agent systems. Simulation examples are further provided to verify the effectiveness of the proposed algorithm.

Consensus Control via Iterative Learning for Singular Multi-Agent Systems With Switching Topologies

For the state consensus tracking of the singular multi-agent system, under the condition of the communication topology randomly switching only along time axis but unchanging along iteration axis, a distributed iterative learning control protocol is proposed. By singular value decomposition method, the singular multi-agent system is transformed into differential algebra system, and thus the state of the system is accordingly divided into two parts. Then applying the derivative of the tracking error for the first part of the state and the tracking error of the second part of the state and combining the switching topology graph, the distributed iterative learning control protocol is constructed. Furthermore, the convergence of the proposed algorithm is proved by the compression mapping method, and the convergence conditions of the algorithm are obtained. The proposed algorithm can make the state gradually approach the desired state with the increase of iterations. When the number of iterations is sufficient large, the state of each agent can completely track the desired state over a finite time interval. Finally, the simulation examples are given to further validate the effectiveness of the proposed algorithm.

Iterative Learning Control for Switched Systems with Sensor Saturation Constraints

To solve trajectory tracking problem of switched system with sensor saturation, an iterative learning control algorithm is proposed. The method uses actual measurement error to modify the control variable of system on the premise that switched rule does not change along iteration axis, but it randomly changes along time axis. Moreover, by dealing with the saturation via diagonal matrix method, the convergence of the algorithm is strictly proved in the sense of λ‐norm, and the convergence condition is derived. The algorithm can achieve complete tracking of desired trajectory in the finite time interval under the random switched rule, as iterations increase. The simulation example verifies the validity of the proposed algorithm.

Distributed formation control for multiple non-holonomic wheeled mobile robots with velocity constraint by using improved data-driven iterative learning

In this paper, a distributed proportional-integral data-driven iterative learning control (PI-DDILC) algorithm is developed to achieve the formation problem for non-holonomic and velocity constrained wheeled mobile robots (WMRs) under repeatable operation environment. Firstly, the formation problem is transformed into a tracking problem with a certain deviation from the reference trajectory. And a distributed kinematics control algorithm is designed by using leader-follower strategy and graph theory. Then, to solve the problem of unknown dynamic model, the relationship between WMR’s output and input is first derived by utilizing the iteration-domain dynamical linearization technique. After that, the improved data-driven iterative learning dynamics control algorithm is provided, which includes both proportional and integral terms along the iteration axis. This algorithm can ensure a group of WMRs to realize formation and only use I/O data of each WMR. Compared with DDILC, PI-DDILC can significantly enhance the response speed and transient performance of WMR system formation. The excellence of the improved algorithm is certified by simulation, and a performance index is designed to quantify the results of the two on formation performance.

Event-triggered Iterative Learning Control for Perfect Consensus Tracking of Non-identical Fractional Order Multi-agent Systems

This paper is devoted to the perfect tracking problem of output consensus for a class of non-identical fractional order multi-agent systems (NIFOMASs), in which different agents have different and unknown factional orders and dynamic functions. For the NIFOMASs including one leader agent and multiple follower agents, by designing the event-triggered mechanism along an iteration axis and introducing it into the iterative learning controller, an event-triggered iterative learning consensus protocol is proposed to reduce the number of controller update and to save the communication resource. By analyzing the convergence of learning process, the sufficient conditions are derived to guarantee that the output consensus tracking can be perfectly achieved over the finite time interval as the iteration step goes to infinity. Finally, three numerical examples are presented to demonstrate the effectiveness and wide application scope of the proposed control strategy.

Data-Driven Robust Iterative Learning Consensus Tracking Control for MIMO Multiagent Systems Under Fixed and Iteration-Switching Topologies

In the study, a MIMO model-free-adaptive-iterative-learning-control-based (MFAILC-based) consensus tracking scheme for multiagent systems (MASs) has been proposed. The dynamics of agents are heterogeneous and unknown. And the compact form dynamic linearization (CFDL) technique is utilized to describe the unknown nonlinear dynamics of agents along iteration axis. Then, the MIMO MFAILC-based consensus tracking algorithm is proposed for MASs under fixed topology. From the proof, we can obtain that the consensus tracking error can converge to zero along iteration axis asymptotically. Next, the MFAILC-based consensus tracking algorithm is extended to controlling the MASs under iteration-switching topologies and the MASs with external disturbances, respectively. Compared with prior work, the main features of this article are the MFAILC-based consensus strategy can be utilized for MIMO MASs, and the framework of robust MFAILC is built for MIMO MASs with external disturbances. Finally, three simulations are given to verify the effectiveness of the consensus strategy for MASs under fixed and switching topology and MASs with external disturbances, respectively.

