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optimal distributed control for a Model of Homogeneous Incompressible Two-Phase Flows

JOURNAL OF DYNAMICAL AND control SYSTEMS 2021年第1期27卷 153-177页

作者： Li, Fang You, Bo Xidian Univ Sch Math & Stat Xian 710126 Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China

The main objective of this paper is to study the optimal distributed control for a model of homogeneous incompressible two-phase flows. We apply the well-posedness and regularity results to establish the existence of optimal controls as well as the first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid.

关键词： distributed optimal control First-order necessary optimality conditions Adjoint state system Two-phase flow model

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distributed infinite-horizon optimal control of continuous-time linear systems over network

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR control 2021年第6期31卷 2082-2096页

作者： Battilotti, Stefano Cacace, Filippo D'Angelo, Massimiliano Sapienza Univ Rome Dept Comp Control & Management DIAG Rome Italy Campus Biomed Roma Rome Italy

This article deals with the distributed infinite-horizon linear-quadratic-Gaussian optimal control problem for continuous-time systems over networks. In particular, the feedback controller is composed of local control stations, which receive some measurement data from the plant process and regulates a portion of the input signal. We provide a solution when the nodes have information on the structural data of the whole network but takes local actions, and also when only local information on the network are available to the nodes. The proposed solution is arbitrarily close to the optimal centralized one (in terms of cost index) when a design parameter is set sufficiently large. Numerical simulation validate the theoretical results.

关键词： consensus filters cyber‐ physical systems distributed optimal control networked control systems

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Multibattery optimal Coordination control for Home Energy Management Systems via distributed Iterative Adaptive Dynamic Programming

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2015年第7期62卷 4203-4214页

作者： Wei, Qinglai Liu, Derong Shi, Guang Liu, Yu Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China Chinese Acad Sci Inst Automat Beijing 100190 Peoples R China

In this paper, a novel distributed iterative adaptive dynamic programming (ADP) method is developed to solve the multibattery optimal coordination control problems for home energy management systems. According to system transformations, the multi-input optimal control problem is transformed into a single-input optimal control problem, where all the batteries are implemented at their worst performance. Next, based on the worst-performance optimal control law, an effective distributed iterative ADP algorithm is developed, where, in each iteration, only a single-input optimization problem is implemented. Convergence properties of the distributed iterative ADP algorithm are developed to show that the iterative performance index function converges to the optimum. Finally, numerical analysis is given to illustrate the performance of the developed algorithm.

关键词： Adaptive critic designs adaptive dynamic programming (ADP) approximate dynamic programming distributed optimal control smart grid smart home

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optimal distributed control of Two-Dimensional Nonlocal Cahn-Hilliard-Navier-Stokes Systems with Degenerate Mobility and Singular Potential

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APPLIED MATHEMATICS AND OPTIMIZATION 2020年第3期81卷 899-931页

作者： Frigeri, Sergio Grasselli, Maurizio Sprekels, Jurgen Univ Cattolica Sacro Cuore Brescia Dipartimento Matemat N Tartaglia Via Musei 41 I-25121 Brescia Italy Politecn Milan Dipartimento Matemat Via E Bonardi 9 I-20133 Milan Italy Weierstrass Inst Appl Anal & Stochast Mohrenstr 39 D-10117 Berlin Germany Humboldt Univ Dept Math Unter Linden 6 D-10099 Berlin Germany

In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier-Stokes equations, nonlinearly coupled with a convective nonlocal Cahn-Hilliard equation. The system rules the evolution of the (volume-averaged) velocity u of the mixture and the (relative) concentration difference phi of the two phases. The aim of this work is to study an optimal control problem for such a system, the control being a time-dependent external force v acting on the fluid. We first prove the existence of an optimal control for a given tracking type cost functional. Then we study the differentiability properties of the control-to-state map v bar right arrow [u,phi], and we establish first-order necessary optimality conditions. These results generalize the ones obtained by the first and the third authors jointly with Rocca (SIAM J control Optim 54:221-250, 2016). There the authors assumed a constant mobility and a regular potential with polynomially controlled growth. Here, we analyze the physically more relevant case of a degenerate mobility and a singular (e.g., logarithmic) potential. This is made possible by the existence of a unique strong solution which was recently proved by the authors and Gal (WIAS preprint series No. 2309, Berlin, 2016).

关键词： Navier-Stokes equations Nonlocal Cahn-Hilliard equations Degenerate mobility Incompressible binary fluids Phase separation distributed optimal control First-order necessary optimality conditions

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optimal distributed control OF A NONLOCAL CONVECTIVE CAHN-HILLIARD EQUATION BY THE VELOCITY IN THREE DIMENSIONS

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SIAM JOURNAL ON control AND OPTIMIZATION 2015年第3期53卷 1654-1680页

作者： Rocca, E. Sprekels, J. Weierstrass Inst Appl Anal & Stochast D-10117 Berlin Germany Univ Milan Dipartimento Matemat I-20133 Milan Italy Humboldt Univ Inst Mathemat D-12489 Berlin Germany

In this paper we study a distributed optimal control problem for a nonlocal convective Cahn-Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking type, the control problem under investigation cannot easily be treated via standard techniques for two reasons: the state system is a highly nonlinear system of PDEs containing singular and degenerating terms, and the control variable, which is given by the velocity of the motion occurring in the convective term, is nonlinearly coupled to the state variable. The latter fact makes it necessary to state rather special regularity assumptions for the admissible controls, which, while looking a bit nonstandard, are, however, quite natural in the corresponding analytical framework. In fact, they are indispensable prerequisites to guarantee the well-posedness of the associated state system. In this paper, we employ recently proved existence, uniqueness, and regularity results for the solution to the associated state system in order to establish the existence of optimal controls and appropriate first-order necessary optimality conditions for the optimal control problem.

