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optimal control of a Phase Field System Modelling Tumor Growth with Chemotaxis and Singular Potentials (Oct, 10.1007/s00245-019-09618-6, 2019)

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APPLIED MATHEMATICS AND OPTIMIZATION 2021年第3期84卷 3569-3570页

作者： Colli, Pierluigi Signori, Andrea Sprekels, Jurgen Univ Pavia Dipartimento Matemat F Casorati Via Ferrata 5 I-27100 Pavia Italy Humboldt Univ Dept Math Unter Linden 6 D-10099 Berlin Germany Weierstrass Inst Appl Anal & Stochast Mohrenstr 39 D-10117 Berlin Germany

A Correction to this paper has been published: https://***/10.1007/s00245-019-09618-6

关键词： Adjoint system Cancer treatment Chemotaxis distributed optimal control Evolution equations Necessary optimality conditions Phase field system Tumor growth

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Neural network-based optimal fault compensation control of the nonlinear multi-agent system and its application to UAVs formation flight

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND control ENGINEERING 2023年第9期237卷 1635-1644页

作者： Duan, Dandan Liu, Chunsheng Dai, Jiao Sun, Jingliang Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing Peoples R China Jiangsu Dongyin Intelligent Engn Technol Res Inst Nanjing Peoples R China Beijing Inst Technol Beijing Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Automat Engn 29 Jiangjun Ave Nanjing 211106 Jiangsu Peoples R China

This article investigates the optimal consensus problem for unmanned aerial vehicle formation systems with actuator faults based on nonlinear multi-agent systems. Initially, for fault-free multi-agent system, the distributed optimal controllers are constructed based on the adaptive dynamic programming technique. A critic neural network is applied to approximate the solution of the nonlinear Hamilton-Jacobi-Bellman equations, in which the weight updating laws are built to guarantee the weight vectors of the critic neural network convergence. Second, the fault compensators and corresponding tuning laws are proposed to compensate for actuator faults. Through a combination of optimal controllers and fault compensators, the distributed optimal fault-tolerant controllers are obtained. Then, according to Lyapunov extension theorem, some stability criteria for ensuring the stability of the aircraft and the normal flight of the unmanned aerial vehicle formation are established in the event of an actuator failure. Finally, an example of an unmanned aerial vehicle formation system is introduced to verify the efficiency and reliability of the designed optimal fault-tolerant control scheme.

关键词： Adaptive dynamic programming distributed optimal control fault-tolerant control multi-agent system

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Research on voltage and power control strategy of distribution network

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INTERNATIONAL JOURNAL OF ELECTRONICS 2024年第1期111卷 204-222页

作者： Le, Jian Qi, Gan Liao, Xiaobing Zhao, Liangang Jin, Rui Wuhan Univ Sch Elect Engn Wuhan Peoples R China Wuhan Inst Technol Sch Elect & Informat Engn Wuhan Peoples R China Wuhan Univ Sch Elect Engn Wuhan 430072 Peoples R China

Traditional central control system is unable to deal with the optimal control tasks of modern distribution networks due to its low reliability, high computation and communication burden and poor expansibility. Based on distributed collaboration principle, this paper presents a multiple-object distributed optimisation control strategy for distribution network utilising DG grouping method. distributed control strategy for node voltage control group is developed by taking the capacity utilisation ratio (CUR) of DG as the consensus variable, to comply with the feature of high resistance/reactance ratio of distribution network feeder line. distributed control strategies for exchanged power control groups, which respectively takes CUR and power factor as the consensus variable, are formulated according to the different conditions of exchanged power imbalance. The parameter tuning method for three kinds of distributed optimisation control strategies are presented. The correctness and effectiveness of the proposed method are verified by simulation examples in the IEEE 14-node system, and simulation results on the IEEE 33-node test system are presented to show the robustness of the method to the disturbances related with distributed generation.

关键词： distributed generations distributed optimal control CUR power factor consensus protocol

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Regularization for Design

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IEEE TRANSACTIONS ON AUTOMATIC control 2016年第12期61卷 3991-4006页

作者： Matni, Nikolai Chandrasekaran, Venkat CALTECH Dept Control & Dynam Syst Pasadena CA 91125 USA CALTECH Dept Computat & Math Sci Pasadena CA 91125 USA CALTECH Dept Elect Engn Pasadena CA 91125 USA

When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given. The task of designing this architecture is now as important as the design of the control laws themselves. By interpreting controller synthesis (in a model matching setup) as the solution of a particular linear inverse problem, we view the challenge of obtaining a controller with a desired architecture as one of finding a structured solution to an inverse problem. Building on this conceptual connection, we formulate and analyze a framework called Regularization for Design (RFD), in which we augment the variational formulations of controller synthesis problems with convex penalty functions that induce a desired controller architecture. The resulting regularized formulations are convex optimization problems that can be solved efficiently;these convex programs provide a unified computationally tractable approach for the simultaneous co-design of a structured optimal controller and the actuation, sensing and communication architecture required to implement it. Further, these problems are natural control-theoretic analogs of prominent approaches such as the Lasso, the Group Lasso, the Elastic Net, and others that are employed in structured inference. In analogy to that literature, we show that our approach identifies optimally structured controllers under a suitable condition on a "signal-to-noise" type ratio.

