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An algorithm for robust explicit/multi-parametric model predictive control

AUTOMATICA 2013年第2期49卷 381-389页

作者： Kouramas, K. I. Panos, C. Faisca, N. P. Pistikopoulos, E. N. Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England AspenTech Reading RG2 6DT Berks England

A new algorithm for robust explicit/multi-parametric Model Predictive Control (MPC) for uncertain, linear discrete-time systems is proposed. Based on previous work on Dynamic programming (DP), multi-parametric programming and Robust Optimization, the proposed algorithm features, (i) a DP reformulations of the MPC optimization problem, (ii) a robust reformulation of the constraints, and (iii) a multi-parametric programming step, where the control variables are obtained as explicit functions of the state variable, such that the state and input constraints are satisfied for all admissible values of the uncertainty. A key feature of the proposed procedure is that, as opposed to previous methods, it only solves a convex multi-parametric programming problem for each stage of the DP procedure. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Explicit/multi-parametric MPC Model predictive control Robust control multi-parametric programming

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Stabilizing low complexity feedback control of constrained piecewise affine systems

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AUTOMATICA 2005年第10期41卷 1683-1694页

作者： Grieder, P Kvasnica, M Baotic, M Morati, M ETH Automat Control Lab CH-8092 Zurich Switzerland

Piecewise affine (PWA) systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. In addition, few results are available which address the issue of computing stabilizing controllers for PWA systems without placing constraints on the location of the origin. This paper first introduces a method to obtain stability guarantees for receding horizon control of discrete-time PWA systems. Based on this result, two algorithms which provide low complexity state feedback controllers are introduced. Specifically, we demonstrate how multi-parametric programming can be used to obtain minimum-time controllers, i.e., controllers which drive the state into a pre-specified target set in minimum time. In a second segment, we show how controllers of even lower complexity can be obtained by separately dealing with constraint satisfaction and stability properties. To this end, we introduce a method to compute PWA Lyapunov functions for discrete-time PWA systems via linear programming. Finally, we report results of an extensive case study which justify our claims of complexity reduction. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： piecewise affine system optimal control model predictive control multi-parametric programming

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Efficient demand response location targeting for price spike mitigation by exploiting price-demand relationship

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APPLIED ENERGY 2024年 376卷

作者： Zhang, Yufan Wen, Honglin Feng, Tao Chen, Yize Univ Calif San Diego Dept Elect & Comp Engn San Diego CA USA Shanghai Jiao Tong Univ Dept Elect Engn Shanghai Peoples R China Hong Kong Polytech Univ Dept Logist & Maritime Studies Hong Kong Peoples R China Univ Alberta Dept Elect & Comp Engn Edmonton AB Canada

Demand response (DR) leverages demand-side flexibility, offering a promising approach to enhance market conditions like mitigating wholesale price spikes. However, poorly chosen DR locations can inadvertently increase electricity prices. For that, we introduce a method to rigorously select DR locations and corresponding demand reductions. We formulate a bilevel program where the upper level determines the DR locations and demand reductions while ensuring the average nodal prices meet a predetermined target. The lower level tackles an economic dispatch (ED) problem and feeds the resulting nodal prices back to the upper level based on post-DR demands. This bilevel formulation presents challenges due to the lower-level non-convexity affecting the upper-level constraints on average nodal prices. To address this, we propose to replace the lower level with a piecewise linear function representing the price-demand relationship, solving iteratively for each linear segment. This results in a tractable mixed-integer linear program. An acceleration strategy is proposed to further reduce the computation time. Numerical studies demonstrate the ability of the proposed approach to reduce prices to a desired level. Besides, we empirically show that the proposed approach is robust against inaccurate system parameters and can reduce computation time by over 50%.

