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In this work, we consider systems whose components suffer from clock offsets and quantization and study the effect of those on a reinforcement learning (RL) algorithm. Specifically, we consider an off-policy iterative RL algorithm for continuous-time systems, which uses input and state data to approximate the Nash-equilibrium of a zero-sum game. However, the data used by this algorithm are not consistent with one another, in that each of them originates from a slightly different time instant of the past, hence putting the convergence of the algorithm in question. We prove that, given that these timing inconsistencies remain below a certain threshold, the iterative off-policy RL algorithm will still converge epsilon-closely to the desired Nash policy. However, this result is conditional to a certain Lipschitz continuity and differentiability condition on the input-state data collected, which is indispensable in the presence of clock offsets. A similar result is also derived when quantization of the measured state is considered. Finally, unlike prior work, we provide a sufficiently rich data condition for the execution of the iterative RL algorithm, which can be verified a priori across all iteration indices. Simulations are performed, which verify and clarify theoretical findings. [ABSTRACT FROM AUTHOR]

Layerwise processes are common in industrial applications and have been well-studied in the control literature. A layerwise process has repeated layers in a spatial and/or temporal domain, which may differ over iterations. Height map control for layerwise processes is an important control problem, especially in the context of model mismatch and process constraints. In this work, we provide a layer-preview iterative learning controller to develop a novel learning-based control framework for layerwise processes. We utilize both the measurement data from previous layers and the gradient information from the model of the layer-to-layer process to develop the learning controller. This structure provides a hybrid approach where data and model information is efficiently used for improved controller performance. Simulation case studies on an additive manufacturing process with layerwise varying dynamics illustrate the utility of our approach under constrained inputs. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed model predictive control (DMPC) problem for multiple dynamically-decoupled heterogeneous linear systems subject to both local state and input constraints and coupled non-convex constraints (e.g., collision avoidance constraints). To solve the resulting non-convex optimal control problem (OCP) at each time step, successive convex approximation (SCA) technique is a promising convexification approach. However, an algorithm that is fully distributed, computationally efficient, and recursively feasible for both local and coupled non-convex constraints remains an open problem. In this paper, we propose an inner–outer layer framework that integrates three important modifications into the SCA scheme for solving each OCP. Specifically, (i) in the inner layer, we utilize a distributed dual fast gradient approach to enable the distributed execution, (ii) as for the outer layer, instead of requiring the optimal solution at each iteration by classical SCA scheme, we improve computational efficiency by relying solely on a suboptimal solution achieved through flexible termination, and (iii) an adaptive tightening strategy imposing on the convexified coupled constraints is developed which permits both the inner and outer layers to terminate in advance with the guarantee of the closed-loop non-convex coupled constraints satisfaction. Under some reasonable assumptions, convergence of the proposed inner–outer layer framework, recursive feasibility of the proposed DMPC algorithm and stability of the resulting whole closed-loop system are ensured. Simulation results on multi-agent control with non-convex coupled collision avoidance constraints and comparisons against some benchmark solutions using the centralized method are carried out to verify the performance of the proposed DMPC method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we present an approximate optimal dynamic output feedback control learning algorithm to solve the linear quadratic regulation problem for unknown linear continuous-time systems. First, a dynamic output feedback controller is designed by constructing the internal state. Then, an adaptive dynamic programming based learning algorithm is proposed to estimate the optimal feedback control gain by only accessing the input and output data. By adding a constructed virtual observer error into the iterative learning equation, the proposed learning algorithm with the new iterative learning equation is immune to the observer error. In addition, the value iteration based learning equation is established without storing a series of past data, which could lead to a reduction of demands on the usage of memory storage. Besides, the proposed algorithm eliminates the requirement of repeated finite window integrals, which may reduce the computational load. Moreover, the convergence analysis shows that the estimated control policy converges to the optimal control policy. Finally, a physical experiment on an unmanned quadrotor is given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

