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Complexity reduction of explicit MPC based on fuzzy reshaped polyhedrons for use in industrial controllers

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2023年第3期54卷 463-477页

作者： Changizi, Nematollah Salahshoor, Karim Siahi, Mehdi Islamic Azad Univ Sci & Res Branch Dept Mech Elect & Comp Engn Tehran Iran Petr Univ Technol Dept Instrumentat & Ind Automat Ahwaz Iran

The explicit model predictive control (EMPC) generates the rules of control defined for a set of polyhedral regions. Online EMPC calculations consist of searching a look-up table to find the appropriate control law according to a particular state. This paper discusses the complexity of online computation and the memory required to store data in an EMPC implementation. Therefore, a new reshaping method is applied to the active regions so that the definition of the polyhedron has regular boundaries. This approach has made some improvements. First, the usable memory will be a lot less for the actual implementation compared to the traditional EMPC approach. Second, the small number of new clusters reduces search time in explicit lookup tables and speeds up overall implementation. To this end, fuzzy clustering is used to introduce a novel method of transforming polyhedrons in the context of fuzzy explicit model predictive (FEMPC) control, followed by a new fuzzy-based piece-wise affine (PWA) explicit formulation for control law calculations. The stability of the proposed method is investigated using the Lyapunov stability criteria. The proposed algorithm has been tested on a nonlinear continuous stirred tank reactor (CSTR) benchmark system and simulation tests show that the proposed approach involves a compromise between storage space requirements and online efficiency.

关键词： Explicit model predictive control (EMPC) multi-parametric programming complexity reduction polyhedrons fuzzy explicit MPC (FEMPC)

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On the performance of observer-based explicit model predictive control

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2015年第6期37卷 769-779页

作者： Bayat, Farhad Univ Zanjan Dept Engn Zanjan *** Iran

This paper addresses the performance recovery of explicit model predictive control (eMPC) when states of the system are not available via measurement. It is shown that the performance of the closed-loop system under the eMPC controller can be degraded when using a state observer instead of measurement. To moderate this degradation, an optimization-based approach is proposed that enables the designer to systematically design an optimal observer. It is proved that the proposed approach leads to the maximum achievable performance (in some sense) when compared to the desired performance (i.e. when states are available via measurement). Simulation results illustrate the performance and effectiveness of the proposed approach compared to a set of observers designed using a robust pole-placement approach.

关键词： Explicit model predictive control output feedback eMPC multi-parametric programming performance optimization

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Linear Machine Solution to Point Location Problem

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2017年第3期62卷 1403-1410页

作者： Airan, Astha Bhushan, Mani Bhartiya, Sharad Indian Inst Technol Dept Chem Engn Mumbai 400076 Maharashtra India

Linear machine has been recently proposed as an elegant solution for solving the point location problem arising in multi-parametric programming (mp-P) based online optimization. Linearmachine associates a linear discriminant function with each polytopic region in the parametric space. The solution to the point location problem is then obtained by simply evaluating these discriminant functions and finding their maximum value. In this technical note, we rigorously establish the correctness of the linear machine generation procedure and identify a necessary condition for existence of linear machine. A modified procedure, involving systematic subdivision of the parametric space, is proposed when this condition is not satisfied. Analysis of complexity and storage requirements, along with computational experiments on a large sized example, indicate that linear machine can be an efficient tool for solving the point location problem.

关键词： Discriminant functions explicit model predictive control multi-parametric programming online optimization

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Application of an explicit min-max MPC to a scaled laboratory process

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CONTROL ENGINEERING PRACTICE 2005年第12期13卷 1463-1471页

作者： de la Peña, DM Ramírez, DR Camacho, EF Alamo, T Univ Seville Escuela Super Ingn Dept Ingn Sistemas & Automat Seville 41092 Spain

Min-max model predictive control (MMMPC) requires the on-line solution of a min-max problem, which can be computationally demanding. The piecewise affine nature of MMMPC has been proved for linear systems with quadratic performance criterion. This paper shows how to move most computations off-line obtaining the explicit form of this control law by means of a heuristic algorithm. These results are illustrated with an application to a scaled laboratory process with dynamics fast enough to preclude the use of numerical solvers. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： predictive control minimax techniques multi-parametric programming piecewise linear controllers uncertainty

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On Robust Tie-Line Scheduling in multi-Area Power Systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第4期33卷 4144-4154页

作者： Guo, Ye Bose, Subhonmesh Tong, Lang Cornell Univ Sch Elect & Comp Engn Ithaca NY 14850 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

The tie-line scheduling problem in a multi-area power system seeks to optimize tie-line power flows across areas that are independently operated by different system operators (SOs). In this paper, we leverage the theory of multi-parametric linear programming to propose algorithms for optimal tie-line scheduling, respectively, within a deterministic and a robust optimization framework. Aided by a coordinator, the proposed methods are proved to converge to the optimal schedule within a finite number of iterations. A key feature of the proposed algorithms, besides their finite step convergence, is that SOs do not reveal their dispatch cost structures, network constraints, or natures of uncertainty sets to the coordinator. The performance of the algorithms is evaluated using several power system examples.

