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Optimal constrained control allocation in marine surface vessels with rudders

CONTROL ENGINEERING PRACTICE 2008年第4期16卷 457-464页

作者： Johansen, Tor A. Fugseth, Thomas P. Tondel, Petter Fossen, Thor I. Norwegian Univ Sci & Technol Dept Engn Cybernet 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. It is suggested to decompose the attainable thrust region into a finite union of convex polyhedral sets and 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 is derived. 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 therefore 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. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： ship control multi-parametric programming disjunctive programming quadratic programming constrained control control allocation

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Simultaneous design of explicit/multi-parametric constrained moving horizon estimation and robust model predictive control

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COMPUTERS & CHEMICAL ENGINEERING 2013年 54卷 24-33页

作者： Voelker, Anna Kouramas, Konstantinos Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England United Technol Res Ctr Ireland Cork Ireland

In this work we present a rigorous methodology for the simultaneous design of moving horizon estimation (MHE) and robust model predictive control based on multi-parametric programming. First, an explicit/multi-parametric solution of the MHE is derived. Then, a novel method is presented that allows for the derivation of the estimation error dynamics, the bounding set of the estimation error, and the state estimate dynamic equations of constrained MHE. A framework is then presented for the design of robust explicit/multi-parametric model predictive control (MPC) controllers, based on tube-based MPC methods, which ensures that no constraints are violated due to the estimation error and the process noise in the system. This framework is first shown for the Kalman filter and unconstrained MHE and is then extended to the constrained MHE. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Moving horizon estimation MHE Error dynamics multi-parametric programming Robust MPC Explicit MPC

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A Framework for Evaluating the Best Achievable Performance by Distributed Lifetime-Efficient Routing Schemes in Wireless Sensor Networks

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2015年第6期14卷 3231-3246页

作者： Habibi, Jalal Aghdam, Amir G. Ghrayeb, Ali Concordia Univ Dept Elect & Comp Engn Montreal PQ H3G 1M8 Canada Texas A&M Univ Qatar Dept Elect & Comp Engn Doha Qatar

This paper is concerned with energy-efficient routing in wireless sensor networks. Most of the existing routing schemes assign energy-related costs to network links and obtain the shortest paths for the nodes to balance the flowing traffic within the network and increase its lifetime. However, the optimal link cost values and the maximum achievable lifetime are not known for the majority of the existing schemes. A framework is provided in this work to analytically derive the best achievable performance that can be obtained by any distributed routing algorithm based on the shortest-path approach. Given a network configuration and an energy consumption model, the presented framework provides the optimal link cost assignment which yields the maximum lifetime in a distributed shortest-path routing strategy. The results are extended to the case of variable link cost assignment as well. A heuristic algorithm is also developed to obtain approximate solutions to the best performance problem with limited computational complexity. In particular, the proposed framework provides the optimal route selection as a benchmark to evaluate the energy efficiency of existing routing algorithms.

关键词： Distributed shortest-path routing lifetime maximization minimum-cost routing multi-parametric programming wireless sensor networks

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Explicit MPC Based on the Galerkin Method for AGC Considering Volatile Generations

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IEEE TRANSACTIONS ON POWER SYSTEMS 2020年第1期35卷 462-473页

作者： Qiu, Yiwei Lin, Jin Liu, Feng Song, Yonghua Tsinghua Univ Dept Elect Engn State Key Lab Control & Simulat Power Syst & Gene Beijing 100087 Peoples R China Univ Macau Dept Elect & Comp Engn Macau 999078 Peoples R China Tsinghua Univ Dept Elect Engn Beijing 100087 Peoples R China

