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A Fixed-Point Iteration Scheme for Sensitivity-Based distributed optimal control

IEEE TRANSACTIONS ON AUTOMATIC control 2025年第4期70卷 2778-2785页

作者： von Esch, Maximilian Pierer Volz, Andreas Graichen, Knut Friedrich Alexander Univ Erlangen Nurnberg FAU Chair Automatic Control D-91058 Erlangen Germany

This article presents a sensitivity-based algorithm for distributed optimal control problems (OCP) of multi-agent systems with nonlinear dynamics and state/input couplings, as they arise, for instance, in distributed model predictive control. The algorithm relies on first-order sensitivities to cooperatively solve the distributed OCP in parallel. The solutions to the resulting local OCPs are computed with a fixed-point scheme and communicated within one communication step per algorithm iteration to the neighbors. Convergence results are presented under the inexact minimization of the local OCP. The algorithm is evaluated in numerical simulations for an example system.

关键词： Heuristic algorithms Convergence Couplings Costs Trajectory Sensitivity Prediction algorithms optimal control Vectors Predictive control Agents and autonomous systems distributed optimal control nonlinear systems optimization algorithms

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distributed optimal control of Nonlinear Time-Delay System Subject to Delayed Measurements and Communication Disruptions

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Journal of Systems Science & Complexity 2021年第4期34卷 1426-1437页

作者： SU Baili DUAN Yuxing College of Engineering Qu/il Normal UniversityRizhao 276826China

This paper is focused on a distributed optimal control design for a class of nonlinear timedelay systems with delayed measurements and communication *** innovation lies in three *** distributed optimal control method which includes an optimal controller and a bounded controller is designed based on Lyapunov *** availability of data transmitted through the communication channel depends on a feasibility *** a sufficient condition to guarantee ultimate boundedness of the system is given based on appropriate *** significance of this paper is that this distributed optimal control method is applied to time-delay ***,a simulation example is given to verify the effectiveness of the proposed method.

关键词： Communication disruptions delayed measurements distributed optimal control nonlinear time-delay systems

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distributed optimal control of Reactive Power and Voltage in Islanded Microgrids

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2017年第1期53卷 340-349页

作者： Wang, Yanbo Wang, Xiongfei Chen, Zhe Blaabjerg, Frede Aalborg Univ Dept Energy Technol DK-9220 Aalborg Denmark

This paper presents a distributed optimal control strategy for islanded microgrids, which allows performing reactive power sharing and voltage regulation without using a communication system. To perform the twofold objectives, a small signal model is first developed to reconstruct the system input-output relationship, which is evaluated through sensitivity analysis. A state estimator is then constructed to observe reactive power distribution and system voltages by local measurement. An optimal regulator is developed to perform both reactive power sharing and system voltage restoration. And the dynamic performance of the optimal controller is analyzed, from which the guideline for choosing controller parameters is formulated. The results obtained from sensitivity analysis, simulations, and experiments show that the proposed approach provides the expected reliability and flexibility for optimizing the reactive power sharing and system voltages restoration.

关键词： distributed optimal control islanded microgrid reactive power sharing state estimator voltage regulation

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distributed optimal control of Energy Storages in DC Microgrids for Operation Loss Minimization With Communication Delays

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IEEE TRANSACTIONS ON SMART GRID 2024年第6期15卷 5284-5297页

作者： Liu, Hui Zhang, Yiming Su, Jinshuo Wang, Ni Chen, Bing Guangxi Univ Sch Elect Engn Nanning 530004 Peoples R China State Grid Jiangsu Elect Power Co Ltd Elect Power Res Inst Renewable Energy & Distribut Network Technol Dept Nanjing 210000 Peoples R China

