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Privacy-Preserving distributed optimal control for Vehicular Platoon With Quantization

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2024年第10期25卷 14572-14585页

作者： He, Yejie Chen, Yong Pan, Chengwei Ali, Ikram Univ Elect Sci & Technol China Sch Automat Engn Chengdu 611731 Sichuan Peoples R China Sichuan Prov Engn Technol Res Ctr Elect Vehicle Dr Chengdu 611731 Sichuan Peoples R China Shenzhen Univ Natl Engn Lab Big Data Syst Comp Technol Shenzhen 518060 Peoples R China

In this paper, the distributed optimal control for vehicular platoons with quantized states and control inputs is studied and the preservation of vehicles' privacy is investigated. Firstly, the structure of system composed of cloud servers, eavesdroppers, and the vehicular platoon with unknown nonlinear dynamics and disturbance is established. Secondly, to restrain the uncertainty and nonlinearity, a policy iteration algorithm integrating quantized control inputs is proposed to stabilize vehicles without knowing their dynamics. The optimality and convergence of the iteration are proved rigorously. Then, the algorithm is utilized by the actor-critic framework with quantized states and control inputs. Due to the reason that conventional distributed control approaches for platoon will inevitably leak privacy, by introducing leveled fully homomorphic encryption, the actor-critic framework is modified to work in a privacy-preserving manner, and the privacy of each vehicle is protected from unauthorized entities. Finally, the comparison results demonstrate that with proposed scheme, the average instant cost of each vehicle is improved (at least 56.52% under experiment condition) and the stability, efficiency and security of system with proposed method are verified by simulations.

关键词： Vehicular platoon distributed optimal control quantization privacy-preserving

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Discontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2022年 128卷 1-11页

作者： Wang, Tao Li, Binjie Xie, Xiaoping China Nucl Power Technol Res Inst Co Ltd Shenzhen 518028 Peoples R China Sichuan Univ Sch Math Chengdu 610064 Peoples R China

This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of state and co -state are decomposed into singular and regular parts, and some growth estimates are obtained for the singular parts. By following the variational discretization concept, a full discretization is applied to the corresponding state and co-state equations by using linear conforming finite element method in space and piecewise constant discontinuous Galerkin method in time. Error estimates are derived by employing the growth estimates. In particular, graded temporal grids are adopted to obtain the first-order temporal accuracy. Finally, numerical experiments are performed to verify the theoretical results.

关键词： distributed optimal control Time fractional diffusion equation Growth estimate Finite element Discontinuous Galerkin method Error estimate

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Using distributed optimal control in economics: A numerical approach based on the finite element method

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optimal control APPLICATIONS & METHODS 2001年第5-6期22卷 231-249页

作者： Calzada, EC Goetz, RU Univ Zaragoza Dept Econ Anal Zaragoza 50005 Spain Univ Girona Dept Econ Girona 17071 Spain

The finite element method is employed to transform a distributed optimal control problem into a discrete optimization problem which can be solved with standard mathematical techniques. We use distributed optimal control in order to determine the optimal selective logging regime of a privately owned non-homogeneous forest. This regime has become nowadays a standard approach for the management of public forest. However, resource economists still have not come forward yet with an economic model for this widely applied management technique and base their economic analysis of the optimal management of a homogeneous forest on a clear cutting regime utilizing the Faustmann-Pressier-Ohlin Theorem. Copyright (C) 2001 John Wiley Sons, Ltd.

