Iteration Domain Research Articles

Distributed Iterative Learning Control of Nonlinear Multiagent Systems Using Controller-Based Dynamic Linearization Method.

When applied to the consensus tracking of repetitive leader-follower multiagent systems (MASs), most of existing distributed iterative learning control (DILC) methods assume that the dynamics of agents are exactly known or up to the affine form. In this article, we study a more general case where the dynamics of agents are unknown, nonlinear, nonaffine, and heterogeneous, and the communication topologies can be iteration-varying. More specifically, we first apply the controller-based dynamic linearization method in the iteration domain to obtain a parametric learning controller using only the local input-output data collected from neighboring agents in a directed graph, and then propose a data-driven distributed adaptive iterative learning control (DAILC) method through the parameter-adaptive learning methods. We show that for each time instant, the tracking error is ultimately bounded in the iteration domain for both of the cases with iteration-invariant and iteration-varying communication topologies. The simulation results show that the proposed DAILC method has faster convergence speed, higher tracking accuracy, and more robust learning and tracking in comparison with a typical DAILC method.

Non-lifted norm optimal iterative learning control for networked dynamical systems: A computationally efficient approach

Iterative learning control (ILC) is widely used for trajectory tracking in networked dynamical systems, which execute repetitive tasks. Traditional norm optimal ILC (NOILC) based on the lifted approach provides an analytical expression for the optimal ILC update law, but it raises a computational complexity issue. As the trial length N (i.e., the number of sampling points in one trial) increases, the computational cost of the lifted approach increases exponentially, which is obviously impractical for long trials. To address this issue, this paper proposes a non-lifted norm optimal ILC (N-NOILC) approach by developing a new non-lifted cost function to improve computationally efficiency. The N-NOILC approach achieves monotonic convergence in the iteration domain, and the computational complexity decreases from O(N3) of the lifted NOILC approach to O(N). Therefore, the proposed approach can be applied to large repetitive tasks. Based on the N-NOILC approach, this paper develops a centralized as well as a distributed algorithm for networked dynamical systems. Simulations are presented to validate the effectiveness of two algorithms and demonstrate the significant advantage of the N-NOILC approach in computational efficiency.

Model-free compensation learning control of asymmetric hysteretic systems with initial state learning

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.

Improved nonlinear model‐free adaptive iterative learning control in DoS attack environment

AbstractThis paper investigates the design of a model‐free adaptive iterative learning controller(MFAILC) based on sampled‐data under the presence of denial‐of‐service(DoS) attacks in nonlinear networked control systems. First, the MFAILC is presented only using I/O data, where a compensation mechanism for DoS attacks is proposed. With dynamic linearization techniques, the nonlinear system is transformed into a linear system in the iteration domain. Then an improved MFAILC is designed to actively compensate the lost data caused by DoS attacks, where the estimation of pseudo‐partial derivative (PPD) is improved by establishing the AR model. The proposed algorithm can weaken the adverse effects of the DoS attacks and ensure the excellent tracking performance of the system. Finally, the stability of the method is proved, and the effectiveness of the proposed algorithm is demonstrated by a numerical example.

A distributed MPC approach — Local agents decide network convergence

In an earlier work, the Limited Communication-Distributed Model Predictive Control (LC-DMPC) scheme for controlling networks with dynamically coupled and locally constrained linear systems is presented. The scheme has an iterative and cooperative structure in which the systemwide optimum point is achieved by the distributed controllers requiring only coupled agents to cooperate. For assessing the network convergence, it is essential to possess complete information pertaining to all subsystems which has to be available to a central monitor. The current work endeavors to investigate this challenging point by distributing the network convergence within the local agents. With the new version of the algorithm, the convergence of the network is now guaranteed through the dissipativity of the local information exchange dynamics in the iteration domain. This is accomplished by introducing a set of free design variables into the distributed problems which are utilized by the agents to fulfill a simple local LMI problem employing local information only. Despite that the new approach is eliminating the necessity for a centralized observer, it may result in suboptimal local solutions. This is because the convergence of the information sharing loop between the coupled subsystems is insured by the small gain theorem. The new algorithm exhibits enhanced modularity due to the novel introduced convergence condition, implying that any updates to a subsystem physicals or design parameters do not require corresponding updates to neighboring subsystems or the network. The presented concepts are demonstrated by simulating a network of eight interconnected tanks.