Iterative learning control using faded measurements without system information: a gradient estimation approach

This paper studies iterative learning control (ILC) using faded measurements without system information. The measurements are transmitted through fading channels, where the fading phenomenon is modelled by a multiplicative random variable. The system matrices are assumed unknown a priori and a random difference technique is applied to estimate the gradient using the available tracking data. An online ILC algorithm is established with strict convergence analysis along the iteration axis, followed by practical variants and discussions. The generated input sequence is proved to converge to the desired one in the almost sure sense. Illustrative simulations are presented to verify the theoretical results.

Learning Tracking Control Over Unknown Fading Channels Without System Information.

A novel data-driven learning control scheme is proposed for unknown systems with unknown fading sensor channels. The fading randomness is modeled by multiplicative and additive random variables subject to certain unknown distributions. In this scheme, we propose an error transmission mode and an iterative gradient estimation method. Unlike the conventional transmission mode where the output is directly transmitted back to the controller, in the error transmission mode, we send the desired reference to the plant such that tracking errors can be calculated locally and then transmitted back through the fading channel. Using the faded tracking error data only, the gradient for updating input is iteratively estimated by a random difference technique along the iteration axis. This gradient acts as the updating term of the control signal; therefore, information on the system and the fading channel is no longer required. The proposed scheme is proved effective in tracking the desired reference under random fading communication environments. Theoretical results are verified by simulations.

High‐order internal model‐based iterative learning control design for nonlinear distributed parameter systems

SummaryThis article deals with the problem of iterative learning control algorithm for a class of nonlinear parabolic distributed parameter systems (DPSs) with iteration‐varying desired trajectories. Here, the variation of the desired trajectories in the iteration domain is described by a high‐order internal model. According to the characteristics of the systems, the high‐order internal model‐based P‐type learning algorithm is constructed for such nonlinear DPSs, and furthermore, the corresponding convergence theorem of the presented algorithm is established. It is shown that the output trajectory can converge to the desired trajectory in the sense of (L2,λ)‐norm along the iteration axis within arbitrarily small error. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Model-Free Iterative Learning Control With Nonrepetitive Trajectories for Second-Order MIMO Nonlinear Systems—Application to a Delta Robot

A model-free iterative learning control strategy (ILC) in nonrepetitive trajectories, applied to robotic manipulators is presented in this article. The development of this ILC controller is derived in general case for second-order nonlinear multi-input multi-output (MIMO) systems subjected to external disturbances. Unlike most of the ILC implementations in the literature, which considers both the resetting condition and periodic trajectories; the proposed ILC controller is model-free and works under the practical alignment condition and noncyclic desired trajectories. Furthermore, these trajectories may vary in magnitude and in the starting and terminal points. The Lyapunov stability approach is combined with a time scale transformation to synthesize the control law. The asymptotic convergence of both the position and velocity tracking errors are demonstrated along the iteration axis. Finally, experimental results in pick and place operations of a parallel Delta robot are presented and discussed. These results are very effective and clearly point out the high potential of the developed model-free ILC technique for industrial robotic applications.

Fast data-driven iterative event-triggered control for nonlinear networked discrete systems with data dropouts and sensor saturation

The tracking control problem is investigated for a class of nonlinear networked discrete systems with random data-dropout and sensor saturation, and a novel data-driven iterative learning event-triggered control scheme is proposed. First, a new model is established to describe random data-dropout processes. Then, the fixed threshold iterative learning control scheme based on randomly received saturated output data is designed to track the desired trajectory and reduce the update number of iterations. Further, in order to obtain a faster convergence or learning speed, a novel method based on varying parameter along iteration axis is given. In the end, the resulting closed-loop system is proved to be stable and the relationship between the upper bound of the consecutive data-dropout number and system stability is revealed. Complete simulations are exploited to verify theoretical results.

Cooperative Adaptive Iterative Learning Fault-Tolerant Control Scheme for Multiple Subway Trains.

In this article, a cooperative adaptive iterative learning fault-tolerant control (CAILFTC) algorithm with the radial basis function neural network (RBFNN) is proposed for multiple subway trains subject to the time-iteration-dependent actuator faults by using the multiple-point-mass dynamics model. First, an RBFNN is utilized to cope with the unknown nonlinearity of the subway train system. Next, a composite energy function (CEF) technique is applied to obtain the convergence property of the presented CAILFTC, which can guarantee that all train speed tracking errors are asymptotic convergence along the iteration axis; meanwhile, the headway distances of neighboring subway trains are kept in a safety range. Finally, the effectiveness of theoretical studies is verified through a subway train simulation.