The imbalance of generation and load caused by the increasing integration of volatile generations poses challenges on frequency regulation. AGC is required to respond to the generation fluctuations without violating operational and security constraints. Explicit model predictive control (EMPC) provides an approach to reaching such requirements, which calculates the control laws of MPC in an explicit form, allowing for offline validation of the controller and enabling fast online computation. However, the partition number of EMPC & x0027;s piecewise affine control laws grows exponentially with the number of constraints and prediction/control horizons, which hinders its application in large systems. In this paper, we propose an alternative explicit control approach for AGC by approximating the control laws of EMPC using Legendre polynomial series expansions, thus entirely eliminating the partition issue. The Galerkin method is applied to the KKT conditions of EMPC & x0027;s multiparametric quadratic programming (mp-QP) problem to compute the approximation. Case studies in an illustrative system and IEEE 118-Bus System verify the performance and efficiency of the proposed controller.

关键词： Automatic generation control Frequency control Power system dynamics Predictive control Optimization Method of moments Optimal control Automatic generation control explicit model predictive control galerkin projection legendre polynomials multi-parametric programming optimal control spectral method

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Power system operational reliability assessment based on the data center energy consumption elastic space

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FRONTIERS IN ENERGY RESEARCH 2024年 12卷

作者： Zhang, Sheng Gao, Jinkun Qian, Hao Yu, Juan Luo, Shaojie Guo, Qiang Hangzhou Yuhang Dist Power Supply Co State Grid Zhejiang Elect Power Co Ltd Hangzhou Zhejiang Peoples R China Chongqing Univ State Key Lab Power Transmiss Equipment & Syst Sec Chongqing Peoples R China Hangzhou Elect Power Equipment Mfg Co Ltd Yuhang Qunli Complete Elect Mfg Branch Hangzhou Zhejiang Peoples R China

In the era of big data, data centers with high energy consumption, interconnectivity, and load flexibility have developed rapidly. However, due to data privacy issues, the traditional power-system operational reliability assessment (ORA) struggles to precisely consider the load flexibility of data centers, leading to inaccurate evaluation. To this end, this article proposes an ORA method considering the load flexibility of data centers via the energy consumption elastic space. By transforming the inner operation constraints of data centers into an equivalent elastic space, the ORA does not require any private data to complete the evaluation. Specifically, the energy consumption model of data centers is established to accurately describe the load flexibility. Then, based on multi-parametric programming techniques, the energy consumption elastic space of data centers is characterized by data centers' power demand constraints, which do not involve privacy data, and no privacy concerns exist. Finally, the ORA model and the evaluation method based on the energy consumption elastic space can be constructed. With a lot of data center operation constraints being replaced by power demand constraints, the proposed method can complete an evaluation faster without accuracy loss. Its effectiveness is validated through simulations using the IEEE RTS 24-bus system and a provincial 661-bus system.

关键词： data center multi-parametric programming power system operational reliability assessment data privacy

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parametric Distribution Optimal Power Flow With Variable Renewable Generation

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IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第3期37卷 1831-1841页

作者： Guo, Zhongjie Wei, Wei Chen, Laijun Dong, ZhaoYang Mei, Shengwei Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing 100084 Peoples R China Qinghai Univ New Energy Ind Res Ctr Xining 810016 Peoples R China Univ New South Wales Sch Elect Engn & Telecom Sydney NSW 2052 Australia Univ New South Wales UNSW DGFI Sydney NSW 2052 Australia

The output of renewable generation depends on the real-time weather conditions and changes rapidly;so the economic operating point of the power system varies over time. This paper aims to find the explicit mapping from variable renewable power to optimal power flow solutions. To this end, we propose a parametric distribution optimal power flow (P-DOPF) method, which gives the optimal dispatch strategy and power flow status as analytical functions of the renewable output. With the established distribution optimal power flow problem based on the relaxed Distflow model, the first step is to perform a global polyhedral approximation on the second-order cone constraints to develop a linearized formulation. The second step is to obtain the P-DOPF model by treating renewable power output as parameters;then, the P-DOPF problem gives rise to a multi-parametric linear program (mp-LP). Third, we prove that the optimal solution and optimal value of the P-DOPF are piecewise linear functions of the parameters and we design an adaptive-sampling algorithm to construct the optimal value and optimal solution functions, as well as the partition of the parameter set, subject to a given error tolerance;this algorithm is not influenced by model degeneracy, a common difficulty of existing mp-LP algorithms. The P-DOPF framework provides an explicit real-time control policy of generators in response to the renewable output. Case studies on the IEEE 33 and 69-bus systems verify the effectiveness and performance of the proposed method;by comparison, the proposed method outperforms the established affine policy method in computational efficiency and optimality by 24.5% and 4.62%, respectively.

