Using ``modulating functions'', we sample one sufficiently informative input-output trajectory produced by a controllable, linear, continuous time-invariant system. We show that a matrix constructed from such samples can be used to compute every input-output trajectory of the system. Using geometric techniques, we show that informativity of the input-output trajectory is preserved by sampling using modulating functions on almost every set of sampling instants. We apply our results to the problem of data-driven simulation of continuous-time systems. Since our approach provides an algebraic characterisation of all trajectories of the system, it can be implemented in existing data-driven predictive control and iterative learning control frameworks.

In a wind farm, cooperative turbine control is crucial for mitigating wake interactions between turbines and significantly improving the overall power output. However, accurately modeling wake interactions is very challenging for complex-terrain wind farms due to the complexity of the interactions. Many data-driven wind farm power optimization methods have been developed. These methods however typically require large amounts of real-time measurements due to their slow convergence, resulting in lower power performance, especially for large-scale wind farms. This paper proposes a decentralized data-driven wind farm power optimization method using simultaneous perturbation stochastic approximation. The presented method has fast convergence and thus can obviously enhance the power output of large-scale wind farm only by real-time power generation data. It does not need any extra communication channels between turbines (required by distributed algorithms) that is not always possible or desirable in practice. Furthermore, the method can adapt to changing turbine configurations due to decentralized design and is capable of addressing time-varying wind conditions through a hierarchical framework. Simulation tests demonstrate the effectiveness of the proposed method for the power optimization of the large-scale wind farm.

We employ Chebyshev polynomial bases and approximation theory to solve data-driven continuous-time iterative learning control (ILC) problems. Our approach is based on the transformation of continuous-time system trajectories into the discrete sequences consisting of their Chebyshev coefficients. Using one “sufficiently informative” system trajectory one can compute every system trajectory without using an explicit system model and thus one can solve a range of ILC design problems, including norm-optimal ILC, point-to-point tracking, constrained norm-optimal, and parameter-optimal ILC design. We present results using a gantry robot system model as an exemplary application to demonstrate the proposed design framework.

The subject of this paper is aerodynamic load control for wind turbines, which has the potential to increase power extraction efficiency, including economic competitiveness when compared to other sources of alternative energy. The general feasibility of this approach is developments in sensor and actuator technology, which enables their embedding into the rotor blades. Minimizing lift fluctuations due to disturbances is feasible when combined with active control to modify the blade section aerodynamics. Previous research has shown that it is possible to combine such an actuator sensor combination with a control law for this application. In general, this approach will require a model-based design, and previously published results have shown that proper orthogonal decompositions can produce finite-dimensional models from the computational fluid dynamics-based representations of the defining partial differential equations and enable control law design.

High-performance consensus tracking problem, which requires all the subsystems operating repetitively to track a desired reference, has found a number of important applications in the last decade. To achieve the high-performance requirement, recent designs use iterative learning control (ILC) to avoid the use of an accurate model that is usually required in conventional control methods. However, most of the existing distributed ILC algorithms have poor scalability (i.e., they will have difficulties when applied to large-scale and/or changing networks). Their performance (e.g., monotonic tracking error norm convergence) is heavily dependent on the choice of control parameters and they cannot handle general point-to-point tasks either. To address these limitations, this article proposes a novel distributed ILC algorithm using the well-known norm optimal ILC framework. By designing a performance index that explicitly incorporates the convergence performance, the resulting ILC design guarantees the tracking error norm converges monotonically to zero, which is appealing in practice. Using the alternating direction method of multipliers, a distributed implementation of the algorithm is obtained, where each subsystem's input is updated locally, such that the algorithm can be applied to large-scale and/or changing networks without any issues. Furthermore, the proposed algorithm can be extended to solve point-to-point consensus tracking problem, and applied to both homogeneous and heterogeneous networks, as well as nonminimum phase systems, which is of great practical relevance. Convergence and robustness of the algorithms are analyzed rigorously. Numerical examples are given to verify the effectiveness of the proposed algorithms.

We present a data-driven Iterative Learning Control (ILC) scheme for continuous-time systems using a 'Gramian' approach. We present some numerical experiments using Chebyshev Polynomial Orthogonal Bases (CPOB) in both model-driven and data-driven ILC for continuous-time systems. We show that in the model-driven ILC case, the utilisation of a CPOB framework results in improved performance over discrete-time methods for applications requiring high precision. In the data-driven case, the advantages of a CPOB approach are less evident and we discuss some of the open problems being investigated. Copyright (c) 2025 The Authors.