关键词： Demand response Price spike Price-demand relationship multi-parametric programming

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Active fault diagnosis: A multi-parametric approach

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AUTOMATICA 2017年 79卷 223-230页

作者： Marseglia, G. Roberto Raimondo, Davide M. Univ Pavia Dept Elect Comp & Biomed Engn Pavia Italy

This paper considers the design of an input signal for minimizing the time and energy required to detect' and isolate faults in the outputs of a system. Faults are represented by discrete switches between affine models with bounded disturbances and bounded measurement errors. Within this framework, previous work has demonstrated that a minimally harmful input guaranteeing fault diagnosis can be obtained by solving a Mixed Integer Quadratic Program (MIQP). A closed-loop approach allows to reduce the length and/or norm of this input by solving an MIQP at each time instant with the newly available measurements. However, solving such programs online can be computationally demanding. In this paper, we employ multi-parametric (mp) programming to move most of the computation offline, thus allowing, the application of the closed-loop approach to fast processes. Still, the mp-MIQP complexity becomes' quickly prohibitive as the number of faulty models increases. In order to overcome this problem, we propose a strategy based on mp-optimization and graph theory that takes into account only two models at a time. While this approach is suboptimal compared to the case in which all the models are considered simultaneously, simulations show that, in practice, the performance is comparable. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Fault diagnosis Optimization multi-parametric programming

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Computation, approximation and stability of explicit feedback min-max nonlinear model predictive control

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AUTOMATICA 2009年第5期45卷 1134-1143页

作者： Grancharova, Alexandra Johansen, Tor A. Bulgarian Acad Sci Inst Control & Syst Res BU-1113 Sofia Bulgaria Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway

This paper presents an approximate multi-parametric Nonlinear programming (mp-NLP) approach to explicit solution of feedback min-max NMPC problems for constrained nonlinear systems in the presence of bounded disturbances and/or parameter uncertainties. It is based on an orthogonal search tree structure of the state space partition and consists in constructing a piecewise nonlinear (PWNL) approximation to the optimal sequence of feedback control policies. Conditions guaranteeing the robust stability of the closed-loop system in terms of a finite l(2)-gain are derived. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Min-max model predictive control multi-parametric programming l(2)-stability

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multi-parametric global optimization approach for tri-level mixed-integer linear optimization problems

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JOURNAL OF GLOBAL OPTIMIZATION 2019年第3期74卷 443-465页

作者： Avraamidou, Styliani Pistikopoulos, Efstratios N. Imperial Coll London Ctr Proc Syst Engn London SW7 2AZ England Texas A&M Univ Artie McFerrin Dept Chem Engn Texas A&M Energy Inst College Stn TX USA

In this work, we present a novel algorithm for the global solution of tri-level mixed-integer linear optimization problems containing both integer and continuous variables at all three optimization levels. Based on multi-parametric theory and our earlier results for bi-level programming problems, the main idea of the algorithm is to recast the lower levels of the tri-level optimization problem as multi-parametric programming problems, in which the optimization variables (continuous and integer) of all the upper level problems, are considered as parameters at the lower levels. The resulting parametric solutions are then substituted into the corresponding higher-level problems sequentially. The algorithm is illustrated through numerical examples, along with implementation and computational studies.

关键词： multi-level mixed-integer optimization Hierarchical optimization Tri-level optimization multi-parametric programming

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Low-complexity control of hybrid systems using approximate multi-parametric MILP

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AUTOMATICA 2016年 63卷 292-301页

作者： Habibi, Jalal Moshiri, Behzad Sedigh, Ali Khaki Morari, Manfred Univ Tehran Coll Engn Sch Elect & Comp Engn Tehran Iran Univ Tehran Control & Intelligent Proc Ctr Excellence Tehran Iran KN Toosi Univ Technol Dept Elect Engn Tehran Iran Swiss Fed Inst Technol Zurich Automat Control Lab CH-8092 Zurich Switzerland

Control of hybrid systems faces computational complexity as a main challenging problem. To reduce the computational burden, multi-parametric programming has been proposed to obtain the explicit solution of the optimal control problems for some classes of hybrid systems. This strategy provides the solution as a function of the state variables which can be obtained in an off-line fashion. A shortcoming of this technique is that the complexity of the explicit solution is again prohibitive for large problems. The main contribution of this paper is the introduction of an approximation algorithm for solving a general class of multi-parametric mixed-integer linear programming (mp-MILP) problems. The algorithm selects those binary sequences that make significant improvement in the objective function, if considered. It is shown that significant reduction in computational complexity can be achieved by introducing adjustable level of suboptimality. A family of suboptimal controllers is obtained by the proposed approach for which the level of error and complexity can be adjusted by a tuning parameter. It is shown that no part of the parameter space is disregarded during the approximation. Also it is proved that the error in the achieved approximate solutions is a monotonically increasing function of the tuning parameter. Assuming that the closed-loop stability is ensured by including some constraints in the formulation of hybrid control, it will be preserved by the suboptimal low-complexity controllers. Illustrative examples are presented to demonstrate the achieved complexity reduction. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Hybrid systems Predictive control Mixed logical dynamical systems multi-parametric programming Mixed integer linear programming Computational complexity