A short-term prediction-based efficient optimization power control strategy for heavy-duty hybrid electric vehicle

This study proposes a short-term prediction-based power control strategy using the modified iteration sequential clustering quadratic programming (MISCQP) algorithm for heavy-duty series hybrid electric vehicles (SHEVs). In this strategy, a power preconditioning method is established on the basis of demand power prediction which guarantees the stable power output under transient high-power condition. Through the prediction sequence, MISCQP algorithm is proposed to solve receding horizon problem and achieve real-time control by improving the iteration efficiency. For this purpose, the clustering algorithm is designed to skip the unnecessary short step in the iteration which is too few to obtain sufficient descent. The iteration points in various iteration domains are clustered and the corresponding cluster centers are obtained. Next, the aforementioned clustering results are introduced to improve the termination criterion. The updated criterion turns to skip the short step when the distance of cluster centers of various iteration domains varies within the set threshold. Finally, the performance of the proposed strategy is validated both in simulation and hardware-in-loop tests. The results reveal that the proposed strategy achieves 5.00 %, 5.86 %, 6.27 % less fuel consumption while maintaining stable power output under all the driving cycles. And the average iteration number of proposed strategy is decreased by 10.36 %, 8.47 %, 9.21 %, respectively.

Robust adaptive event‐triggered ILC scheme design for discrete‐time non‐repetitive nonlinear systems

AbstractIn this study, a robust adaptive event‐triggered iterative learning control (ET‐ILC) method is developed for discrete‐time non‐repetitive nonlinear systems with both time‐varying system parameters and time‐iteration‐varying non‐parametric uncertainty. The proposed method utilizes an iteration‐varying dead‐zone function to estimate both parametric and non‐parametric uncertainties simultaneously. Moreover, an event‐triggered control mechanism including a mixed triggering strategy is employed to minimize the unnecessary usage of communication resource. This strategy updates the controller only when the triggering condition is met, thereby reducing the frequency of controller actions. The results are also extended to a class of multiple‐input–multiple‐output (MIMO) non‐repetitive nonlinear systems. The designed robust adaptive ET‐ILC algorithm not only guarantees perfect learning convergence in the iteration domain but also contributes to saving the system resources. The effectiveness of the presented method is demonstrated by virtue of the rigorous theoretical analysis and the illustrative simulation examples.

Event-Triggered Cooperative Model-Free Adaptive Iterative Learning Control for Multiple Subway Trains With Actuator Faults.

This article investigates the issue of speed tracking and dynamic adjustment of headway for the repeatable multiple subway trains (MSTs) system in the case of actuator faults. First, the repeatable nonlinear subway train system is transformed into an iteration-related full-form dynamic linearization (IFFDL) data model. Then, the event-triggered cooperative model-free adaptive iterative learning control (ET-CMFAILC) scheme based on the IFFDL data model for MSTs is designed. The control scheme includes the following four parts: 1) the cooperative control algorithm is derived by the cost function to realize cooperation of MSTs; 2) the radial basis function neural network (RBFNN) algorithm along the iteration axis is constructed to compensate the effects of iteration-time-varying actuator faults; 3) the projection algorithm is employed to estimate unknown complex nonlinear terms; and 4) the asynchronous event-triggered mechanism operated along the time domain and iteration domain is applied to lessen the communication and computational burden. Theoretical analysis and simulation results show that the effectiveness of the proposed ET-CMFAILC scheme, which can ensure that the speed tracking errors of MSTs are bounded and the distances of adjacent subway trains are stabilized in the safe range.

Feedback higher-order iterative learning control for nonlinear systems with non-uniform iteration lengths and random initial state shifts

For nonlinear discrete-time systems with non-uniform iteration lengths and random initial state shifts, this paper developed a feedback higher-order iterative learning control (ILC) approach. To compensate the absent information of last iteration caused by non-uniform iteration lengths, the tracking information in both iteration domain and time domain is included in ILC design with the help of higher-order control and feedback control, respectively, while the general ILC schemes just adopt the information in iteration domain. A sufficient condition based on the higher-order ILC gains is derived. It is guaranteed that as the iteration number goes to infinity, the asymptotic bound of tracking error is proportional to random initial state shifts in mathematical expectation sense. Specifically, as the expectation of initial state shifts is zero, the ILC tracking error can be controlled to zero along the iteration direction. Two examples with different initial conditions are provided to validate the proposed ILC approach.

ESO-Based Model-Free Adaptive Iterative Learning Energy-Efficient Control for Subway Train With Disturbances and Over-Speed Protection

An extended state observer based model-free adaptive iterative learning energy-efficient control (ESO-based MFAILEEC) scheme for subway train speed tracking with external disturbances and over-speed protection under the constraint on traction/braking force is proposed. Firstly, the continuous-time train motion dynamics is formulated into a discrete-time data model with consideration of external disturbances by applying the iterative dynamic linearization. Meanwhile, the external disturbances and the unknown nonlinear uncertainties of the train are transformed into a new state, which is estimated by an ESO designed in the iteration domain. Then, the ESO-based energy-efficient controller with learning ability is designed, which enables the train to achieve the purpose of energy efficiency by reducing the input force. Further, over-speed protection with trigger mechanism is developed to ensure the train operates within safe speed range. All the control strategies are designed under the constraint on traction/braking force by considering the practical limitation of the train system. No model information is involved in the whole design processes and it is a pure data-driven iterative learning approach. Rigorous mathematical analysis proves the feasibility and the robustness of the proposed method, which can guarantee the train operates safely and reliably. Finally, the simulation results further demonstrate the effectiveness of the proposed algorithm.

