This paper develops a parametric Koopman operator framework for Stochastic Model Predictive Control (SMPC), where the Koopman operator is parametrized by Polynomial Chaos Expansions (PCEs). The model is learned from data using the Extended Dynamic Mode Decomposition -- Dictionary Learning (EDMD-DL) method, which preserves the convex least-squares structure for the PCE coefficients of the EDMD matrix. Unlike conventional stochastic Galerkin projection approaches, we derive a condensed deterministic reformulation of the SMPC problem whose dimension scales only with the control horizon and input dimension, and is independent of both the lifted state dimension and the number of retained PCE terms. Our framework, therefore, enables efficient nonlinear SMPC problems with expectation and second-order moment constraints with standard convex optimization solvers. Numerical examples demonstrate the efficacy of our framework for uncertainty-aware SMPC of nonlinear systems.
Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful for formulating linear model predictive control (MPC) of nonlinear dynamical systems with reduced computational complexity. However, the robustness of the closed-loop Koopman MPC under modeling approximation errors and possible exogenous disturbances is still a crucial issue to be resolved. Aiming at the above problem, this paper presents a robust tube-based M…
Electrical neuromodulation as a palliative treatment has been increasingly used in the control of epilepsy. However, current neuromodulations commonly implement predetermined actuation strategies and lack the capability of self-adaptively adjusting stimulation inputs. In this work, rooted in optimal control theory, we propose a Koopman-MPC framework for real-time closed-loop electrical neuromodulation in epilepsy, which integrates i) a deep Koopman operator based dynamical model to predict the temporal evolution of epileptic EEG with an approximate finite-dimensional linear dynamics and ii) a …
Deep Koopman risk-preview supervised LTV-MPC for direct yaw moment control of distributed drive electric vehicles
College of Mechanical and Vehicle Engineering, Chongqing University（重庆大学机械与车辆工程学院）；Department of Automotive Engineering, Hanyang University（汉阳大学汽车工程系）；School of Vehicle Engineering, Chongqing University of Technology（重庆理工大学车辆工程学院）
This paper continues in the work from arXiv:1903.06103 [math.OC] where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system typically features a lot of nonlinearities such as rigid-body dynamics, coordinate system transformations and most importantly the tire. These nonlinearities are approximated in a predefined subset of the state-space by the linear Koopman operator and used for a linear Model Predictive Control (MPC) design in the high-dimension state space where the nonlinear system…
Physics-based Online Adaptive Koopman Model Predictive Attitude Control for Combined Spacecraft with Dynamic Uncertainties
Zhengzhou Advanced Research Institute, Harbin Institute of Technology（郑州先进研究院，哈尔滨工业大学）；Department of Control Science and Engineering, Harbin Institute of Technology（控制科学与工程系，哈尔滨工业大学）；School of Engineering, Newcastle University（纽卡斯尔大学工程学院）
MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems
Water Research Institute (NEWRI), Nanyang Technological University, Singapore（新跃大学水研究 institute（NEWRI））；School of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, Singapore（新跃大学化学、化工与生物技术学院）；Soft Robotics Lab, ETH Zurich, Switzerland（苏黎世联邦理工学院软机器人实验室）；Department of Civil and Environmental Engineering, National University of Singapore, Singapore（新加坡国立大学土木与环境工程系）
Control of warm-water supply for dialysis treatment in a hospital environment is typical of safety-critical control problems. In order to guarantee the continuity of warm-water supply satisfying physical specifications for a wide range of operating conditions, it is inevitable to consider the nonlinearity involved in a dynamic model of a warm-water supply system for the control design. In this paper, we propose to incorporate control specifications described by signal temporal logic, which is a temporal logic with semantics over finite-time signals in formal methods, into the so-called Koopman…
Hubei University（湖北大学）；Shenzhen Institute of Artificial Intelligence and Robotics for Society (AIRS)（深圳市人工智能与机器人研究院）；The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen)（香港中文大学（深圳））；Manchester Metropolitan Joint Institute, Hubei University（湖北大学曼城联合学院）
Maximum-likelihood reprojections for reliable Koopman predictors of parametric nonlinear dynamical systems
The University of Sydney（悉尼大学）；Technische Universität Chemnitz（开姆尼茨工业大学）；The Australian National University（澳大利亚国立大学）；Technische Universität Ilmenau（伊尔梅瑙工业大学）
Multi-segment Soft Robot Control via Deep Koopman-based Model Predictive Control
Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University（上海智能自主系统研究院，同济大学）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；School of Biomedical Engineering, Tsinghua University（清华大学生物医学工程学院）；Beijing Soft Robot Tech Co., Ltd.（北京软机器人技术有限公司）；School of Clinical Medicine, Tsinghua University（清华大学临床医学学院）；Department of Informatics, University of Hamburg（汉堡大学信息学院）；School of Mechanical Engineering and Automation, Beihang University（北航机械工程与自动化学院）；Huawei Noah’s Ark Lab（华为诺亚实验室）
This paper presents a distributed data-driven control to regulate the voltage in an alternate current microgrid (MG). Following the hierarchical control frame for MGs, a secondary control for voltage is designed with a data-driven strategy using the Koopman operator. The Koopman operator approach represents the nonlinear behavior of voltage as a linear problem in the space of observables or lifted space. The representation in the lifted space is used together with linear consensus to design a model predictive control (MPC). The complete algorithm is proved in an MG model including changes in l…
Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness (and/or safety) guarantees for systems the dynamics of which are extracted via the Koopman operator. In this paper, we propose a way to quantify the prediction error because of noisy measurements when the Koopman operator is approximated via Extended Dynamic Mode Decomposition. We further develop an enhanced robot control strategy to endow robustness to a class of…
Koopman operator theory: fundamentals, control, and applications
Department of Mechanical Engineering, University of California, Santa Barbara（加州大学圣芭芭拉分校机械工程系）；Department of Mechanical and Aerospace Engineering, University of California, San Diego（加州大学圣地亚哥分校机械与航空航天工程系）；Optimization-based Control Group, TU Ilmenau（图林根工业大学优化控制组）；Constrained Control of Complex Systems Lab, Control Systems Group, Department of Electrical Engineering, TU Eindhoven（埃因霍温理工大学复杂系统约束控制实验室，控制系统组，电气工程系）；Department of Electrical and Computer Engineering, National University of Singapore（新加坡国立大学电气与计算机工程系）
In the framework of Model Predictive Control (MPC), the control input is typically computed by solving optimization problems repeatedly online. For general nonlinear systems, the online optimization problems are non-convex and computationally expensive or even intractable. In this paper, we propose to circumvent this issue by computing a high-dimensional linear embedding of discrete-time nonlinear systems. The computation relies on an algebraic condition related to the immersibility property of nonlinear systems and can be implemented offline. With the high-dimensional linear model, we then de…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start…
The dynamics-aware economic dispatch (DED) problem embeds low-level generator dynamics and operational constraints to enable near real-time scheduling of generation units in a power network. DED produces a more dynamic supervisory control policy than traditional economic dispatch (T-ED) that leads to reduced overall generation costs. However, the incorporation of differential equations that govern the system dynamics makes DED an optimization problem that is computationally prohibitive to solve. In this work, we present a new data-driven approach based on differentiable programming to efficien…
