Optimization-based Iterative Learning Control Research Articles

Input Mapping Design for Batch-to-Batch Optimization With Limited Memory

This brief discusses data-driven design techniques for batch-to-batch optimization problems and proposes a new input-mapping-based online uncertainty compensation method for optimization-based iterative learning control (ILC) with limited memory. Since process uncertainties are generally inevitable, we collect historical data that incorporates past inputs and outputs to provide more insight into plant uncertain dynamics, resulting in a more accurate optimization model for optimal ILC solution. Instead of learning from a single step, our proposed method maintains a memory of the latest executed steps and updates the ILC solution using a linear combination of the memory and quadratic programming. A rigorous theoretical analysis shows that such a design provides robust benefits as well as asymptotic and monotonic stability properties under mild conditions. Finally, we demonstrate our design through an illustrative numerical example.

On Robustness in Optimization-Based Constrained Iterative Learning Control

Iterative learning control (ILC) is a control strategy for repetitive tasks wherein information from previous runs is leveraged to improve future performance. Optimization-based ILC (OB-ILC) is a powerful design framework for constrained ILC where measurements from the process are integrated into an optimization algorithm to provide robustness against noise and modelling error. This paper proposes a robust ILC controller for constrained linear processes based on the forward-backward splitting algorithm. It demonstrates how structured uncertainty information can be leveraged to ensure constraint satisfaction and provides a rigorous stability analysis in the iteration domain by combining concepts from monotone operator theory and robust control. Numerical simulations of a precision motion stage support the theoretical results.

A Gaussian Process Iterative Learning Control for Aircraft Trajectory Tracking

This article proposes a recursive Gaussian process regression with a joint optimization-based iterative learning control algorithm to estimate and predict disturbances and model uncertainties affecting a flight. The algorithm proactively compensates for the predicted disturbances, improving precision in aircraft trajectory tracking. Higher precision in trajectory tracking implies an improvement of the aircraft trajectory predictability and, therefore, of the air traffic management system efficiency. Airlines can also benefit from this higher predictability by reducing the number of alterations when following their designed trajectories, which entails a reduction of costs and emissions. The iterative learning control algorithm is divided into two steps: first, a recursive Gaussian process regression estimates and predicts perturbations and model errors with no need for prior knowledge about their dynamics and with low computational cost, and second, this information is used to update the control inputs so that the subsequent aircraft intending to fly the same planned trajectory will follow it with greater precision than the previous ones. This method is tested on a simulated commercial aircraft performing a continuous climb operation and compared to an iterative learning algorithm using a Kalman filter estimator in a similar scenario. The results show that the proposed approach provides 62 and 42% precision improvement in tracking the desired trajectory, as compared to the Kalman filter approach, in two experiments, where no prior knowledge of the unmodeled dynamics was available, also achieving it in less iterations.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control (ILC) problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties. A new optimization-based method is proposed to design and analyze adaptive ILC, for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices. It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC, where the boundedness of system trajectories and estimated parameters can be ensured, regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties. Two simulation tests, especially implemented for an injection molding process, demonstrate the effectiveness of our robust optimization-based ILC results.

A Two-Step Optimization-Based Iterative Learning Control for Quadrotor Unmanned Aerial Vehicles

Abstract This paper presents a two-step optimization-based design method for iterative learning control and applies it onto the quadrotor unmanned aerial vehicles (UAVs) trajectory tracking problem. Iterative learning control aims to improve the tracking performance through learning from errors over iterations in repetitively operated systems. The tracking errors from previous iterations are injected into a learning filter and a robust filter to generate the learning signal. The design of the two filters usually involves nontrivial tuning work. This paper presents a new two-optimization design method for the iterative learning control, which is easy to obtain and implement. In particular, the learning filter design problem is transferred into a feedback controller design problem for a purposely constructed system, which is solved based on H-infinity optimal control theory thereafter. The robust filter is then obtained by solving an additional optimization to guarantee the learning convergence. Through the proposed design method, the learning performance is optimized and the system's stability is guaranteed. The proposed two-step optimization-based design method and the regarding iterative learning control algorithm are validated by both numerical and experimental studies.

Efficient Implementation of a Binary Iterative Learning Control

Iterative learning control (ILC) is an adequate control approach to handle various types of cyclic control tasks. However, when in each iteration the calculation of the control trajectory requires the solution of a high dimensional constrained quadratic program, the algorithm is bound to be infeasible for real-time applications with very small cycle lengths in the order of milliseconds due to the prohibitively large computational cost. In this contribution, an approach is presented to reduce the computational burden to solve an optimization-based iterative learning control that is restricted to a binary domain by orders of magnitude. The method is suitable for control trajectories that contain only few 1’s, but a large number of 0’s in each iteration for a specific class of problems, e.g., for cyclic firing synchronization of combustion tubes.The presented setup is tested experimentally at an acoustic mock-up of an annular pulse detonation combustor to determine an appropriate fire synchronization. More specifically, it is used to adjust the firing pattern of multiple simulated combustion tubes in order to reduce pressure fluctuations measured downstream in an annular plenum, which is a prerequisite to apply such a new thermodynamically efficient combustion process in a real gas turbine.

A tube feedback iterative learning control for batch processes

Optimization-based iterative learning control (OILC) has been widely applied to batch processes due to its fast convergence, good control performance and ability to handle constraints. However, how to guarantee constraint satisfaction and convergence of tracking error in the presence of unknown system nonlinearity remains open in the framework of OILC. It is important to address this issue since unknown nonlinearity is common in practice and detrimental to good control performance. In this paper, we propose a tube feedback OILC to investigate the applicability of linear-model based control strategy on batch processes with an unknown nonlinear term. First, a state feedback control law is designed to stabilize the system. The stabilized system is then decomposed into two subsystems: repeatable and unrepeatable subsystems; Second, an invariant set of states corresponding to the unrepeatable subsystem is computed, based on which an OILC is further developed for the repeatable subsystem to improve the control performance. Meanwhile, the feedback controller steers the states within a tube around the trajectory of OILC. In this way, convergence and constraint satisfaction are ensured simultaneously. Compared with the currently existing methods, the proposed method has the following advantages: (1) generality covering both stable and unstable systems; (2) low computation complexity; and (3) rigorous stability. The simulation results on injection molding velocity control demonstrate that the proposed method has superior performance.

Predictive optimal iterative learning control

A new optimization-based iterative learning control algorithm is proposed and its properties derived. An important characteristic of this algorithm is that it uses present and future predicted errors to compute the current control, in a similar manner to model-based predictive control using a receding horizon. In particular, it enables the algorithm designer to achieve good control over convergence rate. The actual implementation has a multimodel structure but uses standard linear quadratic regulator methods for a causal formulation (in the iterative learning sense) of what is originally a non-causal algorithm. The results are illustrated by simulations.