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Dynamic modelling and parametric control for the polymer electrolyte membrane fuel cell system

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JOURNAL OF POWER SOURCES 2013年 232卷 270-278页

作者： Zhao, Yuehong Pistikopoulos, Efstratios Chinese Acad Sci Inst Proc Engn State Key Lab Multiphase Complex Syst Beijing 100190 Peoples R China Univ London Imperial Coll Sci Technol & Med Ctr Proc Syst Engn London SW7 2AZ England

This paper addresses the development of a parametric controller for the Polymer Electrolyte Membrane (PEM) fuel cell system, and the investigation of its performance. First, the dynamic modelling is carried out to obtain the transient performance of the PEM fuel cell system and to form the basis for the controller design. Then, a parametric controller is designed to optimize its operation, focussing on tracking the output voltage and stack temperature set points by suitably manipulating the oxygen and hydrogen excess ratios, and cooling water flow rate. It is realized by formulating a Model Predictive Control (MPC) problem, which is solved via parametric programming technique to obtain the explicit control action function. The closed-loop simulation results show that the designed parametric controller can track the set points well, and ensures reliable performance in the presence of the current load fluctuations. Compared to proportional integral derivative controller (PID), it has the advantages of satisfying the imposed constraints, the potential of simple hydrogen control operation and lower hydrogen consumption. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Polymer electrolyte membrane fuel cell Dynamic modelling parametric control multi-parametric programming

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Methodology for robust multi-parametric control in linear continuous-time systems

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JOURNAL OF PROCESS CONTROL 2019年 73卷 58-74页

作者： Sun, Muxin Villanueva, Mario E. Pistikopoulos, Efstratios N. Chachuat, Benoit Imperial Coll London Dept Chem Engn Ctr Proc Syst Engn London England Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX USA ShanghaiTech Univ Sch Informat Sci & Technol Shanghai Peoples R China

This paper presents an extension of the recent multi-parametric (mp-)NCO-tracking methodology by Sun et al. [Comput. Chem. Eng. 92 (2016) 64-77] for the design of robust multi-parametric controllers for constrained continuous-time linear systems in the presence of uncertainty. We propose a robustcounterpart formulation and solution of multi-parametric dynamic optimization (mp-DO), whereby the constraints are backed-off based on a worst-case propagation of the uncertainty using either interval analysis or ellipsoidal calculus and an ancillary linear state feedback. We address the case of additive uncertainty, and we discuss approaches to dealing with multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservativeness. In order to assist with the implementation of these controllers, we also investigate the use of data classifiers based on deep learning for approximating the critical regions in continuous-time mp-DO problems, and subsequently searching for a critical region during on-line execution. We illustrate these developments with the case studies of a fluid catalytic cracking (FCC) unit and a chemical reactor cascade. (C) 2018 The Author(s). Published by Elsevier Ltd.

关键词： Constrained linear-quadratic regulator Robust model predictive control multi-parametric programming multi-parametric NCO-tracking Neural network classifier

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Robust optimal control of material flows in demand-driven supply networks

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2006年第1期363卷 24-31页

作者： Laumanns, M Lefeber, E ETH Dept Math Inst Operat Res CH-8092 Zurich Switzerland Eindhoven Univ Technol Dept Mech Engn Syst Engn Grp NL-5600 MB Eindhoven Netherlands

We develop a model based on stochastic discrete-time controlled dynamical systems in order to derive optimal policies for controlling the material flow in supply networks. Each node in the network is described as a transducer such that the dynamics of the material and information flows within the entire network can be expressed by a system of first-order difference equations, where some inputs to the system act as external disturbances. We apply methods from constrained robust optimal control to compute the explicit control law as a function of the current state. For the numerical examples considered, these control laws correspond to certain classes of optimal ordering policies from inventory management while avoiding, however, any a priori assumptions about the general form of the policy. (c) 2006 Elsevier B.V. All rights reserved.

关键词： supply networks discrete dynamical systems constrained robust optimal control multi-parametric programming

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