Robust Iterative Learning Control Research Articles

A robust iterative learning control for linear system with variable initial state and trail length

AbstractTo address the variable initial state and trail length this paper first presents a robust PD‐type open‐closed‐loop iterative learning control (ILC) law for a multiple‐input‐multiple‐output (MIMO) linear discrete‐time system. It is demonstrated that the convergence condition is dependent on the PD‐type feed‐forward learning gains, while an appropriate feedback learning gain can improve the ILC convergence performance. As a special case of PD‐type open‐closed‐loop ILC law, P‐type and D‐type open‐closed‐loop ILC laws are deduced. The three developed ILC laws ensure that as the number of iterations approaches infinity, the expectation of ILC tracking error will be constrained within a limited range, where the boundary is proportional to the initial state variation. Through a numerical simulation, the effectiveness of the proposed ILC laws is illustrated.

Robust iterative learning control for discrete-time systems with random initial state shifts

This paper presents the sufficient conditions of the stability for discrete-time systems with random initial state shifts when applying iterative learning control. Different sufficient conditions have been developed for systems with different characteristics to ensure boundedness of tracking errors and convergence of the learning process under random initial condition. First, the relationship between the initial shifts of two adjacent iterations is addressed with the help of the transition matrix. And the different analysis models are established for each type of systems: one-dimensional matrix analysis model and 2-D Roesser model. Second, the new and sufficient conditions are established for the proposed learning control law to ensure systems convergence by matrix theory and two-dimensional system theory. Third, solving the linear matrix inequality (LMI) yields the control gains. Finally, digital simulations illustrate the effectiveness and sufficiency of the presented conditions.

An integrated tube robust iterative learning model predictive control strategy based on dynamic partial least squares algorithm for batch processes

AbstractIn this paper, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

Data-driven robust iterative learning control of linear systems

We propose a data-driven robust iterative learning control (ILC) technique to multi-input-multi-output (MIMO) linear systems. Control of MIMO linear systems, particularly with strong cross-axis coupling, is challenging as modeling of a MIMO system can be complicated, time-consuming, and often requires a trade-off between robustness and performance. As such, limitations exist in current ILC techniques. The aim of this paper is to develop an efficient and easy-to-use data-driven ILC technique to output tracking of MIMO linear systems under random disturbance. Through the proposed technique, the complicated modeling process and the robustness-accuracy trade-off are avoided, and the up-to-now system dynamics is captured by constructing and updating the iteration gain using the input and output data in the last iteration. It is shown that monotonic convergence of the ILC algorithm is guaranteed, and an optimal gain can be obtained to maximize the convergence rate and minimize the residual tracking error. The proposed technique is illustrated through experiments on a three-input three-output piezoelectric actuator system, with comparison to the adaptive multi-axis inversion-based iterative control (A-MAIIC) technique. The experimental results show rapid convergence and improved formance of the proposed technique when the cross-axis coupling is strong.

Neural network compensator-based robust iterative learning control scheme for mobile robots nonlinear systems with disturbances and uncertain parameters

Aiming at the problem of trajectory tracking control for mobile robot nonlinear systems with non-repetitive uncertain parameters, we propose a novel neural network compensator-based robust iterative learning control (NNRILC) scheme to achieve excellent tracking performance and uncertainty compensation. The NNRILC scheme consists of a parallel structure that includes a robust iterative learning control (RILC) term and a neural network (NN) compensator. The RILC term is used to ensure robust control performance and promise closed-loop stability. The compensator based on the neural network is employed to handle the uncertainties resulted from the nonlinear dynamics as well as the suppressed disturbances in the mobile robot nonlinear systems. Additionally, the fourth-order Runge-Kutta algorithm is employed to solve the state differential equation of the mobile robot. Consequently, The H∞ robust technique is used to construct an iterative learning control update rule to reduce the impact of disturbances. Meanwhile, the RILC scheme is designed to optimize the neural network initial parameters and weights of the NN compensator at each trial. Then the convergence of the proposed NNRILC scheme is analyzed, and the results are incorporated into the control update for the next process trial. Finally, the effectiveness of the proposed method is verified by mobile robot simulation.

Improving Tracking Accuracy for Repetitive Learning Systems by High-Order Extended State Observers.