Energy storages (ESs) have been widely utilized in DC microgrids to regulate power surplus/deficit cooperatively, such that renewable energy sources can be liberated to capture maximum energy independently. However, minimizing the operation loss of DC microgrids by ESs while ensuring nominal system voltage and ES safety is the desired control objective that needs further exploration. This paper formulates the desired control objective as a non-smooth convex optimization problem and designs a distributed optimal controller for ESs to achieve this objective. To bridge the gap between the optimization problem and controller design, an optimality condition, which is more unified and concise than the traditional KKT condition, is proposed based on the projection operation. Additionally, considering unavoidable time delays in communication systems, the adverse effect of communication delays on the proposed controller is analyzed from a novel perspective of disturbance injection. Furthermore, a robust control strategy is proposed to eliminate the adverse effect of communication delays by imitating the feedback control model from the Lagrange dual problem. Numerical simulations on a detailed switch-level model demonstrate the stability, optimality, robustness, resilience, and scalability of the proposed distributed optimal controller in minimizing the operation loss of DC microgrids.

关键词： Microgrids Delays Voltage control Safety optimal control Power system stability Minimization DC microgrid energy storage distributed optimal control non-smooth optimization communication delay

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distributed optimal control of Energy Hubs for Micro-Integrated Energy Systems

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2021年第4期51卷 2145-2158页

作者： Qu, Ming Ding, Tao Jia, Wenhao Zhu, Shanying Yang, Yongheng Blaabjerg, Frede Xi An Jiao Tong Univ Dept Elect Engn Xian 710049 Peoples R China Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Aalborg Univ Dept Energy Technol DK-9220 Aalborg Denmark

Integrated energy systems become more and more important to realize the energy complementary property. Micro-integrated energy system, served as the terminal integrated energy system, will have the electricity delivered directly to the local customers by energy hubs (EHs). Here, the data and information of the EHs during the operation are confidential and should be kept by each owner. Therefore, this article designs a dual-decomposition-based distributed algorithm to address this problem, where the optimal consensus problem is used for the dual problem to update the multipliers. The primary and dual problems are alternatively solved until the Karush-Kuhn-Tucher condition is satisfied. For the proposed distributed algorithm, the feasibility can be strictly guaranteed during the iteration process. Moreover, theorems and lemmas are proved for the linear convergence rate. The numerical results verify the effectiveness of the proposed algorithm.

关键词： Natural gas Cost function distributed algorithms Resistance heating Economics distributed optimal control dual decomposition (DD) energy hubs (EHs) micro-integrated energy systems (m-IESs)

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distributed optimal control for Linear Multiagent Systems on General Digraphs

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IEEE TRANSACTIONS ON AUTOMATIC control 2021年第1期66卷 322-328页

作者： Zhang, Zhuo Yan, Weisheng Li, Huiping Northwestern Polytech Univ Sch Marine Sci & Technol Xian 710072 Peoples R China

This article is concerned with the distributed optimal control of multiagent systems (MASs) with general linear dynamics. The cooperative tracking model consisting of multiple followers and one leader is constructed. distributed optimal controllers are presented using the linear quadratic regulator, which guarantee the leader-following consensus of MASs and the optimization of global performance index. The global information of topology is unneeded for solutions of optimization equations. The topology graph is a general digraph, and the only requirement is that the digraph should contain a directed spanning tree. Numerical examples are finally reported to demonstrate the efficiency of presented approach.

关键词： Topology optimal control Optimization Laplace equations Performance analysis Indexes Protocols Cooperative control distributed optimal control linear quadratic regulator (LQR) multiagent systems (MASs)

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distributed optimal control of a nonstandard system of phase field equations

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CONTINUUM MECHANICS AND THERMODYNAMICS 2012年第4-6期24卷 437-459页

作者： Colli, Pierluigi Gilardi, Gianni Podio-Guidugli, Paolo Sprekels, Juergen Weierstrass Inst Appl Anal & Stochast D-10117 Berlin Germany Univ Pavia Dipartimento Matemat F Casorati I-27100 Pavia Italy Univ Roma Tor Vergata Dipartimento Ingn Civile I-00133 Rome Italy

We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion;it has been introduced recently in Colli et al. (SIAM J Appl Math), on the basis of the theory developed in Podio-Guidugli (Ric. Mat. 55:105-118, 2006), and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.

