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Dealing with infeasibility in multi-parametric programming for application to explicit model predictive control

AUTOMATICA 2023年第1期157卷

作者： Falsone, Alessandro Bianchi, Federico Prandini, Maria Politecn Milan Dipartimento Elettron Informaz & Bioingn Via Ponzio 34-5 I-20133 Milan Italy Ric Sistema Energet RSE SpA Dept Generat Technol & Mat Via Rubattino 54 I-20134 Milan Italy

Motivated by explicit model predictive control, we address infeasibility in multi-parametric quadratic programming according to the exact penalty function approach, where some user-chosen parameter dependent constraints are relaxed and the 1-norm of their violation is penalized in the cost function. We characterize the relation between the resulting multi-parametric quadratic program and the original one and show that, as the penalty coefficient grows to infinity, the solution to the former provides a piecewise affine continuous function, which is an optimal solution for the latter over the feasibility region, while it minimizes the 1-norm of the relaxed constraints violation over the infeasibility region.& COPY;2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Multi-parametric programming explicit model predictive control Exact penalty

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Integrating learning and explicit model predictive control for unit commitment in microgrids

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APPLIED ENERGY 2022年第PartA期306卷 118026-118026页

作者： Huo, Yuchong Bouffard, Francois Joos, Geza McGill Univ Dept Elect & Comp Engn Montreal PQ H3A 0E9 Canada Grp Etud & Rech Anal Decis GERAD Montreal PQ H3T 1J4 Canada

In this paper, we apply flexibility-based operational planning method to microgrid (MG) unit commitment (UC). The problem is formulated based on model predictive control (MPC) paradigm. Conventionally, such paradigm requires the online solution of a mixed-integer optimization problem, which faces difficulties in practical field implementations in a low-power computing microgrid controller. The explicit model predictive control (EMPC) can address this problem of MPC by computing the control laws of MPC in an explicit form offline to enable fast online computation. However, the complexity of the explicit control laws usually grows exponentially with the dimension of the problem, which hinders the application of EMPC in larger systems. In this paper, we integrate learning and EMPC to develop a computationally efficient and rigorous approach for implementing flexibility-based unit commitment paradigms in a microgrid controller with limited computational power. The computational complexity of the proposed approach can be adjusted to meet the hardware limitation of any given microgrid controller, while preserving as much as possible the optimality of the full-fidelity EMPC. This overcomes the drawbacks of traditional EMPC. Moreover, compared to the existing learning-based methods for accelerating optimization algorithms, the proposed approach is able to handle the variables and constraints of the original unit commitment problem systematically, which guarantees the feasibility of its output unit commitment schedules. We conduct case studies to demonstrate the effectiveness of the proposed approach.

关键词： explicit model predictive control Flexibility Machine learning Microgrid Microgrid controller Unit commitment

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Demand response of an Electric Vehicle charging station using a robust-explicit model predictive control considering uncertainties to minimize carbon intensity

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2024年 38卷

作者： Cabrera-Tobar, Ana Blasuttigh, Nicola Pavan, Alessandro Massi Spagnuolo, Giovanni Politecn Milan Dept Energy I-20156 Milan Italy Univ Trieste Ctr Energy Dept Engn & Architecture Environm & Transport Giacomo Ciamician Trieste Italy Univ Salerno Dept Informat Engn Elect Engn & Appl Math Salerno Italy

This paper presents a novel approach to address uncertainties and enable demand response in Electric Vehicle (EV) charging station optimization. A two -stage optimization strategy is proposed, integrating Robust Optimization and explicit model predictive control (eMPC). The first stage involves day -ahead planning using Robust Optimization technique to limit the hourly power consumption of EVs, considering worst -case scenarios caused by uncertainties in EV consumption and CO 2 emissions. The objective is to minimize environmental impact by reducing CO 2 emissions. An explicit model predictive control strategy is developed in the second stage for real-time operation. The explicit solution, calculated offline, models uncertainties such as the initial state of charge of the battery energy storage, photovoltaic power production, and EV power consumption. During real-time operation, the explicit solution is accessed using measured data from the charging station, refining the schedule derived from the first stage. The proposed solution is implemented and evaluated at an EV charging station in Trieste, Italy. The results demonstrate a significant 69% reduction in CO 2 emissions compared to a deterministic approach while maintaining a real-time computation time of less than 0.1 s.