For systems executing repetitive tasks, how to realize the perfect tracking objective is generally desirable, for which an effective method called "iterative learning control (ILC)" emerges thanks to the incorporation of the repetitive execution of systems into an ILC design framework. However, nonrepetitive (iteration-varying) uncertainties are often inevitable in practice and greatly degrade the tracking accuracy of ILC, which has not been treated well, regardless of considerable robust ILC results. This motivates this article to develop a new design method to improve the tracking accuracy of ILC by adopting a high-order extended state observer (ESO) to address ill effects of nonrepetitive uncertainties and uncertain system models. With the designed ESO-based ILC, the robust tracking of any desired trajectory can be achieved such that the tracking error can be decreased to vary in a small bound depending continuously on the bounds of high-order variations of nonrepetitive uncertainties with respect to the iteration. It makes the tracking accuracy of ILC possible to be regulated through the design of ESO, of which the validity is demonstrated by including a simulation example.

Robust iterative learning control via adaptive backstepping for oscillation displacement system of continuous casting mold driven by a servo motor

AbstractIn order to solve the tracking problem of oscillation displacement system of continuous casting mold driven by a servo motor in the present of the time‐varying load, parameter uncertainties, unknown dynamics and external disturbances, a robust iterative learning control (ILC) via adaptive backstepping is proposed in this paper. Firstly, backstepping technique is used to design controller due to the mismatched disturbances. Secondly, the periodic component of the lumped disturbances is estimated by ILC method, while the aperiodic component is attenuated by switching term with adaptive gain. In addition, a time‐varying boundary layer approach is employed to overcome the identical initial condition limitation of the ILC. Through a proper composite energy function, the convergence of the closed‐loop system is analyzed. Finally, simulation and experimental results are given to illustrate the effectiveness of the proposed method.

Extension of iterative learning control design for batch processes with time-delay in the input subject to random cycle-varying uncertainties

For uncertain time-delay batch processes with repetitive nature, this work deals with an unresolved problem of robust iterative learning control (ILC) design, in which we simultaneously remove the conventional assumptions of cycle-invariant uncertainties in reference trajectories, initial states, external disturbances, process dynamics, and time-delay. Moreover, we consider the variation of all existing uncertainties from a random point of view. Based on the idea of the internal model control (IMC) and indirect ILC, a novel IMC-based ILC structure is proposed. Then, we derive the practical convergence conditions, which have two design functions. By introducing a simple method for adjusting these functions, not only can we ensure that the expected tracking error converges monotonically to zero-neighborhood (in the L2-norm sense) but we can also achieve an acceptable convergence rate. Moreover, it is shown that the satisfaction of derived convergence conditions can always be guaranteed for any process. Simulation tests are provided to demonstrate the effectiveness of the proposed design.

Conic Input Mapping Design of Constrained Optimal Iterative Learning Controller for Uncertain Systems.

In this article, we study the optimal iterative learning control (ILC) for constrained systems with bounded uncertainties via a novel conic input mapping (CIM) design methodology. Due to the limited understanding of the process of interest, modeling uncertainties are generally inevitable, significantly reducing the convergence rate of the control systems. However, huge amounts of measured process data interacting with model uncertainties can easily be collected. Incorporating these data into the optimal controller design could unlock new opportunities to reduce the error of the current trail optimization. Based on several existing optimal ILC methods, we incorporate the online process data into the optimal and robust optimal ILC design, respectively. Our methodology, called CIM, utilizes the process data for the first time by applying the convex cone theory and maps the data into the design of control inputs. CIM-based optimal ILC and robust optimal ILC methods are developed for uncertain systems to achieve better control performance and a faster convergence rate. Next, rigorous theoretical analyses for the two methods have been presented, respectively. Finally, two illustrative numerical examples are provided to validate our methods with improved performance.

Robust Iterative Learning Control for Pneumatic Muscle With Uncertainties and State Constraints

In this article, we propose a new iterative learning control (ILC) scheme for trajectory tracking of pneumatic muscle (PM) actuators with state constraints. A PM model is constructed in three-element form with both parametric and nonparametric uncertainties, while full state constraints are considered for enhancing operational safety. To ensure that system states are within the predefined bounds, the barrier Lyapunov function (BLF) is used in the analysis, which reaches infinity when some of its arguments approach limits. The proposed ILC incorporates the BLF with the composite energy function (CEF) approach and ensures the boundedness of CEF in the closed-loop, thus, assuring that those limits are not transgressed. Through rigorous analysis, we show that under the proposed ILC scheme, uniform convergences of PM state tracking errors are guaranteed. Simulation studies and experimental validations are conducted to illustrate the efficacy of the proposed scheme. Experimental results show that the proposed ILC satisfies the state constraint requirements and the tracking error is less than 2.5% of the desired trajectory.

Robust Data-Driven Iterative Learning Control for Linear-Time-Invariant and Hammerstein-Wiener Systems.