关键词： distributed optimal control first-order necessary optimality conditions nonlocal models integrodifferential equations convective Cahn-Hilliard equation phase separation

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On the formulation and numerical simulation of distributed-order fractional optimal control problems

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2017年 52卷 177-189页

作者： Zaky, M. A. Tenreiro Machado, J. A. Natl Res Ctr Dept Appl Math Giza 12622 Egypt Univ Sci & Technol Zewail City Sci & Technol Giza 12588 Egypt Inst Engn Polytech Porto Dept Elect Engn Rua Dr Antonio Bernardino de Almeida P-4249015 Oporto 431 Portugal

In a fractional optimal control problem, the integer order derivative is replaced by a fractional order derivative. The fractional derivative embeds implicitly the time delays in an optimal control process. The order of the fractional derivative can be distributed over the unit interval, to capture delays of distinct sources. The purpose of this paper is twofold. Firstly, we derive the generalized necessary conditions for optimal control problems with dynamics described by ordinary distributed-order fractional differential equations (DFDEs). Secondly, we propose an efficient numerical scheme for solving an unconstrained convex distributed optimal control problem governed by the DFDE. We convert the problem under consideration into an optimal control problem governed by a system of DFDEs, using the pseudo-spectral method and the Jacobi-Gauss-Lobatto (J-G-L) integration formula. Next, we present the numerical solutions for a class of optimal control problems of systems governed by DFDEs. The convergence of the proposed method is graphically analyzed showing that the proposed scheme is a good tool for the simulation of distributed control problems governed by DFDEs. (C) 2017 Elsevier B.V. All rights reserved.

关键词： distributed optimal control optimality conditions distributed-order fractional derivative Psedo-spectral method Fractional diffusion equation

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optimal distributed control of the Cahn-Hilliard-Brinkman system with regular potential

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2019年 182卷 226-247页

作者： You, Bo Li, Fang Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Xidian Univ Sch Math & Stat Xian 710126 Shaanxi Peoples R China

The main objective of this paper is to study the optimal distributed control of the three dimensional Cahn-Hilliard-Brinkman system with regular potential. We apply recently proved well-posedness and regularity results in order to establish the existence of optimal controls as well as the first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow. (C) 2018 Published by Elsevier Ltd.

关键词： distributed optimal control First-order necessary optimality conditions Cahn-Hilliard-Brinkman system Adjoint state system Phase separation

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distributed Fuzzy Adaptive Backstepping optimal control for Nonlinear Multimissile Guidance Systems With Input Saturation

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2019年第3期27卷 447-461页

作者： Sun, Jingliang Liu, Chunsheng Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing 211100 Jiangsu Peoples R China

This paper investigates the distributed optimal tracking control problem for nonlinear multiagent systems with a fixed directed graph. The dynamics of followers are in strict-feedback form with unknown nonlinearities and input saturation. Fuzzy logic systems and auxiliary system are introduced to identify the unknown nonlinearities and compensate the effect of input saturation, respectively. Then, by using the command-filtered backstepping technique, the distributed optimal tracking control problem is transformed into a distributed optimal regulation problem of tracking error dynamics in affine form. Subsequently, the distributed optimal feedback controller is derived via adaptive dynamic programming technique, in which a critic network is constructed to approximate the associated cost function online with a designed weight update law. Therefore, the whole controller, consisting of distributed adaptive feedforward tracking controller and distributed optimal feedback controller, not only guarantees that all signals in the closed-loop system are uniformly ultimately hounded, but also guarantees that the cooperative cost function is minimized. The effectiveness of the proposed method is demonstrated by simulation on the cooperative guidance problem of multimissile systems.

关键词： Adaptive dynamic programming (ADP) cooperative guidance distributed optimal control fuzzy backstepping technique input saturation multimissile system

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distributed Secondary Voltage optimal control of Active Distribution Network and the System Stability Investigation

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JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY 2023年第3期18卷 1573-1586页

作者： Le, Jian Qi, Gan Zhao, Lian-gang Cui, Jian-yong Wuhan Univ Sch Elect Engn & Automat Wuhan Peoples R China

This paper presents a distributed secondary voltage optimal control strategy for active distribution network (ADN), and synthetizes the state-space model to investigate the system stability of the ADN under this control framework. A leader-follower type distributed voltage control strategy is formulated utilizing consensus protocol that can effectively decompose the node voltage control task while preserving a satisfactory voltage regulation performance. The small-signal models of distributed generation units adopting the distributed control law and the power network are established. The state-space model of the whole ADN is further established by integrating the linearized versions of these models together, and the system small-signal stability is studied utilizing eigenvalue analysis method. Finally, the IEEE-33 node distribution network under several operation scenarios is simulated to demonstrate the effectiveness of the proposed methods, and the stability of the system is also analysed.

关键词： Active distribution network distributed generation distributed optimal control Voltage regulation Small-signal stability

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optimal distributed control of the Three-dimensional Planetary Geostrophic Equations

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JOURNAL OF DYNAMICAL AND control SYSTEMS 2022年第2期28卷 351-373页

作者： You, Bo Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China

The main objective of this paper is to study the optimal distributed control of the three-dimensional planetary geostrophic equations. We apply the well-posedness and regularity results proved in Cao and Titi (Commun Pure Appl Math 56:198-233, 2003) to establish the existence of an optimal control as well as the first-order necessary optimality condition for an associated optimal control problem in which a distributed control is applied to the temperature.

关键词： distributed optimal control First-order necessary optimality conditions Adjoint state system Planetary geostrophic equations

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