关键词： Tie-line scheduling robust optimization multi-parametric programming

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parametric optimization and control for a smart Proton Exchange Membrane Water Electrolysis (PEMWE) system

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JOURNAL OF PROCESS CONTROL 2020年 91卷 37-49页

作者： Ogumerem, Gerald S. Pistikopoulos, Efstratios N. Texas A&M Univ Texas A&M Energy Inst College Stn TX 77843 USA Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA

Hydrogen production from Proton Exchange Membrane Water Electrolysis (PEMWE) system is attracting attention due to its ability to circumvent the effect of the intermittent nature of variable renewal energy. However, the relatively high operating temperatures of the PEMWE system exacerbates the degradation of polymer membranes in PEMWE system. This paper describes the development of an optimal thermal management strategy for a PEMWE system that can attenuate the long-term effects of high operating temperatures or rapid temperature changes on the polymer membranes. The thermal management strategy is tested on a laboratory scale smart PEMWE system. First, a high fidelity mathematical model of the smart PEMWE is developed and validated based on which the application of the PARameteric Optimization and Control (PAROC) framework results in the design of an explicit model predictive controller which is deployed into the laboratory PEMWE system. It is shown that the smart PEMWE prototype system empowered with the embedded control policy achieves effective temperature control across the electrolyzer maintaining the integrity of the membrane electrode assembly. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Smart manufacturing PEM electrolysis multi-parametric programming Explicit MPC-on-a-chip

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Approximate explicit receding horizon control of constrained nonlinear systems

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AUTOMATICA 2004年第2期40卷 293-300页

作者： Johansen, TA Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway

An algorithm for the construction of an explicit piecewise linear state feedback approximation to nonlinear constrained receding horizon control is given. It allows such controllers to be implemented via an efficient binary tree search, avoiding real-time optimization. This is of significant benefit in applications that requires low real-time computational complexity or low software complexity. The method has a priori guarantee of asymptotic stability with region of attraction being a close inner approximation to the stabilizable set. This is achieved by ensuring that the approximation error does not exceed the stability margin. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： optimal control multi-parametric programming piecewise linear control

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Robust fault tolerant explicit model predictive control

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AUTOMATICA 2018年 97卷 248-253页

作者： Sheikhbahaei, Reza Alasty, Aria Vossoughi, Gholamreza Sharif Univ Technol Sch Mech Engn Tehran Iran

In this study, a new algorithm for explicit model predictive control of linear discrete-time systems subject to linear constraints, disturbances, uncertainties, and actuator faults is developed. The algorithm is based on dynamic programming, constraint rearrangement, multi-parametric programming, and a solution combination procedure. First of all, the dynamic programming is used to recast the problem as a multi-stage optimization problem. Afterwards, the constraints are rearranged in an innovative manner to take into account the worst admissible situation of unknown bounded disturbances, uncertainties, and actuator faults. Then, the explicit solution of the reformulated optimization problem for each stage is obtained using the multi-parametric programming approaches. Finally, a recursive procedure for combination and substitution of the solutions is presented to extract the desired explicit control law. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Explicit model predictive control Fault tolerant Robust multi-parametric programming Dynamic programming

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Incorporating uncertainty into a supplier selection problem

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2011年第2期134卷 344-356页

作者： Li, Lei Zabinsky, Zelda B. Univ Washington Seattle WA 98195 USA

Supplier selection is an important strategic supply chain design decision. Incorporating uncertainty of demand and supplier capacity into the optimization model results in a robust selection of suppliers. A two-stage stochastic programming (SP) model and a chance-constrained programming (CCP) model are developed to determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. Both models include several objectives and strive to balance a small number of suppliers with the risk of not being able to meet demand. The SP model is scenario-based and uses penalty coefficients whereas the CCP model assumes a probability distribution and constrains the probability of not meeting demand. Both formulations improve on a deterministic mixed integer linear program and give the decision maker a more complete picture of tradeoffs between cost, system reliability and other factors. We present Pareto-optimal solutions for a sample problem to demonstrate the benefits of the SP and CCP models. In order to describe the tradeoffs between costs and risks in an analytical form, we use multi-parametric programming techniques to more completely analyze the alternative Pareto-optimal supplier selection solutions in the CCP model. This analysis gives insights into the robustness of the solutions with respect to number of suppliers, costs and probability of not meeting demand. Published by Elsevier B.V.

关键词： Robust supplier selection Plan for uncertainty Stochastic programming Chance-constraint programming multi-parametric programming Tradeoffs between risk and cost

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Cloud Computing and Local Chip-Based Dynamic Economic Dispatch for Microgrids

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IEEE TRANSACTIONS ON SMART GRID 2020年第5期11卷 3774-3784页

作者： Wang, Siyuan Wang, Xuanding Wu, Wenchuan Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing 100084 Peoples R China Guangdong Power Exchange Ctr Guangzhou 510080 Peoples R China

Dynamic economic dispatch in microgrids is usually realized in a centralized energy management system (EMS). However, centralized systems are subject to single-point failure problems. In rural areas and islands, a failed EMS cannot be recovered in a timely manner due to lack of technical support. In this paper, we propose a cloud and edge computing-based framework to realize dynamic economic dispatch, which is conducted on a local Digital Signal Processor (DSP) chip and a remote cloud computing platform (CCP). Based on the multi-parametric programming algorithm, the dispatch process is divided into two parts: offline calculation and real-time decision making. These calculation tasks can be conducted on the remote cloud computing platform and the DSP chip of the inverter in an arbitrary renewable generator, respectively. The tests are carried out on the Amazon Web Service (AWS) EC2 instance and an autonomous microgrid with DSP TMS320F28335 chip. The results show that the proposed method can obtain the same results as the conventional method, with significantly improved reliability.

关键词： Microgrids Economics Cloud computing Inverters Energy management Power generation Real-time systems Microgrid multi-parametric programming economic dispatch cloud and edge computing

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