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ROBUST OUTPUT FEEDBACK MODEL PREDICTIVE CONTROL: A STOCHASTIC APPROACH

ASIAN JOURNAL OF CONTROL 2017年第6期19卷 2085-2096页

作者： Mohammadkhani, Mohammadali Bayat, Farhad Jalali, Ali Akbar Iran Univ Sci & Technol Dept Elect Engn Tehran Iran Univ Zanjan Dept Elect Engn Zanjan Iran

This paper addresses the robust explicit model predictive control scheme for linear systems with input and output constraint in the presence of disturbances and noise. Conditions for disturbance rejection are established by incorporating a full state/disturbance observer. The separation principle is applied to design an optimal observer in the unconstrained problem. Then, an efficient algorithm is developed to explicitly design observer gains by minimizing a quadratic performance criterion. It is shown that the solution includes a set of regions with piecewise affine functions of the state and reference vectors and a set of regions with optimal observers. In the proposed method, two sets of partitions associated with the control law and the observer gains are obtained. Therefore, the online computation includes finding the active regions of both observer and control law partitions in which the current state is located. The proposed technique is particularly attractive for a wide range of practical problems where the exact model of the actual system is not available.

关键词： model predictive control robust output feedback multi-parametric programming estimation disturbance observer

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

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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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A coordinated scheme for transmission and distribution expansion planning: A Tri-level approach

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ELECTRIC POWER SYSTEMS RESEARCH 2021年 196卷

作者： El-Meligy, Mohammed A. Sharaf, Mohamed Soliman, Ahmed T. King Saud Univ Adv Mfg Inst Riyadh 11421 Saudi Arabia King Saud Univ Coll Engn Ind Engn Dept POB 800 Riyadh 11421 Saudi Arabia

In traditional power system planning problems, transmission and distribution networks are separated, which is not suitable for future power systems due to the rapid development of active distribution networks. This paper presents a hierarchy framework to optimize the transmission and distribution network expansion in a simultaneous manner. The proposed decentralized decision-making architecture forms a Tri-level structure where the first level is the transmission expansion planning (TEP) problem solved by the transmission system operator (TSO) as the leader, while the second level is the distribution expansion planning (DEP) problem solved by the distribution system operators (DSOs) as the second level followers. The third level problem is the optimal economic dispatch problem solved by the independent system operator (ISO) as the third level follower. The economic dispatch problem is replaced by its primal-dual (PD) formulation leading to a bilevel multi-follower mixed-integer linear programming (BMF-MILP) problem. Then, by using multi-parametric programming (MPP) method, the BMF-MILP problem is recast as several single level independent optimization problems. Numerical experiments are shown to corroborate the efficiency and tractability of the presented model. The results show the new coordinated transmission and distribution expansion planning (CTDEP) model provides additional flexibility and reduces the total cost.

关键词： Bilevel multi-follower optimization Coordinated planning Distribution expansion planning Transmission expansion planning multi-parametric programming Primal-dual formulation

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Integrated stochastic transmission network and wind farm investment considering maximum allowable capacity

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ELECTRIC POWER SYSTEMS RESEARCH 2023年 215卷

作者： Alnowibet, Khalid A. Alrasheedi, Adel F. Alshamrani, Ahmad M. King Saud Univ Coll Sci Stat & Operat Res Dept Riyadh 11451 Saudi Arabia

This research presents a novel mathematical methodology for integrated transmission network and wind farm investment (ITWI) considering maximum allowable capacity (MAC). The joint problem of transmission and wind farm investment planning is carried out under a central planner perspective, where load and wind power un-certainties are managed using scenario-based stochastic programming. Distinct from the existing models in which the installation capacity of wind farms is restricted only by the available investment budget, the wind power capacity is limited by MAC considering strength measures. In this regard, the investment problem is addressed as a bi-level programming model where the upper level seeks to minimize the investment cost asso-ciated with transmission lines and wind farms plus the operation cost while the lower level determines the MAC of wind farms. The existence of integer decision variables in the lower level renders Karush-Kuhn-Tucker (KKT) conditions invalid. Thus, the multi-parametric programming (MPP) method is utilized to solve the mixed-integer bi-level linear programming (MIBLP). Numerical tests on two different power systems corroborate the efficiency of the proposed model. The comparable results demonstrate that ignoring the MAC of wind farms leads to inefficient solutions due to additional unnecessary investment in the wind energy sector.

关键词： Maximum allowable capacity Mixed-integer bi-level linear programming multi-parametric programming Stochastic programming Transmission network investment Wind power investment

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Simultaneous design & control of a reactive distillation system - A parametric optimization & control approach

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CHEMICAL ENGINEERING SCIENCE 2021年 230卷

作者： Tian, Yuhe Pappas, Iosif Burnak, Baris Katz, Justin 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

We present a detailed dynamic model for a reactive distillation system, based on which we develop design-dependent explicit optimal control strategies. A mixed-integer dynamic optimization formulation is then proposed integrating design, control and operational components, the solution of which allows us to derive explicit closed-loop strategies that maintain stable and operable conditions in the presence of process disturbances. The simultaneous approach is illustrated with the design of a methyl tert-butyl ether reactive distillation system example as a part of the developed model library in the RAPID SYNOPSIS project. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Reactive distillation Simultaneous design and control multi-parametric programming Explicit model predictive control Mixed-integer dynamic optimization

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Some Necessary and Sufficient Conditions for Correctness of Linear Machine in Presence of Numerical Errors

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IFAC-PapersOnLine 2020年第2期53卷 11368-11373页

作者： Aditi Sharma Mani Bhushan Department of Chemical Engineering Indian Institute of Technology Bombay India

