Robust iterative learning control for systems with norm‐bounded uncertainties

In this paper, the uncertain model of the robotic system is decomposed into repetitive and non-repetitive parts, and the norm model of the system is taken into account. By using the Lyapunov method, an adaptive robust iterative learning control scheme is presented for the robotic system with both structured and unstructured uncertainty, and the overall stability of the system in the iteration domain is established. In the scheme the bound parameters estimated as well as the iterative learning control input are adjusted in the iteration domain. The validity of the scheme is illustrate through a simulation example.

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

Data-Based Control for Learning Systems With Nonlinear Dynamics: A Case Study

SummaryThis paper proposes robust iterative learning control schemes for continuous‐time nonlinear systems with various nonparametric uncertainties under nonuniform trial length circumstances. The nonuniform trial length is described by a random variable, which causes a random data missing problem while designing and analyzing algorithms for the precise tracking problem. Three common types of nonparametric uncertainties are taken into account: norm‐bounded uncertainty, variation‐norm‐bounded uncertainty, and norm‐bounded uncertainty with unknown coefficients. A novel composite energy function is introduced with the help of a newly defined virtual tracking error for the asymptotical convergence of the proposed schemes. Extensions to multiple‐input–multiple‐output cases are also elaborated. Illustrative simulations are provided to verify the theoretical results.

This paper deals with designing of iterative learning control schemes for uncertain systems with static nonlinearities. More specifically, the nonlinear part is supposed to be sector bounded and system matrices are assumed to range in the polytope of matrices. For systems with such nonlinearities and uncertainties the repetitive process setting is exploited to develop a linear matrix inequality based conditions for computing the feedback and feedforward (learning) controllers. These controllers guarantee acceptable dynamics along the trials and ensure convergence of the trial-to-trial error dynamics, respectively. Numerical examples illustrate the theoretical results and confirm effectiveness of the designed control scheme.

This paper addresses robust performance analysis and synthesis of lifted system iterative learning control (ILC). By applying the full block S-procedure, sufficient conditions for the robust performance of ILC with both unstructured and structured uncertainty are derived. In the synthesis problem, we consider the design of the learning filter Q for modelinversion based ILC. The problem is reformulated as a convex optimization problem such that the converged tracking error is minimized subject to the monotonic convergence condition. This synthesis approach enables full automation of the ILC design since neither an uncertainty model has to be identified nor a robustness filter has to be chosen. The advantages of this novel robust performance ILC technique are demonstrated on an experimental linear motor test setup.

In this paper we present a linear computational complexity framework for design and implementation of (constrained) lifted Iterative Learning Control (ILC) systems with quadratic cost. The problem of designing constrained lifted ILC with quadratic cost is formulated as a convex optimization problem. We solve this problem using the primal-dual interior point method. High computational complexity of the primal-dual method, which render this method computationally infeasible for high dimensional lifted ILC systems, is significantly decreased by exploiting the sequentially semi-separable (SSS) structure of lifted system matrices. More precisely, O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) computational cost of one iteration of the primal-dual method is reduced to O(N), where N characterizes the size of the lifted system matrices. Furthermore, by exploiting the SSS structure the large lifted system matrices can be efficiently stored in computer memory. We also show that SSS structure can be exploited to efficiently implement analytical solution of the unconstrained lifted ILC problem with quadratic cost and for calculation of the norm and stability radius of ILC system.

In 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.

In learning systems, high operation precision is often a desirable objective for the algorithm design. Though centralized algorithms are generally adopted, they are subjected to restrictive hypotheses on the learning systems. To overcome this challenging problem, we aim to propose some distributed learning algorithms that focus specifically on achieving the perfect tracking tasks for iterative learning control (ILC) systems. By noting the equivalent relation between the perfect tracking problem of ILC systems and the solving problem of linear algebraic equations (LAEs), we first present an observer-based distributed learning algorithm to solve LAEs, where a multiagent system is constructed with every agent being only required to access some partial information for LAEs. The distributed learning algorithm benefits from integrating both observer-based design and consensus-based design ideas such that for any solvable LAE, all agents can agree on a common solution of it under any initial conditions of agents, regardless of whether it has a unique solution or not. Then, with the distributed learning algorithm for LAEs, we further develop two classes of distributed learning control algorithms for ILC systems, which establish the perfect tracking objective in the presence of the trackable desired output even without using the basic relative degree condition that is generally imposed for conventional ILC.

