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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]

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]

This paper proposes a data-driven model-free inverse reinforcement learning (RL) algorithm to reconstruct the unknown cost function of the demonstrated discrete-time (DT) dynamical systems with antagonistic disturbances. We propose an inverse RL policy iteration scheme that uses system dynamics and the input policies, for deriving our main result of a data-driven off-policy inverse Q-learning algorithm using only demonstrated trajectories of the antagonistic system without knowing system dynamics and the control policy gain. This data-driven algorithm consists of Q -function evaluation, state-penalty weight improvement, and action policies update. We guarantee unbiased estimates in the data-driven algorithm when exploration noises exist for the persistence of the excitation. An example verifies the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the iterative learning problem for discrete-time systems with event-triggered scheme and quantization. The event-triggered scheme is firstly considered in the iterative learning controllers to reduce the number of iteration steps to be updated. Here, the event-triggered scheme is designed depending on time t and iterative learning step k . Quantization is then introduced in the event-triggered controllers and some relaxed conditions are presented to guarantee the tracking problem by using some interval matrix properties. Finally, simulation results are given to illustrate the usefulness of the developed criteria. [ABSTRACT FROM AUTHOR]

This paper proposes a non-model based approach to iterative learning control (ILC) via extremum seeking. Single-input–single-output discrete-time nonlinear systems are considered, where the objective is to recursively construct an input such that the corresponding system output tracks a prescribed reference trajectory as closely as possible on finite horizon. The problem is formulated in terms of extremum seeking control, which is amenable to a range of local and global optimisation methods. Contrary to the existing ILC literature, the formulation allows the initial condition of each iteration to be incorporated as an optimisation variable to improve tracking. Sufficient conditions for convergence to the reference trajectory are provided. The main feature of this approach is that it does not rely on knowledge about the system’s model to perform iterative learning control, in contrast to most results in the literature. [ABSTRACT FROM AUTHOR]

This note proposes convergence analysis of iterative learning control (ILC) for discrete-time linear systems with randomly varying iteration lengths. No prior information is required on the probability distribution of randomly varying iteration lengths. The conventional P-type update law is adopted with Arimoto-like gain and/or causal gain. The convergence both in almost sure and mean square senses is proved by direct math calculating. Numerical simulations verifies the theoretical analysis. [ABSTRACT FROM AUTHOR]

This work is focused on the iterative learning control (ILC) design for linear discrete-time systems with iteration-varying factors, including reference, initial state, and exogenous disturbances. First, multiple high-order internal models (HOIMs) are given for various iteration-varying factors. The reference is generated by an HOIM, and the initial state and the exogenous disturbances ultimately satisfy HOIMs but do not strictly follow HOIMs in finite iteration interval. Then, a new ILC scheme, a special high-order ILC (HO-ILC), is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For simplicity, the case with only iteration-varying reference is first considered, where the asymptotic stability and monotone convergence based ILC design methods are both presented by using the 2-D analysis approach. Next, more iteration-varying factors are further considered. In this situation, the HOIM-based ILC is transformed into a controller design problem of a 2-D Roesser model with non-zero boundary states and disturbances, where the 2-D H ∞ performance is studied. In consequence, an ILC design criterion is presented to achieve perfect tracking and 2-D H ∞ performance. For comparison, the monotone convergence based ILC design method is extended to the situation with more iteration-varying factors. Utilizing information provided by the multiple HOIMs, it is verified that HO-ILC outperforms low-order ILC (LO-ILC) in presence of iteration-varying factors. Meanwhile, the 2-D H ∞ based ILC is shown to be superior to the monotone convergence based ILC. Finally, a microscale robotic deposition system with iteration-varying factors is given to illustrate the advantage of the proposed 2-D H ∞ based ILC. [ABSTRACT FROM AUTHOR]