关键词： EV charging stations Photovoltaic system Battery energy storage CO2 emissions Two-stage optimization Robust Optimization explicit model predictive control Real-time operation Environmental impact Energy management

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Accelerating explicit model predictive control by Constraint Sorting ⁎

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IFAC-PapersOnLine 2020年第2期53卷 11356-11361页

作者： Juraj Holaza Juraj Oravec Michal Kvasnica Raphael Dyrska Martin Mönnigmann Miroslav Fikar Institute of Information Engineering Automation and Mathematics Slovak University of Technology in Bratislava Slovakia Automatic Control and Systems Theory Ruhr-Universität Bochum Germany

explicit MPC represents one of the fastest ways of real-time MPC implementation. As the explicit MPC policy is optimization-free in real-time control, its efficiency is determined by solving a point location problem. This paper proposes the novel concept of accelerating explicit MPC that significantly speeds up the real-time evaluation of the point location problem. The introduced strategy has two layers: (i) an offline phase determines a smart order of the regions to be explored, and (ii) an online phase removes further regions to be explored on the fly based on the current value of the value function. The main advantage of layer (i) is that the order is evaluated offline, therefore, it does not increase the real-time implementation of explicit MPC. The implementation of layer (ii) slightly increases the real-time evaluation but leads to further speed-up of the point location problem. As the proposed layers are based just on the evaluation of some appropriate value function, the main benefit is that these layers are fully applicable also for higher-dimensional systems. Although the accelerated explicit MPC variant does not reduce the worst-case time of solving the point location problem, an extensive case study demonstrates the efficiency of the proposed strategy.

关键词： explicit model predictive control point location problem sequential search

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Robust explicit model predictive control for Uncertain Multirate System

Robust Explicit Model Predictive Control for Uncertain Multi...

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31st Chinese control Conference

作者： Jiang Yali Zou Yuanyuan Niu Yugang East China Univ Sci & Technol Key Lab Adv Control & Optimizat Chen Proc Minist Educ Shanghai 200237 Peoples R China Minist Educ Key Lab Syst Control & Informat Proc Shanghai 200240 Peoples R China

ISBN: (纸本)9789881563811

This paper studies robust explicit model predictive control for multirate system with bounded additive disturbances. First, based on dynamic programming, the optimization problem is decomposed into multi-stages of subproblems with one-step optimal horizon. In the process of solving the subproblem of each stage, considering the influence of additive disturbance, we construct the constraint set of the first predicted state, and then such a constraint set is transformed into the constraint condition dependent on current state and input. After that, the multiparametric quadratic programming (mp-QP) technique is used to obtain the robust explicit control laws. The robust positively invariant set of the multirate system is chosen as the terminal constraint set of the optimization problem such that the robust stability can be ensured. The numerical example shows that the proposed robust explicit predictive control can reduce online computation and satisfy the demand of the multirate system with the fast update speed of input.

关键词： Multirate control system Uncertainties explicit model predictive control Dynamic programming

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Polytopic Approximation Algorithm of explicit model predictive control

Polytopic Approximation Algorithm of Explicit Model Predicti...

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32nd Chinese control Conference (CCC)

作者： Zhang Ju Ma Yanfang He Xuehua Zhejiang Univ Technol Coll Informat Engn Hangzhou 310023 Zhejiang Peoples R China

ISBN: (纸本)9781479900305

Polytopic approximation of explicit model predictive control is an algorithm that compute approximate explicit control laws that trade-off complexity against approximation error for MPC controllers. The approximate method has overcome the shortcomings of explicit model predictive control, reduced the complexity and improved the speed of offline calculation, increased the real-time control action. In this paper, we make a comparison between the polytopic approximate algorithm and the explicit model predictive control algorithms by the simulation of several numerical examples. The advantages of polytopic approximation algorithm are concluded.

关键词： explicit model predictive control polytopic approximation simulation of numerical examples

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Multiparametric/explicit nonlinear model predictive control for quadratically constrained problems

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JOURNAL OF PROCESS control 2021年 103卷 55-66页

作者： Pappas, Iosif Diangelakis, Nikolaos A. Pistikopoulos, Efstratios N. Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA Texas A&M Univ Texas A&M Energy Inst College Stn TX 77843 USA

explicit model predictive control is an established methodology for the offline determination of the optimal control policy for linear discrete time-invariant systems with linear constraints. Nevertheless, nonlinearities in the form of quadratic constraints naturally appear in process models or are imposed for stability purposes in model predictive control formulations. In this manuscript, we present the theoretical developments and propose an algorithm for the exact solution of explicit nonlinear model predictive control problems with convex quadratic constraints. Our approach is based on a secondorder Taylor approximation of Fiacco's Basic Sensitivity Theorem, which allows for the existence and the analytic derivation of the optimal control actions. The complete exploration of the parameter space is founded on an active set strategy, which employs a pruning criterion to eliminate infeasible active sets. Based on that, the optimal map of solutions is constructed along with the corresponding control actions. The proposed strategy is applied to an explicit nonlinear model predictive control problem with an ellipsoidal terminal set, and comparisons with approximate solutions are drawn to demonstrate the benefits of the presented approach. Furthermore, as a practical application, the optimal operation of a chemostat in the presence of disturbances is exhibited. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Nonlinear model predictive control explicit model predictive control Quadratically constrained quadratic programming Multiparametric programming