Data driven model free adaptive iterative learning perimeter control for large-scale urban road networks

Most perimeter control methods in literature are the model-based schemes designing the controller based on the available accurate macroscopic fundamental diagram (MFD) function with well known techniques of modern control methods. However, accurate modeling of the traffic flow system is hard and time-consuming. On the other hand, macroscopic traffic flow patterns show heavily similarity between days, and data from past days might enable improving the performance of the perimeter controller. Motivated by this observation, a model free adaptive iterative learning perimeter control (MFAILPC) scheme is proposed in this paper. The three features of this method are: (1) No dynamical model is required in the controller design by virtue of dynamic linearization data modeling technique, i.e., it is a data-driven method, (2) the perimeter controller performance will improve iteratively with the help of the repetitive operation pattern of the traffic system, (3) the learning gain is tuned adaptively along the iterative axis. The effectiveness of the proposed scheme is tested comparing with various control methods for a multi-region traffic network considering modeling errors, measurement noise, demand variations, and time-changing MFDs. Simulation results show that the proposed MFAILPC presents a great potential and is more resilient against errors than the standard perimeter control methods such as model predictive control, proportional-integral control, etc.

Adaptive Iterative Learning Control for Subway Trains Using Multiple-Point-Mass Dynamic Model Under Speed Constraint

In this paper, a new adaptive iterative learning control method (AILC) is presented for speed and position tracking of a subway train using multiple-point-mass dynamic model. A composite energy function technique is utilized to obtain the asymptotic convergence of tracking error in the iteration axis for the proposed controller for subway trains. Then a speed constraint adaptive iterative learning control algorithm (CAILC) is designed to avoid over speed, derailment and collision of the subway train for the subway train over-speed protection. Finally, two simulation examples are given for the subway train system to show the effectiveness of theoretical studies.

Robust model‐free adaptive iterative learning formation for unknown heterogeneous non‐linear multi‐agent systems

The formation problem for a class of non-linear multi-agent systems (MASs) is considered under bounded disturbance and repetitive environment. The agent dynamics here is unknown and heterogeneous, and the disturbances are both time-varying and iteration-varying. Based on a novel disturbance-related dynamic linearisation technique, the agent dynamics is first transformed into an equivalent dynamic linearisation data model along the iteration axis. Then, distributed robust model-free adaptive iterative learning protocols are designed to drive the agents to the desired formation pattern. By theoretic analysis, the formation tracking error of the MASs is ultimately bounded and the result is further extended to an iteration-varying topology and pattern case. As a data-driven method, the protocol design has the feature that only the input and output data of neighbouring agents are used. Finally, numerical examples are presented to show the effectiveness and robustness of this method.

Enhancing Accuracy and Numerical Stability for Repetitive Time-Varying System Identification: An Iterative Learning Approach

Time-varying system identification is an appealing but challenging research area. Existing identification algorithms are usually subject to either low estimation accuracy or bad numerical stability. These deficiencies motivate the development of an iterative learning identification algorithm in this paper. Three distinguished features of the proposed method result in the achievement of high estimation accuracy and high numerical stability: i) recursion along the iteration axis, ii) bias compensation, and iii) singular value decomposition (SVD). Firstly, an extra iteration axis associated with the original time axis is introduced in the parameter estimation process. A norm-optimal identification approach with the balance between convergence speed and noise robustness is then proposed along the iteration axis, followed by further analysis on the accuracy and the numerical stability. Secondly, in order to eliminate the estimation bias in the presence of noise and thus to improve the accuracy, a bias compensation algorithm along the iteration axis is proposed. Thirdly, a SVD-based update algorithm for the covariance matrix is developed to avoid the possible numerical instability during iterations. Numerical examples are finally provided to validate the algorithm and confirm its effectiveness.

Data Driven Distributed Bipartite Consensus Tracking for Nonlinear Multiagent Systems via Iterative Learning Control

This article explores a data-driven distributed bipartite consensus tracking (DBCT) problem for discrete-time multi-agent systems (MASs) with coopetition networks under repeatable operations. To solve this problem, a time-varying linearization model along the iteration axis is first established by using the measurement input and output (I/O) data of agents. Then a data-driven distributed bipartite consensus iterative learning control (DBCILC) algorithm is proposed considering both fixed and switching topologies. Compared with existing bipartite consensus, the main characteristic is to construct the proposed control protocol without requiring any explicit or implicit information of MASs' mathematical model. The difference from existing iterative learning control (ILC) approaches is that both the cooperative interactions and antagonistic interactions, and time-varying switching topologies are considered. Furthermore, through rigorous theoretical analysis, the proposed DBCILC approach can guarantee the bipartite consensus reducing tracking errors in the limited iteration steps. Moreover, although not all agents can receive information from the virtual leader directly, the proposed distributed scheme can maintain the performance and reduce the costs of communication. The results of three examples further illustrate the correctness, effectiveness, and applicability of the proposed algorithm.