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 paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which results from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of tracking a position-related periodic signal for an uncertain nonlinear rotational system. Applying the additive-state-decomposition (ASD) technique decomposes the original uncertain nonlinear system into two subsystems: A primary linear time-invariant system that performs spatial repetitive control, and a secondary nonlinear system that ensures robust stability of the whole system with respect to unknown nonlinear dynamics and exogenous disturbances. This method has four features: (i) The ASD technique provides an effective way to deal with the coupling between the spatial periodicity and other factors (temporal and state-dependent uncertainties and disturbances) in a rotational system. This technique ensures satisfactory tracking and disturbance rejection performance; (ii) A real-time digital implementation of a spatial repetitive controller enables repetitive control with an exact period in the position. This ensures the synchronous execution of repetitive control in the position domain and robust stability in the time domain; (iii) The method of accurate phase compensation in a spatial repetitive controller leads to a significant improvement in steady-state tracking performance; and (iv) An extended-state observer precisely estimates the overall effect of disturbances. Integrating a disturbance estimate into a control input effectively compensates for disturbances. Stability criteria and design algorithms are presented in detail. Finally, experiments of a rotational speed-control system demonstrate the effectiveness of this method. [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]

Batch-to-batch (B2B) or run-to-run (R2R) optimization refers to the strategy of updating the operating parameters of a batch run based on the results of previous runs and exploits the repetitive nature of batch process operation. Although B2B optimization uses feedback from previous batch runs to learn about model uncertainty and improve the operation of future runs, the standard techniques have the limitations of passive learning and being myopic in making adjustments. This work proposes a novel way to use the reinforcement learning approach to embed the active learning feature into B2B optimization. For this, the B2B optimization problem is formulated as a maximization of a long-term performance of repeated batch runs, which are modeled as a stochastic process with uncertain parameters. To solve the resulting Bayes-Adaptive Markov decision process (BAMDP) problem in a near-optimal manner, a policy gradient reinforcement learning algorithm is employed. Through case studies, the behavior and effectiveness of the proposed B2B optimization method are examined by comparing it with the traditional certainty equivalence based B2B optimization method with passive learning. [ABSTRACT FROM AUTHOR]

Abstract The use of feedback-based iterative learning control (ILC) has been widely reported in the literature to reduce large transient errors in the iteration-domain. Using both feedback and feed-forward (ILC) would result in large control input. However, due to the existence of hardware limitation, input constraints exist. Such a hard constraint might lead to unacceptable performances such as unstable trajectories in the time-domain and steady-state error in the iteration-domain. In this paper, a feedback-based ILC design is proposed for a class of linear-time-invariant system in the presence of input constraints. The proposed control scheme consists of two parts: one (feedback) deals with the performance in time domain while the other (ILC) ensures ensure the perfect tracking performance. With the help of composite energy function, it is shown that the proposed algorithm can ensure the perfect tracking performance in the presence of hard input constraints under appropriate assumptions. Simulation results support the theoretical findings. [ABSTRACT FROM AUTHOR]

Abstract This paper studies detectability for switched linear differential–algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present an iterative learning algorithm for pulse-shape control applications of optical chirped pulse amplifiers for ultra-short, high-energy light pulses. For this, we first introduce a general nonlinear and infinite-dimensional mathematical model of chirped pulse amplifiers. By reducing the complexity of this detailed model and reformulating the control task, we are subsequently able to apply inversion-based iterative learning control to track desired output pulses. Using the reduced model to estimate both internal states and unknown parameters yields a fast and simple way of consistently estimating the input–output behavior without relying on a calibrated system model. The effectiveness of the resulting adaptive algorithm is finally illustrated with simulation scenarios on an experimentally validated mathematical model. [ABSTRACT FROM AUTHOR]

Abstract This paper considers the learning consensus problem for heterogenous high-order nonlinear multi-agent systems with output constraints. The dynamics consisting of parameterized and lumped uncertainties is different among different agents. To solve the consensus problem under output constraints, two distributed control protocols are designed with the help of a novel barrier Lyapunov function, which drives the control updating and parameters learning. Both convergence analysis and constraint satisfaction are strictly proved by the barrier composite energy function approach. Illustrative simulations are provided to verify the effectiveness of the proposed protocols. [ABSTRACT FROM AUTHOR]

