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UKACC International Conference on Control 2010

作者： Anna Voelker Konstantinos Kouramas Efstratios N. Pistikopoulos Centre for Process Systems Engineering chemical Engineering Imperial College London UK

ISBN: (纸本)9781627481199

We demonstrate how unconstrained Moving Horizon Estimation (MHE) and Model Predictive Control (MPC) can be simultaneously addressed via multi-parametric programming. We show that the estimation error is bounded in an invariant set by first obtaining the error dynamics of unconstrained MHE for linear, time-invariant systems and then using set-theoretical methods to derive bounds on the estimation error. We then use the error dynamics and the error bounds for the design of a robust output feedback explicit/multi-parametric MPC resulting in a simultaneous estimation and control design which we illustrate with an example of robust tube-based output feedback MPC.

关键词： Moving Horizon Estimation MHE Error dynamics Robust explicit MPC multi-parametric programming Predictive control Model predictive control Maximum Allowable Concentration Time invariant systems Horizon programming Estimation error Output feedback design control Moving Concurrency

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Impact of Energy Storage on Economic Dispatch of Distribution Systems: A multi-parametric Linear programming Approach and Its Implications

IEEE OPEN ACCESS JOURNAL OF POWER AND ENERGY

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IEEE OPEN ACCESS JOURNAL OF POWER AND ENERGY 2020年第1期7卷 243-253页

作者： Wei, Wei Wu, Danman Wang, Zhaojian Mei, Shengwei Catalao, Joao P. S. Tsinghua Univ State Key Lab Power Syst Dept Elect Engn Beijing 100084 Peoples R China Univ Porto Fac Engn P-4200465 Porto Portugal INESC TEC P-4200465 Porto Portugal

As a main fiexible resource, energy storage helps smooth the volatility of renewable generation and reshape the load profile. This paper aims to characterize the impact of energy storage unit on the economic operation of distribution systems in a geometric manner that is convenient for visualization. Posed as a multi-parametric linear programming problem, the optimal operation cost is explicitly expressed as a convex piecewise linear function in the MW/MWh parameter of the energy storage unit. Based on duality theory, a dual linear programming based algorithm is proposed to calculate an approximate optimal value function (OVF) and critical regions, circumventing the difficulty of degeneracy, a common challenge in the existing multi-parametric linear programming solvers. When the uncertainty of renewable generation is considered, the expected OVF can be readily established based on OVFs in the individual scenarios, which is scalable in the number of scenarios. The OVF delivers abundant sensitivity information that is useful in energy storage sizing. Leveraging the OVFs, a robust stochastic optimization model is proposed to determine the optimal MW-MWh size of the storage unit subject to a given budget, which gives rise to a simple linear program. Case study provides a clear sketch of the outcome of the proposed method, and suggests that the optimal energy-power ratio of an energy storage unit is between 5 and 6 from the economical perspective.

关键词： Distribution system energy storage unit multi-parametric programming optimal value function approximation

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An improved algorithm for combinatorial multi-parametric quadratic programming

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AUTOMATICA 2013年第5期49卷 1370-1376页

作者： Feller, Christian Johansen, Tor Arne Olaru, Sorin Univ Stuttgart Inst Syst Theory & Automat Control D-70550 Stuttgart Germany NTNU Dept Engn Cybernet N-7491 Trondheim Norway SUPELEC Syst Sci E3S Automat Control Dept F-91192 Gif Sur Yvette France

The goal of multi-parametric quadratic programming (mpQP) is to compute analytic solutions to parameter-dependent constrained optimization problems, e.g., in the context of explicit linear MPC. We propose an improved combinatorial mpQP algorithm that is based on implicit enumeration of all possible optimal active sets and a simple saturation matrix pruning criterion which uses geometric properties of the constraint polyhedron for excluding infeasible candidate active sets. In addition, techniques are presented that allow to reduce the complexity of the discussed algorithm in the presence of symmetric problem constraints. Performance improvements are discussed for two example problems from the area of explicit linear MPC. (c) 2013 Elsevier Ltd. All rights reserved.

关键词： multi-parametric programming Explicit constrained linear quadratic regulators Predictive control

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multi parametric programming and Exact Linearization based Model Predictive Control of a Permanent Magnet Linear Synchronous Motor

Multi Parametric Programming and Exact Linearization based M...

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Annual International Conference on System Science and Engineering (ICSSE)

作者： Dao Phuong Nam Nguyen Hong Quang Nguyen Manh Hung Nguyen Trung Ty Hanoi Univ Sci & Technol Hanoi Vietnam Thai Nguyen Univ Technol Thai Nguyen Vietnam

ISBN: (纸本)9781538634226

Linear motors have many advantages in compare with rotary motors due to directly creating linear motion without gears or belts,... It is hard to apply the online model predictive controller for electro-mechanism systems with input, output and state constraints because it requires the good ability in calculations of microcontroller and the nonlinear property of these models. In this paper, the exact linearization is applied to obtain the corresponding linear model and we propose the offline model predictive control law based on multi-parametric programming (MPP) for permanent magnet linear synchronous motors (PMLSM) to remarkably reduce amount of calculation. Thus, it is convenient for embedding the control law into microcontroller. Several simulation results show the ability of the proposed method in this paper.