关键词： distributed optimal control Nonlinear phase field systems First-order necessary optimality conditions

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distributed optimal control of the viscous Burgers equation via a Legendre pseudo-spectral approach

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2016年第12期39卷 3350-3360页

作者： Sabeh, Z. Shamsi, M. Dehghan, Mehdi Amirkabir Univ Technol Dept Appl Math Fac Math & Comp Sci 424 Hafez Ave Tehran Iran

This paper presents a computational technique based on the pseudo-spectral method for the solution of distributed optimal control problem for the viscous Burgers equation. By using pseudo-spectral method, the problem is converted to a classical optimal control problem governed by a system of ordinary differential equations, which can be solved by well-developed direct or indirect methods. For solving the resulting optimal control problem, we present an indirect method by deriving and numerically solving the first-order optimality conditions. Numerical tests involving both unconstrained and constrained control problems are considered. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： distributed optimal control viscous Burgers equation pseudo-spectral method Pontryagin's minimum principle optimality conditions

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distributed optimal control of nonlinear multi-agent systems based on integral reinforcement learning

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optimal control APPLICATIONS & METHODS 2024年第6期45卷 2596-2612页

作者： Xu, Ying Li, Kewen Li, Yongming Liaoning Univ Technol Coll Sci Jinzhou 121001 Peoples R China

In this article, a distributed optimal control approach is proposed for a class of affine nonlinear multi-agent systems (MASs) with unknown nonlinear dynamics. The game theory is used to formulate the distributed optimal control problem into a differential graphical game problem with synchronized updates of all nodes. A data-based integral reinforcement learning (IRL) algorithm is used to learn the solution of the coupled Hamilton-Jacobi (HJ) equation without prior knowledge of the drift dynamics, and the actor-critic neural networks (A-C NNs) are used to approximate the control law and the cost function, respectively. To update the parameters synchronously, the gradient descent algorithm is used to design the weight update laws of the A-C NNs. Combining the IRL and the A-C NNs, a distributed consensus optimal control method is designed. By using the Lyapunov stability theory, the developed optimal control method can show that all signals in the considered system are uniformly ultimately bounded (UUB), and the systems can achieve Nash equilibrium when all agents update their controllers simultaneously. Finally, simulation results are given to illustrate the effectiveness of the developed optimal control approach. A distributed optimal control approach is proposed for affine nonlinear multi-agent systems with unknown nonlinear dynamics. The game theory is used to formulate the distributed optimal control problem into a differential graphical game problem with synchronized updates of all nodes. In control design, a data-based integral reinforcement learning algorithm is used to learn the solution of the coupled Hamilton-Jacobi equation without prior knowledge of the drift dynamics, and the actor-critic neural networks are used to approximate the control law and the cost function, respectively. image

关键词： affine nonlinear multi-agent systems distributed optimal control integral reinforcement learning Nash equilibrium policy iteration

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distributed optimal control OF THE CAHN-HILLIARD SYSTEM INCLUDING THE CASE OF A DOUBLE-OBSTACLE HOMOGENEOUS FREE ENERGY DENSITY

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SIAM JOURNAL ON control AND OPTIMIZATION 2012年第1期50卷 388-418页

作者： Hintermueller, M. Wegner, D. Humboldt Univ Dept Math D-10099 Berlin Germany Karl Franzens Univ Graz Dept Math & Sci Comp Graz Austria

In this paper we study the distributed optimal control for the Cahn-Hilliard system. A general class of free energy potentials is allowed which, in particular, includes the double-obstacle potential. The latter potential yields an optimal control problem of a parabolic variational inequality which is of fourth order in space. We show the existence of optimal controls to approximating problems where the potential is replaced by a mollified version of its Moreau-Yosida approximation. Corresponding first-order optimality conditions for the mollified problems are given. For this purpose a new result on the continuous Frechet differentiability of superposition operators with values in Sobolev spaces is established. Besides the convergence of optimal controls of the mollified problems to an optimal control of the original problem, we also derive first-order optimality conditions for the original problem by a limit process. The newly derived stationarity system corresponds to a function space version of C-stationarity.

关键词： Cahn-Hilliard system double-obstacle potential mathematical programming with equilibrium constraints distributed optimal control Yosida regularization C-stationarity

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