In this paper, we propose a numerical technique for reference tracking control of discrete-time MIMO nonlinear systems. The technique is based on the derivation of an auxiliary predictor model and on the online computation of an approximate model inversion control sequence. If the predictor model is assumed to be polynomial, then the control input is computed at each time interval by solving a polynomial optimization problem by means of a cyclic coordinate minimization technique. This technique is numerically efficient and guarantees convergence to a so-called coordinate-wise minimum point. We provide a formal proof for boundedness of the tracking error and closed-loop stability of approximate model inversion control. A numerical example involving therapy control for a diabetic patient illustrates the practical potential of the proposed method.

Here the authors concerned with robust iterative learning control (ILC) for uncertain time-delay systems. They demonstrate that the design of a robust ILC is straightforward based on a performance index for the error system. The ILC algorithms under consideration are rather simple. They show that after the two-dimensional analysis of ILC, a Lyapunov-like approach can be used to directly obtain a stable algorithm that achieves monotonic convergence of the control input error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. They also show that the Lyapunov-like approach can be applied to design robust ILC for uncertain systems with time-varying delay or multiple time delays. Numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.

An iterative learning control (ILC) framework based on two-degree-of-freedom control is presented for a linear plant with perturbations. A sufficient condition in the frequency domain is obtained for robust convergence with the bounded asymptotic error in the existence of input disturbance, output disturbance and errors in initial states. Based on the sufficient condition, the problem of designing ILC can be converted to a robust performance problem and a robust ILC against disturbances and initialization errors is derived by structured singular value and mu synthesis

This study first investigates robust iterative learning control (ILC) issue for a class of two‐dimensional linear discrete singular Fornasini–Marchesini systems (2‐D LDSFM) under iteration‐varying boundary states. Initially, using the singular value decomposition theory, an equivalent dynamical decomposition form of 2‐D LDSFM is derived. A simple P‐type ILC law is proposed such that the ILC tracking error can be driven into a residual range, the bound of which is relevant to the bound parameters of boundary states. Specially, while the boundary states of 2‐D LDSFM satisfy iteration‐invariant boundary states, accurate tracking on 2‐D desired surface trajectory can be accomplished by using 2‐D linear inequality theory. In addition, extension to 2‐D LDSFM without direct transmission from inputs to outputs is presented. A numerical example is used to illustrate the effectiveness and feasibility of the designed ILC law.

In this paper is proposed a robust higher-order iterative learning control (ILC) algorithm for discrete-time systems. In contrast to conventional discrete-time learning methods, the proposed learning algorithm is constructed based on both time-domain performance and iteration-domain performance. Also, the proposed learning algorithm use more than one past error in the iteration-domain. It is proved that the proposed method has robustness in the presence of external disturbances and, in absence of all disturbances, the convergence of the proposed learning algorithm is guaranteed. A numerical example is given to show the robustness in the presence of state disturbance and convergence property according to parameters change.

Robustness in identification.- Comments on model validation as set membership identification.- SM identification of model sets for robust control design from data.- Robust identification and the rejection of outliers.- Semi-parametric methods for system identification.- Modal robust state estimator with deterministic specification of uncertainty.- The role of experimental conditions in model validation for control.- Modeling and validation of nonlinear feedback systems.- Towards a harmonic blending of deterministic and stochastic frameworks in information processing.- Suboptimal conditional estimators for restricted complexity set membership identification.- Worst-case simulation of uncertain systems.- On performance limitations in estimation.- Design criteria for uncertain models with structured and unstructured uncertainties.- Robustness and performance in adaptive filtering.- Nonlinear identification based on unreliable priors and data, with application to robot localization.- Robust model predictive control: A survey.- Intrinsic performance limits of linear feedback control.- Puzzles in systems and control.- Robust regional pole placement: An affine approximation.- On achieving L p (?p) performance with global internal stability for linear plants with saturating actuators.- Control under structural constraints: An input-output approach.- Multi-objective MIMO optimal control design without zero interpolation.- Robustness synthesis in l 1: A globally optimal solution.- Optimal control of distributed arrays with spatial invariance.- Numerical search of stable or unstable element in matrix or polynomial families: A unified approach to robustness analysis and stabilization.- A convex approach to a class of minimum norm problems.- Quantified inequalities and robust control.- Dynamic programming for robust control: Old ideas and recent developments.- Robustness of receding horizon control for nonlinear discrete-time systems.- Nonlinear representations and passivity conditions in discrete time.- Robust ripple-free output regulation and tracking under structured or unstructured parameter uncertainties.- An experimental study of performance and fault-tolerance of a hybrid free-flight control scheme.