Privacy protection has become an increasingly pressing requirement in distributed optimization. However, equipping distributed optimization with differential privacy, the state-of-the-art privacy protection mechanism, will unavoidably compromise optimization accuracy. In this paper, we propose an algorithm to achieve rigorous ϵ -differential privacy in gradient-tracking based distributed optimization with enhanced optimization accuracy. More specifically, to suppress the influence of differential-privacy noise, we propose a new robust gradient-tracking based distributed optimization algorithm that allows both stepsize and the variance of injected noise to vary with time. Then, we establish a new analyzing approach that can characterize the convergence of the gradient-tracking based algorithm under both constant and time-varying stepsizes. To our knowledge, this is the first analyzing framework that can treat gradient-tracking based distributed optimization under both constant and time-varying stepsizes in a unified manner. More importantly, the new analyzing approach gives a much less conservative analytical bound on the stepsize compared with existing proof techniques for gradient-tracking based distributed optimization. We also theoretically characterize the influence of differential-privacy design on the accuracy of distributed optimization, which reveals that inter-agent interaction has a significant impact on the final optimization accuracy. Numerical simulation results confirm the theoretical predictions. [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 aims to establish a data-based control design framework for linear iterative learning control (ILC) systems subject to disturbances. Through the proper selection of the test inputs, some output data are collected to exploit two trackability criteria of the desired reference for ILC systems such that the implementability of the perfect tracking objective is ensured, where the persistent excitation condition may not be imposed. Furthermore, two classes of data-based ILC updating laws are presented by incorporating the design idea of the observer, for which the collected input and output data are only leveraged. It is shown that given any trackable desired reference, the perfect tracking objective can be realized for ILC systems under the proposed data-based ILC updating laws in the absence of any model information. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper proposes a unified framework of iterative learning control for typical flexible structures under spatiotemporally varying disturbances. Input constraints and the external disturbances are smoothly tackled through hyperbolic tangent functions. Boundary iterative learning control (BILC) laws are proposed to guarantee the learning convergence. The closed-loop systems can converge to zero along the iteration axis on the basis of time-weighted Lyapunov–Krasovskii-like composite energy functions (CEF). Simulations are implemented to illustrate the effectiveness of the proposed BILC schemes. [ABSTRACT FROM AUTHOR]

In this brief, we develop a novel iterative learning control (ILC) algorithm to deal with trajectory tracking problems for a class of unicycle-type mobile robots with two actuated wheels that are subject to actuator faults. Unlike most of the ILC literature that requires identical reference trajectories over the iteration domain, the desired trajectories in this work can be iteration dependent, and the initial position of the robot in each iteration can also be random. The mass and inertia property of the robot and wheels can be unknown and iteration dependent. Barrier Lyapunov functions are used in the analysis to guarantee satisfaction of constraint requirements, feasibility of the controller, and prescribed tracking performance. We show that under the proposed algorithm, the distance and angle tracking errors can uniformly converge to an arbitrarily small positive constant and zero, respectively, over the iteration domain, beyond a small initial time interval in each iteration. A numerical simulation is presented in the end to demonstrate the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Iterative learning model predictive control (ILMPC) is a technique that combines iterative learning control (ILC) and model predictive control (MPC). The objective is to track a reference trajectory of repetitive processes on a finite time interval while rejecting real-time disturbances. In many repetitive processes, the output is not required to track all the points of a reference trajectory. In this study, we propose a point-to-point ILMPC (PTP ILMPC) technique considering only the desired reference points, and not an entire reference trajectory. In this method, an arbitrary reference trajectory passing through the desired reference values need not be generated. Numerical examples are provided to demonstrate the performances of the suggested approach in terms of PTP tracking, iterative learning, constraint handling, and real-time disturbance rejection. [ABSTRACT FROM AUTHOR]

This work presents an output-feedback policy learning algorithm underlining input–output system data for distributed robust optimal synchronization of heterogeneous multi-agent systems. The output-feedback synchronization problem in the context of this work is formulated via robust output regulation and reinforcement learning modeling the interactions among agents by a zero-sum game. The proposed learning and control structure only requires the local system data for each agent and distributed output data among communicating neighbors. We utilize system-level synchysis for the continuous-time state reconstruction for the distributed learning with convergence and stability proofs under the proposed output-feedback policy for solving the zero-sum game. We further show that policy learning is assured under the proposed data criteria relating to input–output data only rather than any inter-immediate gains from policy iterations. Based on the cooperative robust output regulation, this work gains robustness after the learning is complete and establishes an output data-driven distributed optimal robust synchronization without knowing accurate system dynamics. A numerical example shows the effectiveness of the proposed learning algorithm. [ABSTRACT FROM AUTHOR]