Iterative learning control (ILC) relies on a finite-time interval output predictor to determine the output trajectory in each trial. Robust ILCs intend to model the uncertainties in the predictor and to guarantee the convergence of the learning process subject to such model errors. Despite the vast literature in ILCs, parameterizing the uncertainties with the stochastic errors in the predictor parameters identified from system I/O data and thus robustifying the ILC have not yet been targeted. This work is devoted to solving such problems in a data-driven fashion. The main contributions are two-fold. First, a data-driven ILC method is developed for LTI systems. The relationship is established between the errors in the predictor matrix and the stochastic disturbances to the system. Its robust monotonic convergence (RMC) is then linked with the closed-loop learning gain matrix that contains the predictor uncertainties and is analyzed based on a closed-form expectation of this gain matrix multiplied with its own transpose, that is, in a mean-square sense (MS-RMC). Second, the data-driven ILC and MS-RMC analysis are extended to nonlinear Hammerstein-Wiener (H-W) systems. The advantages of the proposed methods are finally verified via extensive simulations in terms of their convergence and uncorrelated tracking performance with the stochastic parametric uncertainties.

Robust iterative learning control for random switched singular systems in time domain

A robust iterative learning control algorithm is proposed for continuous-time switched singular systems disturbed by random measurement noise. Firstly, the switched singular systems is transformed into a differential-algebraic equation composed of slow subsystem and fast subsystem by nonsingular transformation. Then, the control input is continuously modified by the state measurement errors and the learning gain with attenuation characteristics. The convergence of each subsystem is strictly proved in theory, and the sufficient conditions for the convergence of this algorithm are given. Theoretical analysis shows that the algorithm can effectively suppress the measurement noise and make the system state completely track the desired trajectory in a finite time interval. Finally, compared with the fixed gain iterative learning control method, the simulation results show that the tracking accuracy of the proposed algorithm is significantly improved.

Robust convergence conditions of iterative learning control for time‐delay systems under random non‐repetitive uncertainties

Some of the most fundamental assumptions in the design of iterative learning control (ILC) for uncertain systems are the strict repetitiveness (i.e. iteration-independence) of uncertainties in all factors of plant dynamic, external disturbances, initial conditions, and reference trajectory, which may not always hold in practical applications. The simultaneous relaxation of all these assumptions is a challenging problem that has been addressed only for delay-free systems. This problem is still open for time-delay systems, especially when the time-delay factor also has non-repetitive (i.e. iteration-dependent/varying) uncertainty. Hence, this study extends the problem of robust ILC for a class of time-delay systems under nonrepetitive uncertainties in not only plant dynamic, external disturbances, initial conditions, and reference trajectory but also time-delay. By using the ILC scheme introduced in this work, and based on the frequency domain analysis, it is shown that both monotonic convergence and boundedness of the expected tracking error can be achieved (in the sense of L2-norm) when the non-repetitiveness (i.e. iteration-dependence) of all existing uncertainties from a random viewpoint are taken into account. The effectiveness of the proposed strategy is verified by two simulation examples.

A two-stage robust iterative learning model predictive control for batch processes

Iterative learning model predictive control (ILMPC) has been considered as potential control strategy for batch processes. ILMPC can converge to the desired reference trajectory with high precision along batches and ensure system stability within batches. However, as a model-based control method, the control performance of the ILMPC algorithm deteriorates when exists model parameter uncertainty. Therefore, guaranteeing system tracking performance in the case of model parameter uncertainty is a challenging task in the framework designing of ILMPC method. To this end, we develop a two-stage robust ILMPC strategy for batch processes, which integrates the robust iterative learning control (ILC) in the domain of batch-axis and robust model predictive control (MPC) in the domain of time-axis into one comprehensive control scheme. The integrated control law of the developed two-stage robust ILMPC algorithm is obtained by solving two convex optimization problems. As a result, the developed control method obtains faster convergence speed and better tracking performance in the case of model parameter uncertainty. Moreover, the convergence analysis of the system is presented. Finally, comparative simulations are provided to verify the superiority of the developed control algorithm.

Robust decentralized iterative learning control for large‐scale interconnected systems described by 2‐D Fornasini–Marchesini systems with iteration‐dependent uncertainties including boundary states, disturbances, and reference trajectory

SummaryThis article first investigates robust iterative learning control (ILC) problem of a class of large‐scale interconnected systems, which consist of many subsystems described by two‐dimensional linear discrete first Fornasini–Marchesini systems with iteration‐dependent uncertainties arising from not only boundary states, disturbances, but also reference trajectory. A decentralized P‐type ILC law without any information exchanges with other subsystems is proposed such that the ultimate ILC tracking error of each subsystem can converge to a bounded range, the bound of which depends continuously on the bounds of all iteration‐dependent uncertainties considered. Especially, if these iteration‐dependent uncertainties are convergent progressively along the iteration direction, perfect ILC tracking on 2‐D reference trajectory can be obtained. Additionally, a modified ILC law with compensation technique is used to a class of large‐scale interconnected systems composed of many subsystems represented by two‐dimensional linear discrete second Fornasini–Marchesini systems. Two simulation examples are used to demonstrate the effectiveness and validity of the obtained ILC results. Finally, some comparative discussions are given.