Abstract: The iterative learning control (ILC) is constructed for the discrete-time large scale systems. Each subsystem is affine nonlinear and its observation equation is with noise. Subsystems are nonlinearly connected via the large state vector of the whole system. The possibility of data missing, and communication delay is taken into account. It is proved that ILC given in the paper with probability one converges to the optimal one minimizing the tracking error. The simulation results are consistent with theoretical analysis. [Copyright &y& Elsevier]

Abstract: Iterative Learning Control (ILC) improves the tracking accuracy of systems that repetitively perform the same task. This paper considers model-based ILC for linear time-varying (LTV) systems. The applied feedforward iteratively minimises a quadratic norm of the feedforward update and the error in the next iteration as predicted by the model. The optimal feedforward update can be derived straightforwardly using a matrix description of the system dynamics. However, the implementation of the resulting matrix equation is demanding in terms of computation time and memory. In this paper it is shown that an efficient algorithm can be derived directly from the matrix equation using the associated state-equations. The ILC algorithm is applied to an industrial robot. The configuration dependent robot dynamics can be approximated as LTV for small tracking errors from the large-scale motion along the desired trajectory. It is shown that a substantial reduction of the tracking error at the robot’s tip can be realised by ILC using an LTV model of the robot dynamics and the same reduction cannot be accomplished using an LTI model that ignores the variation of the robot dynamics along the trajectory. [Copyright &y& Elsevier]

Abstract: In this work we present a discrete-time adaptive iterative learning control (AILC) scheme to deal with systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new adaptive ILC can incorporate a Recursive Least Squares (RLS) algorithm, hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis. When the initial states are random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis. [Copyright &y& Elsevier]

Abstract: An optimal iterative learning control (ILC) is proposed to optimize an accumulative quadratic performance index in the iteration domain for the nominal dynamics of linear discrete-time systems. Properties of stability, convergence, robustness, and optimality are investigated and demonstrated. In the case that the system under consideration contains uncertain dynamics, the proposed ILC design can be applied to yield a guaranteed-cost ILC whose solution can be found using the linear matrix inequality (LMI) technique. Simulation examples are included to demonstrate feasibility and effectiveness of the proposed learning controls. [Copyright &y& Elsevier]

Abstract: This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plant Markov parameters are subject to interval uncertainty. Using the so-called super-vector approach to ILC, vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ILC process. It is shown that the stability of such interval ILC systems can be determined by checking the stability of the system using only the vertex points of the interval Markov parameters. [Copyright &y& Elsevier]

Abstract: In iterative learning control schemes for linear discrete time systems, conditions to guarantee the monotonic convergence of the tracking error norms are derived. By using the Markov parameters, it is shown in the time-domain that there exists a non-increasing function such that when the properly chosen constant learning gain is multiplied by this function, the convergence of the tracking error norms is monotonic, without resort to high-gain feedback. [Copyright &y& Elsevier]

This correspondence is concerned with an iterative learning algorithm for MIMO linear time-varying systems. We provide a necessary and sufficient condition for the existence of a convergent algorithm. The result extends the main result in Saab (IEEE Trans. Automat. Control 40(6) (1995) 1138). [Copyright &y& Elsevier]

In this paper, to eliminate the tracking error by using adaptive dynamic programming (ADP) algorithms, a novel formulation of the value function is presented for the optimal tracking problem (TP) of nonlinear discrete-time systems. Unlike existing ADP methods, this formulation introduces the control input into the tracking error, and ignores the quadratic form of the control input directly, which makes the boundedness and convergence of the value function independent of the discount factor. Based on the proposed value function, the optimal control policy can be deduced without considering the reference control input. Value iteration (VI) and policy iteration (PI) methods are applied to prove the optimality of the obtained control policy, and derived the monotonicity property and convergence of the iterative value function. Simulation examples realized with neural networks and the actor–critic structure are provided to verify the effectiveness of the proposed ADP algorithm. [ABSTRACT FROM AUTHOR]