This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the “time” direction, the notion of stability to be evaluated does not require the nonlinear system defining a DRP to be stable in the typical sense. In particular, we study a notion of exponential stability along the discrete iteration dimension of the 2D dynamics, which requires the boundary data for the differential pass dynamics to converge to zero as the iterations evolve. Our main contribution is to show, under standard regularity assumptions, that exponential stability of a DRP is equivalent to that of its linearized dynamics. In turn, exponential stability of this linearization can be readily verified by a spectral radius condition. The application of this result to iterative learning control (ILC) is discussed. Theoretical findings are supported by a numerical simulation of an ILC algorithm. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) is a design technique which can achieve accurate tracking by learning over repeated task attempts. However, long-term stability remains a critical limitation to widespread application, and to-date robustness analysis has overwhelmingly considered structured uncertainties. This paper substantially expands the scope of existing ILC robustness analysis by addressing unstructured uncertainties, a widely used ILC update class, the presence of a feedback controller, and a general task description that incorporates the most recent expansions in the ILC tracking objective. Gap metric based analysis is applied to ILC by reformulating the finite horizon trial-to-trial feedforward dynamics into an equivalent along-the-trial feedback system, as well as deriving relationships to link their respective gap metric values. The results are used to generate a comprehensive design framework for robust control design of the interacting feedback and ILC loops. This is illustrated via application to rehabilitation engineering, an area where they meet an urgent need for high performance in the presence of significant modeling uncertainty. [ABSTRACT FROM AUTHOR]

This paper studies the robust convergence properties of iterative learning control (ILC) for single-input, single-output (SISO), nonrepetitive systems subject to iteration-dependent uncertainties that arise in not only initial states and external disturbances but also plant models. Given an extended relative degree condition, it is possible to propose necessary and sufficient (NAS) conditions for robust ILC convergence. The tracking error bound is shown to depend continuously on the bounds of the iteration-dependent uncertainties. When the iteration-dependent uncertainties are bounded, NAS conditions exist to guarantee bounded system trajectories and output tracking error. If the iteration-dependent uncertainties converge, then NAS conditions ensure bounded system trajectories and zero output tracking error. The results are also extended to a class of affine nonlinear systems satisfying a Lipschitz condition. Simulation tests on a representative batch process demonstrate the validity of the obtained robust ILC convergence results. [ABSTRACT FROM AUTHOR]

We derive frequency-domain criteria for the convergence of linear iterative learning control (ILC) on finite-time intervals that are less restrictive than existing ones in the literature. In particular, the former can be used to establish the convergence of ILC in certain cases where the latter are violated. The results cover ILC with non-causal filters and provide insights into the transient behaviors of the algorithm before convergence. We also stipulate some practical rules under which ILC can be applied to a wider range of applications. [ABSTRACT FROM AUTHOR]

In this work, we present an iterative design method for a coalitional networked control scheme for linear systems. In this scheme, the links in the communication network are enabled or disabled depending on their contribution to the overall system performance. Likewise, the control law is adapted to these changes. In particular, new conditions are included at the design phase, in order to consider constraints on the links and the agents regarding the game theoretical tools utilized while optimizing the matrices that define the controller. [ABSTRACT FROM AUTHOR]

The networked Susceptible–Infected–Susceptible (SIS) model is one of the well-developed models for epidemic spreading processes in networked systems. For a network that has an unstable healthy state, and follows the networked SIS model, a problem of interest is to stabilize the healthy state by increasing the curing rates of individuals, while minimizing the total cost associated with the additional curing rates over the network. Here this minimum control budget problem is reformulated as a standard semidefinite programming problem and an iterative algorithm is developed for determining the optimal additional curing rates for each agent in the network. We address arbitrary undirected topologies, with both symmetric and asymmetric infection rates. For a number of topologies, solutions have been provided for the case of uniform curing and infection rates for all possible ranges of the effective infection rate. Moreover, we have investigated the case of discrete-time SIS models and have shown that the algorithm developed based on the continuous-time model can be extended to this case. Based on the daily COVID-19 infections over the USA, the curing and infection rates have been estimated for a simulation scenario. Using these simulations, the algorithm is shown to have lower complexity than the well-known SDPT3 tool, and to have orders of magnitude lower computational and memory requirements. [ABSTRACT FROM AUTHOR]

Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear systems and adopt a Wasserstein penalty to address the distribution uncertainty of additive stochastic disturbances. By constructing an equivalent deterministic game of the penalized LQR problem, we propose a Q-learning method with convergence guarantees to learn an optimal minimax controller. [ABSTRACT FROM AUTHOR]

In this brief, continuous-time nonlinear systems with extended matching uncertainties are considered. The problem of designing a state-feedback adaptive learning control of reduced complexity — just including a single adaptive learning estimation scheme in the upper subsystem and a high-gain proportional action in the input channel — is addressed. By properly setting the control parameters, exponential output tracking of (sufficiently smooth) periodic reference signals with a known period is achieved. Fourier series expansions are used and estimates of the resulting Fourier coefficients are continuously adapted based on the persistency of excitation conditions that naturally hold due to the orthogonal nature of the sinusoidal basis functions. [ABSTRACT FROM AUTHOR]

This paper considers the problem of linear quadratic tracking control (LQTC) with a discounted cost function for unknown systems. The existing design methods often require the discount factor to be small enough to guarantee the closed-loop stability. However, solving the discounted algebraic Riccati equation (ARE) may lead to ill-conditioned numerical issues if the discount factor is too small. By singular perturbation theory, we decompose the full-order discounted ARE into a reduced-order ARE and a Sylvester equation, which facilitate designing the feedback and feedforward control gains. The obtained controller is proved to be a stabilizing and near-optimal solution to the original LQTC problem. In the framework of reinforcement learning, both on-policy and off-policy two-phase learning algorithms are derived to design the near-optimal tracking control policy without knowing the discount factor. The advantages of the developed results are illustrated by comparative simulation results. [ABSTRACT FROM AUTHOR]

This paper aims to deal with the control analysis and synthesis problem of data-driven learning, regardless of unknown plant models and iteration-varying uncertainties. For the tracking of any desired target, a Kalman state–space approach is presented to transform it into two robust stability problems, which bridges a connection between data-driven control and model-based control. The proposed approach makes it possible to employ the extended state observer (ESO) in the design of data-driven learning to overcome the effect of iteration-varying uncertainties. It is shown that ESO-based data-driven learning ensures model-free systems to achieve the robust tracking of any desired target, and particularly is applicable for realizing the accurate tracking objective subject to the iteration-varying uncertainties with quasi-disappearing variations. Further, our developed results apply to iterative learning control, which is also verified by an example. [ABSTRACT FROM AUTHOR]

In this paper, for a linear system with unknown input, a novelty unknown input observer (UIO) which can produce the asymptotic system state estimation and unknown input reconstruction simultaneously via interval observer is developed. Firstly, under the assumption that the boundary of the unknown input is known, the interval estimation of the output vector is obtained by designing an interval observer. Secondly, by using the upper and lower boundary estimations of the output vector, an algebraic relationship between the unknown input and the system state is set up. Thirdly, based on the algebraic relationship, a Luenberger-like state observer together with an algebraic unknown input reconstruction is designed to form a UIO. Moreover, a UIO is designed for a time-delay system with unknown input by applied the proposed UIO on the time-delay system directly, showing the advantages of the proposed UIO. Finally, simulation examples and some comparisons to the existing results are given to illustrate the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses an optimal output regulation problem for linear time-invariant systems with unknown dynamics. First, a new augmented virtual system is designed to replace the original system and the internal model. Then, by incorporating the data from the augmented virtual system with adaptive dynamic programming (ADP) method, a new iterative learning equation without requiring integral operations or constructing internal model in advance is proposed for establishing the data-driven learning algorithm. Compared with existing ADP-based learning algorithms for linear continuous-time systems, the proposed learning algorithm relaxes both requirements on recording the complete continuous data and setting an initial stabilizing control policy. Finally, the effectiveness of the proposed algorithm is illustrated by an example. [ABSTRACT FROM AUTHOR]

This paper considers fault estimation (FE) and fault-tolerant control (FTC) for linear parameter varying systems with actuator and sensor faults, uncertainties, and disturbances. The inevitable coupling between the FE and FTC functions needs to be taken into account in the design to ensure the overall FE-based FTC closed-loop system performance and robustness. This paper proposes an iterative strategy to achieve the robust integration of FE and FTC by leveraging the concepts of Separation Principle and Small Gain Theorem. The iterative algorithm involves solving multi-objective linear matrix inequality optimisation problems at each iteration and has finite-step convergence guarantee. Efficacy of the proposed algorithm and its advantages over the existing works are illustrated through numerical simulations. [ABSTRACT FROM AUTHOR]