Stability of Sliding Mode ILC Design for a Class of Nonlinear Systems With Unknown Control Input Delay.

This article studied the stability and convergence of a robust iterative learning control (ILC) design for a class of nonlinear systems with unknown control input delay. First, the iterative integral sliding mode (IISM) design was proposed, which comprised iterative actions. The iterative action made the convergence of the tracking error under the ideal sliding mode. Then, a suitable iterative update law was provided for the IISM-based robust ILC controller. The controller had the capability of both minimizing the steady tracking error and suppressing the unrepeatable disturbance. Using the controller, the closed-loop system stability was analyzed, and the stability conditions were given. Consequently, the sliding mode convergence in the iteration domain was proved by a composite energy function (CEF). In addition, by analyzing the influence of affection on the tracking error, several measures were taken to solve the chattering problem of the sliding mode control. Finally, a one-link robotic manipulator and a vertical three-tank system were used to verify the control design. The application simulations validated the performance of the proposed sliding mode iterative learning control (SMILC) design, which achieved the stability of the nonlinear system and overcame the control input time delay.

Robust Iterative Learning Control Algorithm for Lower Limb Rehabilitation Proactive Human-robot Collaboration

At present, the motion control algorithms of lower limb exoskeleton robots have errors in tracking the desired trajectory of human hip and knee joints, which leads to poor follow-up performance of the human-machine system. Therefore, an iterative learning control algorithm is proposed to track the desired trajectory of human hip and knee joints. In this paper, the experimental platform of lower limb exoskeleton rehabilitation robot is built, and the control system software and hardware design and robot prototype function test are carried out. On this basis, a series of experiments are carried out to verify the rationality of the robot structure and the feasibility of the control method. Firstly, the dynamic model of the lower limb exoskeleton robot is established based on the structure analysis of the human lower limb; secondly, the servo control model of the lower limb exoskeleton robot is established based on the iterative learning control algorithm; finally, the exponential gain closed-loop system is designed by using MATLAB software. The relationship between convergence speed and spectral radius is analyzed, and the expected trajectory of hip joint and knee joint is obtained. The simulation results show that the algorithm can effectively improve the gait tracking accuracy of the lower limb exoskeleton robot and improve the follow-up performance of the human-machine system.

Output feedback based robust iterative learning control via a heuristic approach for batch processes with time-varying state delays and uncertainties

This paper proposes an output feedback (OF) based PD-type robust iterative learning control (ILC) scheme for a class of discrete batch processes with time-varying delays and uncertainties in the absence of accurate state measurements, which is convenient for practical applications. Based on a repetitive process model and Lyapunov–Krasovskii theory, sufficient conditions are established in terms of linear matrix inequalities (LMIs) to ensure the robust stability along the trial for all admissible uncertainties. A two-stage heuristic approach is developed to iteratively calculate the feasible ILC gains based on a pre-designed state feedback (SF) controller, which circumvents the non-convex stability conditions expressed in bilinear matrix inequalities caused by OF. In addition, the conditions can be extended to the case of non-repetitive uncertainties in the system and meet the prescribed H∞ performance level. Finally, a simulation of injection molding process is given to demonstrate the effectiveness of the proposed method.

An LMI Approach to Robust Iterative Learning Control for Linear Discrete-time Systems

An LMI Approach to Robust Iterative Learning Control for Linear Discrete-time Systems

Robust iterative learning control for linear discrete-time systems with initial state learning

This paper investigates a new sufficient robust convergence condition of iterative learning control with initial state learning in the presence of iteration-varying uncertainty for multivariable systems in the time domain. The uncertainty in system parameters may lead to divergence of the ILC algorithm. Moreover, in the basic ILC algorithm, the initial state is constant in each iteration and, consequently, always leads to a tracking error. Providing fixed learning gains over time and iteration is a significant achievement of this norm-based method. For this purpose, first, a new robust convergence condition is designed based on the iterative learning control with initial state learning algorithm, and in the next step, a semi-optimal solution is achieved for it by the imperialist competitive algorithm . Finally, the effectiveness of the proposed convergence scheme is evaluated through two numerical examples.