关键词： numerical methods finite element method distributed optimal control forest management selective logging

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Automatic train regulation of complex metro networks with transfer coordination constraints: A distributed optimal control framework

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2018年第PartA期117卷 228-253页

作者： Li, Shukai Zhou, Xuesong Yang, Lixing Gao, Ziyou Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China Arizona State Univ Sch Sustainable Engn & Built Environm Tempe AZ 85281 USA

In designing the automatic train regulation strategy of metro networks subject to frequent disturbances, it is essential to coordinate the trains at the transfer stations among different lines to facilitate passengers transferring. In this paper, we systematically investigate the distributed optimal control method framework for automatic train regulation of large-scale complex urban metro networks with the transfer coordination constraints. A dynamic train traffic model of metro networks is elaborately developed in the form of the state space equation. In case frequent disturbances happen, a dynamic optimization problem is developed to minimize the timetable and headway deviations for each line of the metro network under the interaction constraints of different lines on the transfer coordination. By regarding each line as a subsystem of the whole network, the optimization problem is formulated to coordinate a number of subsystems coupled by the state constraints. To satisfy the real-time control requirement, according to the dual decomposition technique, a new distributed optimal control method based on the distributed message passing mechanism is designed, which effectively decomposes the original large-scale problem spatially and temporally into multiple small-scale optimization subproblems that can be computed completely in parallel on a single computing platform to speed up the solution procedure, and thereby reduces the computational burden of centralized implementations for the large-scale urban metro networks. Numerical examples are given to illustrate the effectiveness of the proposed method. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Metro networks Automatic train regulation Dual decomposition distributed optimal control

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Analysis and finite element approximations for distributed optimal control problems for implicit parabolic equations

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第1期231卷 327-348页

作者： Chrysafinos, Konstantinos Natl Tech Univ Athens Dept Math Athens 15780 Greece

This work concerns analysis and error estimates for optimal control problems related to implicit parabolic equations. The minimization of the tracking functional subject to implicit parabolic equations is examined. Existence of an optimal solution is proved and an optimality system of equations is derived. Semi-discrete (in space) error estimates for the finite element approximations of the optimality system are presented. These estimates are symmetric and applicable for higher-order discretizations. Finally, fully-discrete error estimates of arbitrarily high-order are presented based on a discontinuous Galerkin (in time) and conforming (in space) scheme. Two examples related to the Lagrangian moving mesh Galerkin formulation for the convection-diffusion equation are described. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Error estimates Finite element methods distributed optimal control Implicit parabolic equations Convection-diffusion equations Lagrangian coordinates Moving meshes

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A Practical Factorization of a Schur Complement for PDE-Constrained distributed optimal control

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JOURNAL OF SCIENTIFIC COMPUTING 2015年第2期65卷 576-597页

作者： Choi, Youngsoo Farhat, Charbel Murray, Walter Saunders, Michael Stanford Univ Aeronaut & Astronaut Stanford CA 94305 USA Stanford Univ Mech Engn Aeronaut & Astronaut Stanford CA 94305 USA Stanford Univ Management Sci & Engn Stanford CA 94305 USA

A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution of which is crucial. A new factorization of the Schur complement for such a system is proposed and its characteristics discussed. The factorization introduces two complex factors that are complex conjugate to each other. The proposed solution methodology involves the application of a parallel linear domain decomposition solver-FETI-DPH-for the solution of the subproblems with the complex factors. Numerical properties of FETI-DPH in this context are demonstrated, including numerical and parallel scalability and regularization dependence. The new factorization can be used to solve Schur complement systems arising in both range-space and full-space formulations. In both cases, numerical results indicate that the complex factorization is promising. Especially, in the full-space method with the new factorization, the number of iterations required for convergence is independent of regularization parameter values.

关键词： PDE-constrained optimization Schur complement Poisson operator FETI Range-space method Full-space method distributed optimal control

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APPLICATION OF VISCOSITY SOLUTIONS OF INFINITE-DIMENSIONAL HAMILTON-JACOBI-BELLMAN EQUATIONS TO SOME PROBLEMS IN distributed optimal-control

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1990年第2期64卷 245-268页

作者： BARRON, EN 1. Department of Mathematical Sciences Loyola University Chicago Illinois

We apply the recently developed Crandall and Lions theory of viscosity solutions for infinite-dimensional Hamilton-Jacobi equations to two problems in distributed control. The first problem is governed by differential-difference equations as dynamics, and the second problem is governed by a nonlinear divergence form parabolic equation. We prove a Pontryagin maximum principle in each case by deriving the Bellman equation and using the fact that the value function is a viscosity supersolution.