Hybrid systems form a particularly rich class of dynamical systems based on the combination of multiple continuous subsystems and a discrete mechanism deciding which one of these is active at a given time. Their identification from input–output data involves nontrivial issues that were partly solved over the last twenty years thanks to numerous approaches. However, despite this effort, estimating the number of modes (or subsystems) of hybrid systems remains a critical and open issue. This paper focuses on switched linear systems and proposes an analysis of their identification based on statistical learning theory. This leads to new theoretically sound bounds on the prediction error of switched models on the one hand, and a practical method for the estimation of the number of modes on the other hand. The latter is inspired by the structural risk minimization principle developed in statistical learning for model selection. The proposed analysis is conducted under various assumptions on the model class and regularization schemes for which new algorithms are presented. Numerical experiments are also provided to illustrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Motivated by the goal of learning controllers for complex systems whose dynamics change over time, we consider the problem of designing control laws for systems that switch among a finite set of unknown discrete-time linear subsystems under unknown switching signals. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the proposed online implementation is therefore the ability of the controller to automatically adjust to changes in the operating mode of the system. We show that the proposed control mechanism guarantees stability of the closed-loop switched linear system provided that the switching is slow enough. Effectiveness of the proposed design technique is illustrated for two aerospace applications. [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]

Certain control applications require that performance variables are explicitly distinguished from measured variables. The performance variables are not available for real-time feedback. Instead, they are often available after a task. This enables the application of batch-to-batch control strategies such as Iterative Learning Control (ILC) to the performance variables. The aim of this paper is first to show that the pre-existing ILC controllers may not be directly implementable in this setting, and second to develop a new approach that enables the use of different variables for feedback and batch-to-batch control. The analysis reveals that by using pre-existing ILC methods, the ILC and feedback controllers may not be stable in an inferential setting. Therefore, the complete closed-loop system is cast in a 2D framework to analyze stability. Several solution strategies are outlined. The analysis is illustrated through an application example in a printing system. Finally, the developed theory also leads to new results for traditional ILC algorithms in the common situation where the feedback controller contains a pure integrator. [ABSTRACT FROM AUTHOR]

This article studies iterative learning control (ILC) where multiple heterogeneous linear subsystems (with potentially different individual dynamics) update their input simultaneously based on the error in a collaboratively controlled desired output. A challenge is that convergence of iterative learning for each individual subsystem (when the other subsystems are not learning) may not guarantee convergence under collaborative-(co-) learning. This work proposes an update-partitioning approach for co-learning and demonstrates convergence whenever the individual, iterative learning for each subsystem is convergent. The main contribution of this work is to show that any unity partition (where the sum of the partition is one) of the update law ensures convergence of the co-learning. Since the time partitioning of the update can be chosen independent of the individual learning (convergence) rate of the subsystems, the proposed approach enables the separate design of each individual subsystem’s input-update law followed by conjoining of the individual update laws for co-learning using the partitioning approach. Additionally, an intermittent time partitioning is developed when the desired trajectory is not known to all (but only some) of the co-learning subsystems. [ABSTRACT FROM AUTHOR]

Iterative Learning Control (ILC) can significantly enhance the performance of systems that perform repeating tasks. However, small variations in the performed task may lead to a large performance deterioration. The aim of this paper is to develop a novel ILC approach, by exploiting rational basis functions, that enables performance enhancement through iterative learning while providing flexibility with respect to task variations. The proposed approach involves an iterative optimization procedure after each task, that exploits recent developments in instrumental variable-based system identification. Enhanced performance compared to pre-existing results is proven theoretically and illustrated through simulation examples. [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]