Practical Learning-Tracking Framework Under Unknown Nonrepetitive Channel Randomness

In this study, we consider the learning-tracking problem for stochastic systems through unreliable communication channels. The channels suffer from both multiplicative and additive randomness subject to unknown probability distributions. The statistics of this randomness, such as mean and covariance, are nonrepetitive in the iteration domain. This nonrepetitive randomness introduces non-stationary contamination and drifts to the actual signals, yielding essential challenges in signal processing and learning control. Therefore, we propose a practical framework constituted by an unbiased estimator of the mean inverse, a signal correction mechanism, and learning control schemes. The convergence and tracking performance are strictly established for both constant and decreasing step-lengths. If the statistics satisfy asymptotic repetitiveness in the iteration domain, a consistent estimator applies to the framework while retaining the framework’s asymptotic properties. Illustrative examples are provided to verify the theoretical results.

Dual-Domain Triggered Iterative Learning Control for Networked Switched Systems Against Denial-of-Service Attacks

In this article, dual-domain triggered iterative learning control (ILC) is studied for networked switched systems against denial-of-service (DoS) attacks. Unlike existing research on ILC focusing only on updating between iterations, a novel dual-domain (time and iteration domains) triggered ILC is proposed. The updates between iterations and updates of network feedback information for each iteration on the time scale are performed, reducing the iteration steps and network data transmission frequency within each iteration. In each iteration, the system output is transmitted via a network, which is assumed to be vulnerable to DoS attacks. An attack detection mechanism and buffer-based compensation mechanism are proposed. Then, the boundedness of the iterative tracking error of the networked switched systems is ensured through a switching stability analysis based on the Lyapunov theory. Finally, the advantages of the proposed methods are substantiated by a simulation example consisting of three parts.

Kernel-based regularized iterative learning control of repetitive linear time-varying systems

For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is not chosen carefully, models with either large variance or large bias would be resulted, which is one of the obstacles to further improve the modeling and tracking performances of data-driven ILC in practice. An emerging trend in the system identification community to deal with this issue is using regularization instead of the statistical tests, e.g., AIC, BIC, and one of the representatives is the so-called kernel-based regularization method (KRM). In this paper, we integrate KRM into data-driven ILC to handle a class of repetitive linear time-varying systems, and moreover, we show that the proposed method has ultimately bounded tracking error in the iteration domain. The numerical simulation results show that in contrast with the least squares method and some existing data-driven ILC methods, the proposed one can give faster convergence speed, better accuracy and robustness in terms of the tracking performance.

Adaptive Iterative Learning Kalman Consensus Filtering for High-Speed Train Identification and Estimation

In this study, a data-driven adaptive iterative learning Kalman consensus filtering (DD-AILKCF) method is designed for high-speed trains to address the parameter identification and speed consistent optimal estimation problem. The nonlinear train dynamics model is transformed into a linear-like state-space model by using the Full Form Dynamic Linearization (FFDL) technique. Meanwhile, four types of sensors are used to obtain different kinds of datasets to implement the multi-sensor system. The method proposed in this paper consists of two steps. First, an adaptive iterative learning Kalman filtering (AILKF) algorithm is proposed to estimate the fast-time varying train parameter in the iteration domain. Then, based on the identified parameter, a distributed multi-source heterogeneous network consensus filtering (MHN-CF) algorithm is proposed for the speed estimation of high-speed trains. The convergence of the proposed algorithm is derived based on the Lyapunov Function. The proposed method is compared with existing methods by numerical simulations, and the results indicate that the proposed method achieves good effectiveness in improving the accuracy of high-speed train speed estimation.