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explicit model predictive Speed control for Permanent Magnet Synchronous Motor With Torque Ripple Minimization

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IEEE ACCESS 2023年 11卷 134199-134210页

作者： Nguyen, Ty Trung Nguyen, Ton Hoang Jeon, Jae Wook Sungkyunkwan Univ Dept Elect & Comp Engn Suwon 16419 South Korea

Permanent Magnet Synchronous Motors (PMSMs) are employed in various high-precision industrial applications. However, the torque ripple caused by nonideal factors, such as cogging torque, flux harmonics, and unbalanced stator phase currents diminishes motor performance. Therefore, torque ripple minimization is an important key in designing high-performance controllers for PMSMs. In this paper, an explicit model predictive speed control (EMPSC) is proposed as an advanced strategy for torque ripple minimization. First, the torque ripple is modeled as a periodic disturbance in the speed model. Subsequently, a Lyapunov-based periodic disturbance observer (PDOB) is designed to fast and accurately estimate the torque ripple. The EMPSC updates the estimated disturbance into the prediction model and minimizes the cost function to obtain the optimal control signal. This control signal effectively mitigates torque ripple while enhancing dynamic response performance. Furthermore, this paper introduces an explicit process aimed at significantly reducing the complexity and computational effort of the entire control scheme. Lastly, the simulation and experimental results are presented to demonstrate the effectiveness of the proposed method.

关键词： Torque ripple minimization periodic disturbance observer explicit model predictive control permanent magnet synchronous motor (PMSM)

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A Memory-Efficient explicit model predictive control using Posits

A Memory-Efficient Explicit Model Predictive Control using P...

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control Conference (ICC), 2019 Sixth Indian

作者： Chaitanya Jugade Deepak Ingole Dayaram Sonawane Michal Kvasnica John Gustafson College of Engineering Pune Shivajinagar India IFSTTAR ENTPE University of Lyon Lyon France Slovak University of Technology in Bratislava Slovakia National University of Singapore Singapore

ISBN: (数字)9781728138602

ISBN: (纸本)9781728138619

For explicit model predictive control (EMPC), off-line pre-computed optimal feedback laws need to be stored in a look-up table for on-line evaluation. The need for memory to store the look-up table on embedded hardware limits applicability of EMPC to systems with few states, a small number of constraints, and short prediction horizons. In this paper, we present a novel technique to reduce the memory footprints of EMPC solutions. The idea is based on encoding all data (i.e., the critical regions and the feedback laws) as posit™ numbers, which can be viewed as a memory-efficient replacement for the IEEE 754 floating-point standard. By using the posit number system, we achieve more accuracy with fewer bits, and posits can be efficiently deployed on embedded hardware like PLC, FPGA, DSP, ARM, etc. We show the design and implementation of posit-based EMPC for the control of the coupled tank system. Results show that the total memory footprints can be reduced by 75% without losing control accuracy. An additional advantage of the approach is that it can be applied on the top of existing complexity reduction techniques.

关键词： explicit model predictive control memory reduction floating-point numbers unums posit arithmetic

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Development of Double Closed Loop control based on explicit model predictive control for PMSM

Development of Double Closed Loop Control based on Explicit ...

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第34届中国控制与决策会议

作者： Qian Guo Tianhong Pan School of Electrical and Information Engineering Jiangsu University School of Electrical Engineering and Automation Anhui University

This work deals with the development of double closed loop control based on explicit model predictive control(MPC) for permanent magnet synchronous motor(PMSM) system with *** aim of the proposed controller is to solve the constrained optimization problem for fast-sampling time PMSM system and improve the robustness of the *** recreated mathematical model of PMSM is introduced at *** the proposed explicit MPC controller is designed based on the reformed *** explicit controller is employed to control the mechanical speed and the q-axis current,and the proportional-integral(PI) control is employed to control d-axis *** simulation results demonstrate that the proposed double closed loop control method is effective when the working condition of PMSM changes and the performance of the speed and current is satisfactory.

关键词： explicit model predictive control permanent magnet synchronous motor model recreation double closed loop control

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