Motivated by the prototypical problem of a marching band, this paper studies a class of multi-agent formation problems characterized by two features: (i) the agents attempt to complete a finite duration, coordinated formation task with high precision by repeating the task and (ii) the feedback mechanism by which the agents control their motions is based on relative differences between nearest neighbors, but the underlying graph topology can vary both during a repetition and from one repetition to the next. Adopting the framework of iterative learning control leads to the notion of multi-agent networks with switching topologies along two directions: a finite time axis and an infinite iteration axis. For such systems, we present distributed algorithms using nearest neighbor information whose exponential convergence can be demonstrated. It is shown that as the number of repetition increases, the relative formation between agents approaches the desired formation exponentially fast if and only if at each time step, the union of the interaction graphs has a spanning tree frequently enough along the iteration axis. That is, the agents can “learn to cooperate.” The remarkable point of this result is that it is not necessary to have a spanning tree at any specific time step or iteration in order for the system to converge. Two examples are given to illustrate the ideas, including a general example, where through iteration the agents can form a desired formation, and a special case of it, where an additional agent specifies a reference to regulate the formation shape simultaneously. [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]

In this paper, a novel asynchronous sliding mode-based learning control is proposed for a class of discrete-time semi-Markov jump systems, in which the probability density function of sojourn-time is dependent on two consecutive modes. The asynchronous switching characteristic is employed for the nonsynchronization between the controller and the jump modes. Based on the discrete-time semi-Markov kernel and multiple-Lyapunov functions, sufficient conditions are provided to guarantee the σ -error mean-square stability of the sliding mode dynamics. Furthermore, a recursive sliding mode learning controller is designed such that the sliding modes can be driven onto the designed sliding surface and the chattering caused by the asynchronous switching and mode jump can be effectively suppressed. Finally, numerical simulations on the continuous stirred tank reactor system are given to demonstrate the effectiveness and potential of the proposed techniques. [ABSTRACT FROM AUTHOR]

The standard assumption that a measurement signal is available at each sample in iterative learning control (ILC) is not always justified, e.g., when exploiting time-stamped data from incremental encoders or in systems with data dropouts. The aim of this paper is to develop a computationally tractable ILC framework that is capable of exploiting intermittent data while maintaining favourable properties, including monotonic convergence. A controllability and observability analysis of the intermittent ILC framework leads to appropriate monotonic convergence conditions which allow for missing data. These conditions lead to a new explicit ILC controller design independent of the sampling instances, which is reminiscent of gradient-descent ILC. The approach is demonstrated on both an intuitive example and a practically relevant example which exploits time-varying timestamped data from an incremental encoder. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with formation control problems for multi-agent systems with nonlinear dynamics and switching network topologies. Using the nearest neighbor knowledge, a distributed algorithm is constructed by employing the iterative learning control approach. Sufficient conditions are given to obtain the desired relative formations of agents, which benefits from the strict positiveness of products of stochastic matrices. It is shown that the derived results can effectively work, although the network topologies dynamically change along both time and iteration axes and the corresponding directed graphs may not have spanning trees. Such result is also illustrated via numerical simulations. [Copyright &y& Elsevier]

This paper deals with the distributed iterative learning control (ILC) problem of leaderless consensus in a network of heterogeneous nonlinear agents. For a general case that the topology graph is dynamically changing with respect to both iteration and time axes, an ILC-based consensus protocol is designed for each agent by utilizing its control input and neighboring information from the last iteration. It is shown that under a basic joint spanning tree condition, the states of all agents can exponentially agree on a common trajectory along the iteration axis. Interestingly, by the appropriate design of the agents' dynamics, it is found that the consensus trajectory and the network state can approach the unique optimal point of a convex optimization problem as the time evolves. Simulations demonstrate the validity of the proposed algorithms and theoretical analysis. [ABSTRACT FROM AUTHOR]

In the attitude tracking control tasks of rigid-body systems, initial alignment errors are recognized as one of the main factors that hinder the effective controller design and thus the control accuracy improvement. To overcome this difficulty, we develop a novel adaptive iterative learning control (ILC) scheme to achieve the attitude tracking control tasks with high precision for rigid bodies. Owing to the newly employed deadzone mechanism in the parametric updating law, the proposed adaptive ILC scheme is able to deal with initial alignment errors properly without imposing extra requirements to the system dynamics. Moreover, by utilizing the quaternion-based description in the system dynamics, various uncertainties, including external iteration-varying disturbances and unknown system parameters, can be addressed together by a single scalar estimation scheme. The convergence of the proposed adaptive ILC scheme is analyzed rigorously with a Lyapunov-like theory by virtue of newly introducing a modified composite energy function. In addition, to demonstrate its effectiveness, the proposed adaptive ILC method is applied to the attitude tracking of a spacecraft, which shows excellent control performances despite various uncertainties. [ABSTRACT FROM AUTHOR]