Emerging robust and data‐driven control methods for uncertain learning systems

Emerging robust and data‐driven control methods for uncertain learning systems

Neural network-based iterative learning control of a piezo-driven nanopositioning stage

The piezo-driven nanopositioning stage (PNS) is a key device to provide fast and precise motions for applications such as micromanipulation, microfabrication, and microscopy scanning. However, inherent nonlinearities associated with system perturbations bring difficulties to controller design. Regarding repetitive tasks for a PNS, existing control schemes are mainly dedicated to model inversion-based iterative learning control (ILC), which relies heavily on model accuracy. In this paper, a novel online identification and control scheme named neural network-based ILC (NN-ILC) is proposed for repetitive tracking of the PNS. The ILC scheme reduces repetitive errors due to the linear dynamics and invariable disturbance during each iteration. Neural networks are integrated into the ILC scheme to minimize the residual non-repetitive errors resulting from unknown nonlinear dynamics and model perturbations. Convergence results in both the time and iteration domains are demonstrated according to the Lyapunov stability theory. Comprehensive experiments of sinusoidal and triangular tracking references with different frequencies (5∼20 Hz) and different peak-to-peak amplitudes (5∼20μm) are conducted on a real-time control testbed. Results show that the root mean square error of the proposed NN-ILC for 20 μm tracking cases is improved by up to 37% from feedback proportional-derivative (PD) control with neural networks and by up to 20% from feedforward PD-type ILC.

Formation-Based Decentralized Iterative Learning Cooperative Impedance Control for a Team of Robot Manipulators

We present in this article a new decentralized iterative learning cooperative impedance control (ILCIC) architecture to cooperatively control the impedance for a team of robot manipulators that operate over an iteration domain. With a new definition of the neighborhood impedance error, we propose a novel formation-based cooperative control architecture, so that every manipulator can achieve the desired impedance model, even when some manipulators do not have direct access to the desired angle profiles. Besides, the desired angle profiles as well as the desired impedance model can be iteration varying, which is an important consideration when the team needs to execute different tasks in different iterations. With rigorous mathematical analysis, we show that each manipulator’s impedance error can uniformly converge to zero as the iteration index increases to infinity. A simulation study is discussed in order to further illustrate the effectiveness of the discussed algorithm.

Hybrid Active–Passive Robust Control Framework of a Flexure-Joint Dual-Drive Gantry Robot for High-Precision Contouring Tasks

For high-precision contouring tasks in a typical Cartesian motion system, multiaxis cooperation is a long-standing challenging issue. Inevitably, various factors pose substantial difficulty in the multiaxis cooperation leading to degraded contouring performance, such as the strong coupling effect between different axes, nonlinearity, the unknown dynamics due to the friction, and the difficulties in accurate system identification. To enhance the contouring performance of a flexure-joint dual-drive gantry system against the aforementioned issues, this article presents a hybrid active–passive robust control framework leveraging a model-free architecture. In this control scheme, all the coupling effects, nonlinearity, disturbance, and unknown dynamics are considered as “lumped uncertainty”. Then, a super-twisting sliding mode control method with a signum-type iterative learning law is proposed to passively suppress the lumped uncertainty during iterations; and an extended state observer is deployed to actively compensate the lumped uncertainty and ensure the establishment of sliding motion in the time domain. As supported by theoretical analysis, the proposed controller is shown to exhibit several important properties. First, the establishment of the sliding motion is guaranteed globally, in both the time domain and the iteration domain. Second, the properties of short establishment time of the sliding motion, fast convergence during the iterations, and low chattering are achieved. Moreover, a series of comparative experiments are conducted, and the proposed method is shown to be rather effective in achieving excellent contouring performance in the high-speed and complex-curvature contouring tasks, without relying on the system model.

Decentralized learning control for large-scale systems with gain-adaptation mechanisms

This study investigated the gain-adaptation mechanism of decentralized learning control for large-scale interconnected systems subject to measurement noise. The control objective is to minimize asymptotically averaged tracking errors in the iteration domain. The state-coupling matrix concept is employed to model the interactions among subsystems. Decentralized learning control schemes are proposed with three gain sequences: a predefined decreasing gain sequence, global performance-adaptive gain sequence, and decentralized adaptive gain sequence. The input sequences generated by the proposed schemes are shown to be convergent in the mean-square sense. Illustrative simulations are performed to verify the theoretical results.

Event-Triggered iterative learning control for asynchronously switched systems

Iterative learning control (ILC) is an effective control strategy for complex systems that uses trial and error to obtain desired output trajectories. This paper focuses on the issue of event-triggered ILC for switched systems with asynchronous switching. An event-triggered ILC method is designed to reduce unnecessary controller updates during iterations. The main technical contribution is that the analysis and synthesis are performed in both time and iteration domains. First, in order to solve the asynchronous switching problem in the time direction and the update problem in the iteration direction, a Lyapunov function involving both directions is adopted. Second, to prove the convergence of tracking error and the system stability in both domains, a new prove method is proposed, in which the tracking error is summed over the entire time domain and the average dwell condition is summed over the entire iteration domain. Finally, the feasibility of theoretical result is verified by simulation.