关键词： Permanent magnet linear synchronous motors Model predictive controller multi-parametric programming Exact Linearization KKT

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multi-parametric Linear programming Under Global Uncertainty

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AICHE JOURNAL 2017年第9期63卷 3871-3895页

作者： Charitopoulos, Vassilis M. Papageorgiou, Lazaros G. Dua, Vivek UCL Dept Chem Engn Ctr Proc Syst Engn Torrington Pl London WC1E 7JE England

multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush-Kuhn-Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms. (C) 2017 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers.

关键词： multi-parametric programming left hand side uncertainty linear programming symbolic manipulation uncertainty Groebner bases

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multi-parametric mixed integer linear programming under global uncertainty

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COMPUTERS & CHEMICAL ENGINEERING 2018年 116卷 279-295页

作者： Charitopoulos, Vassilis M. Papageorgiou, Lazaros G. Dua, Vivek UCL Ctr Proc Syst Engn Dept Chem Engn Torrington Pl London WC1E 7JE England

Major application areas of the process systems engineering, such as hybrid control, scheduling and synthesis can be formulated as mixed integer linear programming (MILP) problems and are naturally susceptible to uncertainty. multi-parametric programming theory forms an active field of research and has proven to provide invaluable tools for decision making under uncertainty. While uncertainty in the righthand side (RHS) and in the objective function's coefficients (OFC) have been thoroughly studied in the literature, the case of left-hand side (LHS) uncertainty has attracted significantly less attention mainly because of the computational implications that arise in such a problem. In the present work, we propose a novel algorithm for the analytical solution of multi-parametric MILP (mp-MILP) problems under global uncertainty, i.e. RHS, OFC and LHS. The exact explicit solutions and the corresponding regions of the parametric space are computed while a number of case studies illustrates the merits of the proposed algorithm. (C) 2018 The Authors. Published by Elsevier Ltd.

关键词： Optimisation under uncertainty multi-parametric programming Mixed integer linear programming Cylindrical algebraic decomposition Grobner bases Process scheduling

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On the global solution of multi-parametric mixed integer linear programming problems

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第1期57卷 51-73页

作者： Wittmann-Hohlbein, Martina Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2BY England

This paper deals with the global solution of the general multi-parametric mixed integer linear programming problem with uncertainty in the entries of the constraint matrix, the right-hand side vector, and in the coefficients of the objective function. To derive the piecewise affine globally optimal solution, the steps of a multi-parametric branch-and-bound procedure are outlined, where McCormick-type relaxations of bilinear terms are employed to construct suitable multi-parametric under- and overestimating problems. The alternative of embedding novel piecewise affine relaxations of bilinear terms in the proposed algorithmic procedure is also discussed.

关键词： multi-parametric programming Mixed integer linear programming Global optimization

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Integrated process design, scheduling, and control using multiparametric programming

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COMPUTERS & CHEMICAL ENGINEERING 2019年 125卷 164-184页

作者： Burnak, Baris Diangelakis, Nikolaos A. Katz, Justin Pistikopoulos, Efstratios N. Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77845 USA Texas A&M Univ Texas A&M Energy Inst College Stn TX 77845 USA

A unified theory and framework for the integration of process design, control, and scheduling based on a single high fidelity model is presented. The framework features (i) a mixed-integer dynamic optimization (MIDO) formulation with design, scheduling, and control considerations, and (ii) a multiparametric optimization strategy for the derivation of offline/explicit maps of optimal receding horizon policies. Explicit model predictive control schemes are developed as a function of design and scheduling decisions, and similarly design dependent scheduling policies are derived accounting for the closed-loop dynamics. Inherent multi-scale gap issues are addressed by an offline design dependent surrogate model. The proposed framwork is illustrated by two example problems, a system of two continuous stirred tank reactor, and a small residential combined heat and power (CHP) network. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Enterprise-wide optimization Integration multi-parametric programming Process scheduling Model predictive control Process design

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A dynamic programming based approach for explicit model predictive control of hybrid systems

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COMPUTERS & CHEMICAL ENGINEERING 2015年 72卷 126-144页

作者： Rivotti, Pedro Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Ctr Proc Syst Engn Dept Chem Engn London SW7 2AZ England

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multiparametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： multi-parametric programming Model predictive control Robust model predictive control Dynamic programming Hybrid systems

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New Concepts of Feasibility and Efficiency of Solutions in Fuzzy Mathematical programming Problems

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FUZZY INFORMATION AND ENGINEERING 2014年第2期6卷 203-221页

作者： Attari, H. Nasseri, S. H. Univ Mazandaran Dept Math Babol Sar Iran

Some new concepts in regards to alpha-feasibility and alpha-efficiency of solutions in fuzzy mathematical programming problems are introduced in this paper, where a is a vector of distinct satisfaction degrees. Based on the defined concepts, a new method is suggested to solve fuzzy mathematical programming problems. In this sense, the proposed approach enables decision makers to take into account more flexible solutions by allowing desired distinct satisfactions in constraints. In the case of linear problems with fuzzy constraints, multi-parametric programming is employed to obtain the optimal solution as an affine function of distinct satisfaction degrees. In particular, it proves that the obtained solution is convex and continuous. Therefore, the different optimal solutions can be obtained by a simple substituting the new values of satisfaction parameters into the parametric profiles without any further optimization calculations, which is desirable for online optimization and sensitivity analysis of the profit to satisfaction parameters.

关键词： Feasibility and efficiency of solutions Fuzzy linear programming multi-parametric programming Sensitivity analysis

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