Our work investigates how social robots can efficiently collaborate with human users in a user-aware manner, minimising the generated frustration in human colleagues, thus enhancing their experience. As part of this, we develop a useraware framework for human-robot collaborative learning. We model users' frustration during human-robot interactions based on recent interactions inspired by Psychological principles and develop different frustration-aware interactive preference learning and decision-making models using multi-armed bandit and knapsack methods. Evaluating our approach, 1) we conducted simulated experiments on realistic human-behaviour datasets and 2) a user-study in which participants worked with a TIAGo Steel humanoid robot on a collaboration task using frustration- aware and non frustration-aware (Upper Confidence Bounds and Instruction-based) models. We demonstrate that when collaborating with the frustration-aware robot, users completed the collaboration task 9.04% faster and using 20.54% less number of verbal interactions, with user questionnaire responses reporting less frustration experienced compared to the baseline approaches. Additionally, we create a multimodal dataset containing over 6 hours of human-robot interactions displaying various explicit and implicit user responses.

For control problems that repeat with resets, such as batch processing and robotic trajectory tracking, iterative learning control is an established high-performance control design method. Fast learning is achievable with model-based schemes when the dynamics of the system are known to be described accurately by a prior model, but such accurate models are often difficult or expensive to obtain. The field of sensori-motor control studies the motion control systems of humans and other animals, which appear to quickly achieve accurate trajectory tracking without detailed prior knowledge. In this paper, we present a novel modular-based design inspired by the learning behaviour of these sensorimotor control systems. The ‘modules’ used are a generalisation of pre-defined orthonormal basis functions, and the parameters of these modules are learnt using an alternating direction method of multipliers. We analyse the convergence properties of the proposed design rigorously, and also discuss how this approach may be successfully applied when the reference changes over the trials. Generalising learnt skill in this way is a current challenge in iterative learning control design, and is a key benefit of the modular structure of sensorimotor-inspired schemes.

Iterative learning control (ILC) improves the tracking performance of a system working in a repetitive mode by learning from previous trials. The existing ILC algorithms can achieve high performance but often with the use of a system model or careful parameter tuning. To address this limitation, we propose an alternative approach: stochastic zeroth-order (ZO) optimisation-based ILC. The proposed algorithm can achieve good convergence performance without using a system model or deliberate parameter tuning. A convergence analysis is provided, and the effectiveness of the proposed algorithm is verified by a simulation example.

Inverse Synthetic Aperture Radar (ISAR) images are a popular and effective tool used in the modern age to identify moving targets, particularly in the airborne and space arenas. Much research has been undertaken on the automatic recognition of targets in this area, applying computer vision algorithms to the two dimensional image maps produced when measuring targets via this method. In this document we discuss an on-going programme of work to fully automate space target recognition, and specifically here outline a methodology proposed for automating the identification of specific features of space targets, in order to aid the confidence of an operator making the final decisions. Large scale results are still currently being collected for the project.

Iterative learning control is a feedforward control scheme designed for systems operating in a repetitive setting to achieve high performance tracking for a single fixed reference, with fast learning of a control signal often only achieved when an accurate model of the system is known. On the other hand, biological control systems achieve fast learning without accurate a priori modelling, by learning dynamics and control signals simultaneously. Sensorimotor control studies the motion of humans and animals, and a key observation from this field is that a modular structure facilitates the generalisation of learnt skill, which inspires a new modular approach to iterative learning control design that accurately tracks trial-varying references.

This paper addresses high-performance consensus tracking of repetitively operating networked dynamical systems using an iterative learning control (ILC) algorithm. It circumvents the need for precise model information in traditional methods and guarantees the high-performance by the predictive framework with a novel performance index that takes into account both current and future performance. The proposed algorithm ensures geometric convergence of the tracking error norm to zero and can be applied to both heterogeneous and non-minimum-phase systems. A distributed implementation of the algorithm is developed using the Alternating Direction Method of Multipliers, with detailed convergence analysis and numerical examples confirming its effectiveness.

We present a data-driven, model-free approach to norm-optimal control of discrete repetitive processes, exploiting Willems’ fundamental lemma. The algorithm is described in detail, and a rigorous analysis of its convergence properties is performed. A numerical example is provided to demonstrate the effectiveness of the proposed design methodology.