关键词： Viscosity solution Bellman equation distributed optimal control differential-difference equations parabolic equations Pontryagin maximum principle

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A residual based snapshot location strategy for POD in distributed optimal control of linear parabolic equations

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IFAC-PapersOnLine 2016年第8期49卷 13-18页

作者： Alla, A. Gräßle, C. Hinze, M. Florida State University Department of Scientific Computing 400 Dirac Science Library Tallahassee FL32306 United States Universität Hamburg Bundesstr. 55 Hamburg20146 Germany

In this paper we study the approximation of a distributed optimal control problem for linear parabolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis functions are obtained upon information contained in time snapshots of the parabolic PDE related to given input data. In the present work we show that for POD-MOR in optimal control of parabolic equations it is important to have knowledge about the controlled system at the right time instances. For the determination of the time instances (snapshot locations) we propose an a-posteriori error control concept which is based on a reformulation of the optimality system of the underlying optimal control problem as a second order in time and fourth order in space elliptic system. Finally, we present numerical tests to illustrate our approach and to show the effectiveness of the method in comparison to existing approaches. © 2016

关键词： Location Numerical methods optimal control systems Partial differential equations Principal component analysis distributed optimal control distributed optimal control problems Linear parabolic equation Model order reduction optimal control problem optimal controls Posteriori error control Proper orthogonal decompositions

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distributed optimal control of nonlinear systems using a second-order augmented Lagrangian method

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EUROPEAN JOURNAL OF control 2023年 70卷

作者： Ahmadi, Shervin Parvini Hansson, Anders Linkoping Univ Div Automat Control Linkoping Sweden

In this paper, we propose a distributed second-order augmented Lagrangian method for distributed op-timal control problems, which can be exploited for distributed model predictive control. We employ a primal-dual interior-point approach for the inner iteration of the augmented Lagrangian and distribute the corresponding computations using message passing over what is known as the clique tree of the problem. The algorithm converges to its centralized counterpart and it requires fewer communications between sub-systems as compared to algorithms such as the alternating direction method of multipli-ers. We illustrate the efficiency of the framework when applied to randomly generated interconnected sub-systems as well as to a vehicle platooning problem.(c) 2023 The Author(s). Published by Elsevier Ltd on behalf of European control Association. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： distributed optimal control distributed model predictive control Augmented Lagrangian distributed optimization

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A distributed optimal control Method for Active Distribution Network 11

A Distributed Optimal Control Method for Active Distribution...

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11th UKACC International Conference on control (UKACC control)

作者： Ling, Weifang Chen, Minyou Wei, Zuolin Chen, Feixiong Yu, Lei Yu, David C. Chongqing Univ Sch Elect Engn State Key Lab Power Transmiss Equipment & Syst Se Chongqing Peoples R China China Southern Power Grid Res Inst Guangzhou Guangdong Peoples R China Univ Wisconsin Milwaukee Dept Elect Engn & Comp Sci Milwaukee WI USA

ISBN: (纸本)9781467398916

This paper presents a distributed optimal control method for stable and economical operation of active distribution network (ADN). The method incorporates a distributed constraint optimization problem (DCOP) model with distributed simulated annealing (DSAN) algorithm based on potential game. Moreover, the distributed optimal strategy is developed on the basis of multi-agent system, and the distributed power flow calculation method is utilized to perform the power flow calculation among agents. The performance verification of the distributed optimal control strategy and the comparison with the centralized method are conducted in IEEE 39-bus system with distributed generations (DGs). Finally, the simulation cases are presented and discussed to demonstrate the effectiveness and applicability of the proposed optimal method for ADN.

关键词： active distribution network distributed optimal control multi-agent system potential game

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