关键词： Renewable energy sources Real-time systems Generators Distribution networks Optimization Wind forecasting Uncertainty Distribution system multi-parametric programming real-time optimal power flow renewable generation

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Approximate solution of mp-MILP problems using piecewise affine relaxation of bilinear terms

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COMPUTERS & CHEMICAL ENGINEERING 2014年 61卷 136-155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

We propose an approximate solution strategy for multi-parametric mixed integer linear programming (mp-MILP) problems with parameter dependency at multiple locations in the model. A two-stage solution strategy, consisting of an approximation stage and a multi-parametric programming stage, is introduced. At the approximation stage, surrogate mp-MILP models are derived by overestimating bilinear terms in the constraints over an ab initio partitioning of the domain. We then incorporate piecewise affine relaxation based models using a linear partitioning scheme and a logarithmic partitioning scheme, respectively. The models are tuned by the number of partitions chosen. Problem sizes of the varied models, and computational requirements for the algorithmic procedure are compared. The conservatism of the suboptimal solution of the mp-MILP problem for the piecewise affine relaxation based two-stage method is discussed. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： multi-parametric programming Mixed-integer programming Bilinear programming

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Robust Low Complexity Predictive Control of Constrained Piecewise Affine Systems with Bounded Disturbances

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2010年第2期8卷 439-444页

作者： Chen, Fu Qi, Dong-Lian Zhejiang Univ Dept Syst Sci & Engn Hangzhou 310027 Zhejiang Peoples R China

A robust low complexity model predictive control (M PC) scheme, referred to as robust one-step control, is proposed for constrained piecewise affine (PWA) systems with bounded disturbances. First, the maximal robust stabilizable set is added into the MPC formulation to guarantee the robust feasibility and low complexity. Second, the robust stability is analyzed via linear matrix inequalities (EMI). Extensive numerical examples illustrate the low complexity of the proposed robust one-step control.

关键词： Constrained piecewise affine system linear matrix inequalities model predictive control multi-parametric programming receding horizon control robust invariant set

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multi-Resolution Explicit Model Predictive Control: Delta-Model Formulation and Approximation

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2013年第11期58卷 2979-2984页

作者： Bayat, Farhad Johansen, Tor Arne Univ Zanjan Dept Engn Control Syst Grp Fac Elect Engn Zanjan *** Iran Norwegian Univ Sci & Technol Dept Engn Cybernet Ctr Autonomous Marine Operat & Syst N-7491 Trondheim Norway

This paper deals with the explicit solution and approximation of the constrained linear finite time optimal control problem for systems with fast sampling rates. To this aim, the recently developed explicit model predictive control (eMPC) is reformulated and characterized using the delta-operator to enjoy its promising advantages compared to the time-shift operator. Using the proposed delta-model eMPC formulation, a systematic method is proposed for first designing a low-complexity approximate eMPC solution and then improving its closed loop action without first determining an exact optimal solution that might be of prohibitive complexity. It is shown that the stability and feasibility of the proposed sub-optimal solution is guaranteed.

关键词： Approximate explicit model predictive control delta-operator explicit model predictive control multi-parametric programming multi-resolution model predictive control

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ROBUST OUTPUT FEEDBACK MODEL PREDICTIVE CONTROL: A STOCHASTIC APPROACH

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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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