Linear machine (LM) has been recently proposed (Airan et al., 2017) for solving the point location problem which arises in explicit model predictive control (e-MPC). LM associates a linear discriminant function with each critical region identified in the offline phase in e-MPC. The solution to the online point location problem in the LM approach then simply corresponds to the region whose discriminant function attains the largest value amongst all the discriminant functions. LM involves two steps: (i) identification of neighbouring critical regions, and (ii) finding the discriminant functions by writing constraints involving discriminant functions of neighbouring pairs of regions. Both these steps involve solving linear programming (LP) problems. Similar to any other optimization problem, the constraints of the LP are satisfied with some tolerances. Even though theoretically sound, the resulting LM may not accurately identify the critical region due to the numerical errors arising from these tolerances. In the current work, we identify some conditions which can be used as an aid by the user to judge the accuracy of LM results. In particular, we give a necessary condition for step (i) whose violation will yield incorrect misclassification for some point location problems. We also propose a sufficient condition whose satisfaction guarantees the accuracy of linear machine solution despite numerical errors which may have crept in during step (ii) of the LM design. This condition needs to be evaluated for each specified point during the point location phase. We illustrate these ideas on the well known quadruple tank system.

关键词： point location explicit model predictive control multi-parametric programming

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Explicit Robust Model Predictive Control *

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IFAC Proceedings Volumes 2009年第11期42卷 243-248页

作者： Efstratios N. Pistikopoulos Nuno P. Faísca Konstantinos I. Kouramas Christos Panos Centre for Process Systems Engineering Department of Chemical Engineering Imperial College London SW7 2AZ London UK Process Systems Enterprise Ltd London UK

Abstract Explicit robust multi–parametric feedback control laws are designed for constrained dynamic systems involving uncertainty in the left-hand side(LHS) of the underlying MPC optimization model. Our proposed procedure features: (i) a robust reformulation/optimization step, (ii) a dynamic programming framework for the model predictive control (MPC) problem formulation, and (iii) a multi-parametric programming solution step.

关键词： Robust model predictive control multi-parametric programming dynamic programming multi–parametric control explicit control

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A patchy approximation of explicit model predictive control

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INTERNATIONAL JOURNAL OF CONTROL 2012年第12期85卷 1929-1941页

作者： Hoai-Nam Nguyen Olaru, Sorin Hovd, Morten SUPELEC Syst Sci E3S Dept Automat Control Gif Sur Yvette France Norwegian Univ Sci & Technol Dept Engn Cybernet N-7034 Trondheim Norway

The explicit solution of multi-parametric optimisation problems (MPOP) has been used to construct an off-line solution to relatively small-and medium-sized constrained control problems. The control design principles are based on receding horizon optimisation and generally use linear prediction models for the system dynamics. In this context, it can be shown that the optimal control law is a piecewise linear (PWL) state feedback defined over polytopic cells of the state space. However, as the complexity of the related optimisation problems increases, the memory footprint and implementation of such explicit optimal solution may be burdensome for the available hardware, principally due to the high number of polytopic cells in the state-space partition. In this article we provide a solution to this problem by proposing a patchy PWL feedback control law, which intend to approximate the optimal control law. The construction is based on the linear interpolation of the exact solution at the vertices of a feasible set and the solution of an unconstrained linear quadratic regulator (LQR) problem. With a hybrid patchy control implementation, we show that closed-loop stability is preserved in the presence of additive measurement noise despite the existence of discontinuities at the switch between the overlapping regions in the state-space partition.

关键词： model predictive control multi-parametric programming smooth patchy Lyapunov function positively invariant set piecewise-linear control

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Robust explicit model predictive control for linear systems via interpolation techniques

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2010年第10期20卷 1166-1175页

作者： Sui, D. Feng, L. Ong, C. J. Hovd, M. Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway Natl Univ Singapore Singapore MIT Alliance Singapore 119260 Singapore

This paper presents a novel interpolation-based model predictive control (IMPC) for constrained linear systems with bounded disturbances. The idea of so-called 'pre-stabilizing' MPC is extended by making interpolation among several 'pre-stabilizing' MPC controllers, through which the domain of attraction can be magnificently enlarged. Compared with the standard 'pre-stabilizing' MPC, the proposed approach has the advantage of combining the merits of having a large domain of attraction and a good behavior. Furthermore, such an IMPC problem can be solved off-line by multi-parametric programming. The optimal solution is given in an explicitly piecewise affine form. A simple algorithm for the implementation of the explicit MPC control laws is also proposed. Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： linear constrained systems with bounded disturbances interpolated model predictive control multi-parametric programming model predictive control interpolation

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Optimal constrained control allocation in marine surface vessels with rudders

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IFAC Proceedings Volumes 2003年第21期36卷 181-186页

作者： Tor A. Johansen Thomas P. Fuglseth Petter Tøndel Thor I. Fossen Department of Engineering Cybernetics Norwegian University of Science and Technology NO-7491 Trondheim Norway.

A propeller with a rudder can produce a thrust vector within a range of directions and magnitudes in the horizontal plane for low-speed maneuvering and dynamic positioning. The set of attainable thrust vectors is non-convex because significant lift can be produced by the rudder only with forward thrust. We suggest to decompose the attainable thrust region into a finite union of convex polyhedral sets and derive a mixed-integer-like convex quadratic programming formulation of the optimal control allocation problem for marine vessels with any number of rudders as well as thrusters and other propulsion devices. Actuator rate and position constraints are explicitly taken into account. Using multi-parametric quadratic programming software, an explicit piecewise linear representation of the least-squares optimal control allocation law is pre-computed. It can be implemented with low computational complexity and high software reliability without the use of real-time optimization. The method is illustrated using a scale model ship in a basin.

关键词： Ship control multi-parametric programming disjunctive programming

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