This paper gives a tutorial on iterative learning control nearly five decades after what is widely regarded as the first substantive paper in the literature. The focus is on algorithm development under a number of general headings (linear, optimization, frequency domain, and nonlinear), together with supporting experimental validation/industrial applications and also applications in healthcare.

We study data-driven analysis and control of 2D Fornasini-Marchesini second models. We give necessary and sufficient conditions for the data to be informative for identification, and state a 2D “fundamental lemma". We propose a data-driven approach for stability verification and state-feedback stabilization via LMIs.

High performance collaborative tracking problem, requiring a group of independent subsystems to generate a global output that can precisely track the desired reference in a repetitive manner, has found lots of applications in practice. However, for such an important control task, existing iterative learning control (ILC) methods have not considered the constraint on each subsystem's output, which leads to potential risk within the control process. This paper proposes a novel optimisation based ILC method to address the high performance collaborative tracking problem with output constraints. The proposed ILC framework can guarantee not only each subsystem's output constraint is always satisfied during the control process, but also the monotonic convergence of a well-defined performance index to a possibly minimum value. To avoid huge computational complexity for large scale systems, we further apply the idea of the alternative direction method of multipliers (ADMM) to implement the proposed ILC frame-work in a decentralised manner, which allows the resulting decentralised methods to be applied to large scale and changing systems. Moreover, the decentralised ILC method proposed in this paper is suitable for non-minimum phase, heterogeneous and/or homogeneous systems, which is appealing in practice. Convergence properties of the proposed ILC algorithms are analysed rigorously, and numerical examples are given to demonstrate the algorithms' effectiveness.

In a wind farm, the interactions between turbines caused by wakes can significantly reduce the power output of the wind farm. Accurately modeling the interactions is challenging due to the highly complex nature of the wakes and this limits the performance of model-based wind farm power optimization methods. There are also data-driven approaches, which do not require a system model. However, they generally require a large number of measurement data and the convergence speed can be slow. To address these limitations, this article proposes a model-guided learning (MGL) method for wind farm to improve its power output by leveraging the knowledge of the available simplified power generation model and learning from the real-time power generation data. The proposed method can quickly increase the power output of the wind farm, guarantee implemented control actions to satisfy the control constraints of all turbines, and have the ability to find the optimal solution of the power optimization problem. The presented method is then extended to deal with time-varying wind conditions using a hierarchical framework. Simulation results indicate that the proposed scheme can efficiently improve the power output of the wind farm in different wind conditions compared with some benchmarks. It shows a power efficiency gain of 2.5% over greedy policy and 1.2% than the model-based gradient method in given complex wind conditions, which are substantial improvements in the performance for the considered wind farm power optimization problem.

We present some preliminary ideas on a data-driven Model Predictive Control framework for continuous-time systems. We use Chebyshev polynomial orthogonal bases to represent system trajectories and subsequently develop a data-driven continuous-time version of the classical Model Predictive Control algorithm. We investigate the effects of the parameters in our framework with two numerical examples and draw comparison to model-driven MPC schemes.

Iterative learning control is a control design method for high performance tracking applications. In this paper a novel mechanism for accelerating the convergence of a well-known Norm Optimal Iterative Learning Control (NOILC) Algorithm is presented by modifying the reference signal each iteration using the previously measured tracking error. The change is equivalent to successive application of a gradient and NOILC iteration and can be interpreted as an augmentation of the 'feedback plus feedforward' structure of NOILC by adding further 'feedforward' data from the last iteration. The change is interpreted in terms of the spectrum of the error update operator and the annihilation of spectral components of the error signal. Convergence of the proposed algorithm is analysed rigorously and numerical examples are given to demonstrate the effectiveness of the proposed method.

Robust design to account for model uncertainty and other undesirable performance limitations, such as the effects of disturbances, is as relevant to iterative learning control (ILC) as other areas. This chapter considers robust control based on a linear approximate or nominal model with both the frequency and time domain analysis. It considers robustness of the simple structure inverse and adjoint ILC laws with supporting experimental results, and considers the use of an H ∞ setting. It is possible to give a transfer-function interpretation of the convergence result for the inverse ILC law. The synthesis of ILC laws in an H ∞ setting was considered, using control action that combined current trial error feedback and feedforward from the previous trial. This research gave guidelines for choosing the weighting functions required for H ∞ design.