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Robust explicit model predictive control for linear systems via interpolation techniques

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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Efficient Robust Look-Ahead Dispatch Incorporating Critical Region Preparation in Gap Time

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第5期36卷 4840-4843页

作者： Zheng, Weiye Li, Zhigang Huansheng, Zhou South China Univ Technol Sch Elect Power Guangzhou 510641 Peoples R China

Robust look-ahead dispatch (RLAD) is essential to manage uncertainties in power systems. As its key step, the worst-case scenario identification (WCSI) problem is cast to a max-min program. This computationally intensive procedure has to be performed repeatedly, impairing the computational efficiency of RLAD. To address this issue, an efficient RLAD scheme incorporating critical region preparation in gap time is proposed. The computation burden is mostly transferred from the online decision stage to the gap time via a customized technique based on multi-parametric programming. The accuracy of computing the critical regions is validated by the test in a six-bus system, and the proposed method is shown to cut down 21% of total iterations and save computational time dramatically by the test in a practical-scale system in Northeastern China.

关键词： Uncertainty Wind power generation Power systems Optical wavelength conversion Linear programming Computational efficiency Security Critical region multi-parametric programming robust look-ahead dispatch worst-case scenario identification

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Dynamic programming for scalable just-in-time economic dispatch with non-convex constraints and anytime participation

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2020年 123卷 106217-106217页

作者： Kim, Jinsung Kim, Kwang-Ki K. Inha Univ Dept Elect Engn Incheon 22212 South Korea

This paper considers two classes of dynamic programming frameworks for economic dispatch in power systems. The first framework is of classical continuous convex economic dispatch. We present recursive formulae for computing the parameters of value functions and show that the value functions are generalized quadratic and generalized piecewise quadratic for unconstrained and generation-capacity constrained convex economic dispatch, respectively. The second framework is of discrete dynamic programming for economic dispatch with non-convex cost functions and constraints. The discrete dynamic programming framework is computationally scalable and decentralized. The computations of the value table are scalable in the sense that any newcomers and seceders of generation units can be numerically efficiently taken care of, by not re doing the entire backward induction process but only computing the value tables of the successors. Extension of the discrete dynamic programming framework to dynamic economic dispatch with ramp constraints is also presented. We demonstrate the proposed algorithms by three numerical case studies. One is for non-convex economic dispatch with 15 generation units and prohibited operating zones. Another example of a larger scale system of 53 units with consideration of transmission losses is also studied. For a dynamic case, the proposed method is applied to a dynamic economic dispatch problem with non-convex ramp constraints.

关键词： Smart grid Distributed generation Real-time dispatch Economic dispatch Unit commitment Non-convex optimization Operating prohibited zones multi-parametric programming Dynamic programming

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On-Line Optimization via Off-Line parametric Optimization! – A Guided Tour to parametric programming and Control

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IFAC Proceedings Volumes 2004年第9期37卷 1-7页

作者： Efstratios N. Pistikopoulos Vivek Dua Centre for Process Systems Engineering Imperial College London SW7 2AZ U.K. Centre for Process Systems Engineering University College London WC1E 7JE U.K.

In this paper model predictive control problems are reformulated as multi-parametric programs. The optimal value of control variables is obtained as an explicit function of the state variables. This reduces on-line op... 详细信息

关键词： Real-time optimization model predictive control multi-parametric programming multi-parametric dynamic optimization hybrid control

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A Single-valued Pentagonal Neutrosophic Geometric programming Approach to Optimize Decision Maker's Satisfaction Level

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INTERNATIONAL JOURNAL OF ADVANCED COMPUTER SCIENCE AND APPLICATIONS 2023年第4期14卷 346-356页

作者： Nath, Satyabrata Das, Purnendu Debnath, Pradip Assam Univ Dept Comp Sci Silchar Assam India Assam Univ Dept Appl Sci & Humanities Silchar Assam India

Achieving the desired level of satisfaction for a decision- maker in any decision- making scenario is considered a challenging endeavor because minor modifications in the process might lead to incorrect findings and inaccurate decisions. In order to maximize the decision-maker's satisfaction, this paper proposes a Single-valued Neutrosophic Geometric programming model based on pentagonal fuzzy numbers. The decision-maker is typically assumed to be certain of the parameters, but in reality, this is not the case, hence the parameters are presented as neutrosophic fuzzy values. The decision-maker, with this strategy, is able to achieve varying levels of satisfaction and dissatisfaction for each constraint and even complete satisfaction for certain constraints. Here the decision maker aims to achieve the maximum level of satisfaction while maintaining the level of hesitation and minimizing dissatisfaction in order to retain an optimum solution. Furthermore, transforming the objective function into a constraint adds one more layer to the N-dimensional multi-parametrizes and. The advantages of this multi-parametrized proposed method over the existing ones are proven using numerical examples.

关键词： Decision making pentagonal neutrosophic numbers single-valued neutrosophic geometric programming multi-parametric programming

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Conventional and Explicit Approaches for Simultaneous Moving Horizon Estimation and Model Predictive Control: A Comparative Evaluation 6

Conventional and Explicit Approaches for Simultaneous Moving...

