Robust Learning Model-Predictive Control for Linear Systems Performing Iterative Tasks

Rosolia, Ugo; Zhang, Xiaojing; Borrelli, Francesco

doi:10.1109/tac.2021.3083559

Cited by 16 publications

(8 citation statements)

References 53 publications

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“…Applications of the DDMPC framework range from the mechatronics [120] to home assistance appliances [121]. The reader is referred to the following work [116], [122], [123] for details on the guarantees of the robustness of the DDMPC framework. An overview of the literature on DDMPC is given in Table 4, and the applications of DDMPC to control problems are tabulated in Table 5.…”

Section: B Data-driven Model Predictive Controlmentioning

confidence: 99%

Toward Data-Driven Optimal Control: A Systematic Review of the Landscape

2022

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This literature review extends and contributes to research on the development of data-driven optimal control. Previous reviews have documented the development of model-based and data-driven control in isolation and have not critically reviewed reinforcement learning approaches for adaptive data-driven optimal control frameworks. The presented review discusses the development of model-based to model-free adaptive controllers, highlighting the use of data in control frameworks. In data-driven control frameworks, reinforcement learning methods may be used to derive the optimal policy for dynamical systems. Attractive characteristics of these methods include not requiring a mathematical model of complex systems, their inherent adaptive control capabilities, being an unsupervised learning technique and their decision-making abilities, which are both an advantage and motivation behind this approach. This review considers previous reviews on these topics, including recent work on data-driven control methods. In addition, this review shows the use of data to derive system dynamics, determine the control policy using feedback information, and tune fixed controllers. Furthermore, the review summarises various data-driven methods and their corresponding characteristics. Finally, the review provides a taxonomy, a timeline and a concise narrative of the development of model-based to model-free data-driven adaptive control and underlines the limitations of these techniques due to the lack of theoretical analysis. Areas of further work include theoretical analysis on stability and robustness for data-driven control systems, explainability of black-box policy learning techniques and an evaluation of the impact of the extension of system simulators to include digital twins.INDEX TERMS Data-driven control, adaptive control, model-free, model-based, model predictive control, optimal control, learning-based control, systematic review. A. CONTINUOUS-TIME AND DISCRETE-TIME CONTROL SYSTEMSBased on whether the signal used in a control system is continuous or discrete determines whether the control system is a continuous-time or discrete-time system. A continuoustime control system has all the system's variables defined as a function of time. Conversely, if the system variables are defined at distinct discrete-time steps, then the system is a discrete-time control system [8].

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Section: B Data-driven Model Predictive Controlmentioning

confidence: 99%

Toward Data-Driven Optimal Control: A Systematic Review of the Landscape

2022

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“…and the total nominal iteration cost for iteration j is V j 0→∞ (x j 0 ). Finally, we introduce the barycentric function from [24] and define it based on the nominal state as in [25]:…”

Section: E Terminal Costmentioning

confidence: 99%

“…In [20], the terminal cost and terminal constraint set are determined from data of past iterations with the goal to guarantee stability and constraint satisfaction of the MPC. Formal guarantees have been derived for special cases such as LTI systems [24] and robust learning-based model predictive control (RL-MPC) for LTI systems with bounded process noise [22], [25].…”

Section: Introductionmentioning

confidence: 99%

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RLO-MPC: Robust Learning-Based Output Feedback MPC for Improving the Performance of Uncertain Systems in Iterative Tasks

Brunke¹,

Zhou²,

Schoellig³

2021

Preprint

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In this work we address the problem of performing a repetitive task when we have uncertain observations and dynamics. We formulate this problem as an iterative infinite horizon optimal control problem with output feedback. Previously, this problem was solved for linear time-invariant (LTI) system for the case when noisy full-state measurements are available using a robust iterative learning control framework, which we refer to as robust learning-based model predictive control (RL-MPC). However, this work does not apply to the case when only noisy observations of part of the state are available. This limits the applicability of current approaches in practice: First, in practical applications we typically do not have access to the full state. Second, uncertainties in the observations, when not accounted for, can lead to instability and constraint violations. To overcome these limitations, we propose a combination of RL-MPC with robust output feedback model predictive control, named robust learning-based output feedback model predictive control (RLO-MPC). We show recursive feasibility and stability, and prove theoretical guarantees on the performance over iterations. We validate the proposed approach with a numerical example in simulation and a quadrotor stabilization task in experiments.

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“…Performing iterative tasks in control systems has been extensively studied in the literature (Rosolia et al, 2022; Wabersich and Zeilinger, 2022; Zhang et al, 2021), where one task execution is usually called an “iteration.” Iterative learning control (ILC) is an effective strategy for iterative tasks to achieve high closed-loop performance by learning from previous iterations. At each iteration, the system starts from the same initial condition and the goal is to track a given reference trajectory.…”

Section: Introductionmentioning

confidence: 99%

Automatic tuning of robust model predictive control in iterative tasks using efficient Bayesian optimization

Tong,

Du,

Fan

et al. 2023

Transactions of the Institute of Measurement and Control

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Robust model predictive control (RMPC) is an effective technology for controlling uncertain systems while robustly handling constraints, and its closed-loop performance heavily relies on the selection of objective functions. However, the objective functions are typically chosen to be close to the real control objectives, despite an objective function that leads to less conservative constraints often provides better closed-loop performance. In this paper, we propose an automatic tuning framework for RMPC in iterative tasks. In particular, we parameterize RMPC and develop a Bayesian optimization (BO) method to tune it by solving a black-box optimization problem. We then introduce an efficient transfer learning framework within BO, which speeds up the searching process and enhances the controller performance. The effectiveness of the proposed tuning framework is illustrated on numerical examples.

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Robust Learning Model-Predictive Control for Linear Systems Performing Iterative Tasks

Cited by 16 publications

References 53 publications

Toward Data-Driven Optimal Control: A Systematic Review of the Landscape

Toward Data-Driven Optimal Control: A Systematic Review of the Landscape

RLO-MPC: Robust Learning-Based Output Feedback MPC for Improving the Performance of Uncertain Systems in Iterative Tasks

Automatic tuning of robust model predictive control in iterative tasks using efficient Bayesian optimization

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