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6th Conference on Advances in Control and Optimization of Dynamical Systems (ACODS)

作者： Thosar, Devavrat Mukherjee, Tathagata Gilbile, Pravin Bhushan, Mani Indian Inst Technol Dept Chem Engn Mumbai Maharashtra India

Model Predictive Control (MPC) has been applied across a wide range of engineering applications including process industries. MPC requires complete knowledge of states at the current instant which can either be measured directly or estimated using a state estimator. Of late, Moving Horizon Estimation (MHE) has been widely used as a state estimator owing to its ability to handle constraints. Both MPC and MHE involve solving an optimization problem at each sampling instant which can prove computationally burdensome for fast systems. multiparametric programming based explicit approaches have been proposed in literature as a possible approach for solving the online optimization problems in a computationally efficient manner. In the current work, feasibility of the explicit approaches simultaneously for both MPC and MHE is investigated using simulation as well as experimental studies on a quadruple tank setup. The computational efforts required for this simultaneous implementation of the explicit approaches for MPC and MHE are compared with the conventional optimization approach. Results indicate feasibility of multi-parametric implementation for lower horizon lengths. (C) 2020, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Model Predictive Control Moving Horizon Estimation multi-parametric programming Explicit MPC

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Controller complexity reduction for piecewise affine systems through safe region elimination

Controller complexity reduction for piecewise affine systems...

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46th IEEE Conference on Decision and Control

作者： Christophersen, Frank J. Zeilinger, Melanie N. Jones, Colin N. Morari, Manfred ETH Automat Control Lab CH-8092 Zurich Switzerland

ISBN: (纸本)9781424414970

We consider the class of piecewise affine optimal state feedback control laws applied to discrete-time piecewise affine systems, motivated by recent work on the computation of closed-form MPC controllers. The storage demand and complexity of these optimal closed-form solutions limit their applicability in most real-life situations. In this paper we present a novel algorithm to a posteriori reduce the storage demand and complexity of the closed-form controller without losing closed-loop stability or all time feasibility while guaranteeing a bounded performance decay compared to the optimal solution. The algorithm combines simple polyhedral manipulations with (multi-parametric) linear programming and the effectiveness of the algorithm is demonstrated on a large numerical example.

关键词： constrained systems piecewise affine systems receding horizon control closed-form MPC multi-parametric programming complexity reduction approximation

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Relations between Model Predictive Control and Reinforcement Learning

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IFAC-PapersOnLine 2017年第1期50卷 4920-4928页

作者： Görges D. Juniorprofessorship for Electromobility University of Kaiserslautern Erwin-Schrödinger-Straße 12 Kaiserslautern 67663 Germany

In this paper relations between model predictive control and reinforcement learning are studied for discrete-time linear time-invariant systems with state and input constraints and a quadratic value function. The principles of model predictive control and reinforcement learning are reviewed in a tutorial manner. From model predictive control theory it is inferred that the optimal value function is piecewise quadratic on polyhedra and that the optimal policy is piecewise affine on polyhedra. Various ideas for exploiting the knowledge on the structure and the properties of the optimal value function and the optimal policy in reinforcement learning theory and practice are presented. The ideas can be used for deriving stability and feasibility criteria and for accelerating the learning process which can facilitate reinforcement learning for systems with high order, fast dynamics, and strict safety requirements. © 2017

关键词： actor-critic structure approximate dynamic programming Model predictive control multi-parametric programming reinforcement learning

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Coordination of Distributed Energy Resources in a Distribution Network via Nonlinear Dual Critical Region Exploration

Coordination of Distributed Energy Resources in a Distributi...

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IEEE-Power-and-Energy-Society General Meeting (PESGM)

作者： Liu, Haitian Guo, Ye Tsinghua Univ Tsinghua Berkeley Shenzhen Inst Shenzhen 518055 Guangdong Peoples R China

ISBN: (纸本)9798350381849;9798350381832

In this paper, we proposed a novel coordination scheme called Nonlinear Dual Critical Region Exploration (NDCRE) to coordinate the flexibilities of distributed energy resources. Each bus acts as a local agent and can interact with the system operator in the distribution network to realize the joint operation. The proposed NDCRE leverages multi-parametric programming and dual decomposition for efficient information exchange and high decomposable structure. Such a scheme enables a fast finite convergent property in large-scale second-order cone programming, which significantly enhances the solution ability of CRE proposed in [1]. Numerical results verified its effectiveness in complex distribution grid settings.

关键词： distributed energy resources distributed optimization multi-parametric programming dual decomposition

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The explicit solution of constrained LP-based receding horizon control

The explicit solution of constrained LP-based receding horiz...

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39th IEEE Conference on Decision and Control

作者： Bemporad, A Borrelli, F Morari, M ETH Zentrum Automat Control Lab CH-8092 Zurich Switzerland

ISBN: (纸本)0780366387

For discrete-time linear time-invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, as a function of the initial state, the solution to optimal control problems that can be formulated using a linear program. In particular, we focus our attention on a receding horizon control scheme where the performance criterion is based on a mixed 1/infinity -norm (i.e., 1-norm with respect to time and oo-norm with respect to space). We show that the optimal control profile is a piecewise linear and continuous function of the initial state. Thus, when the optimal control problem is solved at each time step according to a moving horizon scheme, the on-line computation of the resultant MPC controller is reduced to a simple linear function evaluation, instead of the typical expensive linear program required up to now. The technique proposed has both theoretical and practical advantages. From a theoretical point of view, the explicit solution gives insight on the action of the controller in different regions of the state space, and highlights conditions of degeneracy. From a practical point of view, the proposed technique is attractive for a wide range of applications where the simplicity of the on-line computational complexity is a crucial requirement.

关键词： model predictive control constraints piecewise linear control multi-parametric programming linear programming

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