关键词： Atomic norm minimization controller architecture co-design distributed optimal control joint actuator/sensor/communication link placement quadratic invariance

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optimal control of the viscous Dullin-Gottwalld-Holm equation

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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 2010年第1期11卷 480-491页

作者： Shen, Chunyu Tian, Lixin Gao, Anna Jiangsu Univ Dept Student Affairs Zhenjiang 212013 Jiangsu Peoples R China

This paper studies the problem for optimal control of the viscous DGH equation. The existence and uniqueness of weak solution to the equation are proved in a short interval. The optimal control of the viscous DGH equation under boundary condition is given and the existence of optimal solution to the equation is proved. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Viscous DGH equation optimal control optimal solution distributed optimal control

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An HDG method for distributed control of convection diffusion PDEs

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2018年 343卷 643-661页

作者： Chen, Gang Hu, Weiwei Shen, Jiguang Singler, John R. Zhang, Yangwen Zheng, Xiaobo Univ Elect Sci & Technol China Sch Math Sci Chengdu Sichuan Peoples R China Oklahoma State Univ Dept Math Stillwater OK 74078 USA Univ Minnesota Sch Math Minneapolis MN 55455 USA Missouri Univ Sci & Technol Dept Math & Stat Rolla MO 65409 USA Sichuan Univ Coll Math Chengdu Sichuan Peoples R China

We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a distributed optimal control problem governed by an elliptic linear convection diffusion PDE. We use degree k polynomials to approximate the state, adjoint state, their fluxes, and the optimal control, and we show the approximations converge with order k +1 in the L-2 norm. Finally, we use a simple element-by-element postprocessing scheme to obtain new superconvergent approximations of the state, dual state and the control. We show the postprocessed variables converge with order k + 2 in the L-2 norm. We present 2D and 3D numerical experiments to illustrate our theoretical results. (C) 2018 Elsevier B.V. All rights reserved.

关键词： distributed optimal control Linear convection diffusion equation Hybridizable discontinuous Galerkin method Error analysis Postprocessing Superconvergence

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distributed MPC for cooperative highway driving and energy-economy validation via microscopic simulations

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2017年第Apr.期77卷 80-95页

作者： Liu, Peng Ozguner, Umit Zhang, Yeqing Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

Traffic congestion and energy issues have set a high bar for current ground transportation systems. With advances in vehicular communication technologies, collaborations of connected vehicles have becoming a fundamental block to build automated highway transportation systems of high efficiency. This paper presents a distributed optimal control scheme that takes into account macroscopic traffic management and microscopic vehicle dynamics to achieve efficiently cooperative highway driving. Critical traffic information beyond the scope of human perception is obtained from connected vehicles downstream to establish necessary traffic management mitigating congestion. With backpropagating traffic management advice, a connected vehicle having an adjustment intention exchanges control-oriented information" with immediately connected neighbors to establish potential cooperation consensus, and to generate cooperative control actions. To achieve this goal, a distributed model predictive control (DMPC) scheme is developed accounting for driving safety and efficiency. By coupling the states of collaborators in the optimization index, connected vehicles achieve fundamental highway maneuvers cooperatively and optimally. The performance of the distributed control scheme and the energy-saving potential of conducting such cooperation are tested in a mixed highway traffic environment by the means of microscopic simulations. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： distributed optimal control Connected and automated vehicles Energy saving Microscopic traffic simulation

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Communication Delay Co-Design in H₂-distributed control Using Atomic Norm Minimization

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IEEE TRANSACTIONS ON control OF NETWORK SYSTEMS 2017年第2期4卷 267-278页

作者： Matni, Nikolai CALTECH Dept Control & Dynam Syst Pasadena CA 91125 USA

When designing distributed controllers for largescale systems, the actuation, sensing, and communication architectures of the controller can no longer be taken as given. In particular, controllers implemented using dense architectures typically outperform controllers implemented using simpler oneshowever, it is also desirable to minimize the cost of building the architecture used to implement a controller. The recently introduced Regularization for Design framework poses the controller architecture/control law co-design problem as one of jointly optimizing the competing metrics of controller architecture cost and closed-loop performance, and shows that this task can be accomplished by augmenting the variational solution to an optimal control problem with a suitable atomic norm penalty. Although explicit constructions for atomic norms useful for the design of actuation, sensing and joint actuation/sensing architectures are introduced, no such construction is given for atomic norms used to design communication architectures. This paper describes an atomic norm that can be used to design communication architectures for which the resulting distributed optimal controller is specified by the solution to a convex program. Using this atomic norm, we then show that in the context of H-2 - distributed optimal control, the communication architecture/control law codesign task can be performed through the use of finite-dimensional second-order cone programming.

关键词： Atomic norm minimization controller architecture co-design distributed optimal control joint actuator/sensor/communication link placement quadratic invariance

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distributed Eco-Driving control of a Platoon of Electric Vehicles Through Riccati Recursion

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2023年第3期24卷 3048-3063页

作者： Lacombe, Remi Gros, Sebastien Murgovski, Nikolce Kulcsar, Balazs Chalmers Univ Technol Dept Elect Engn S-41296 Gothenburg Sweden NTNU Dept Engn Cybernet N-7034 Trondheim Norway

This paper presents a distributed optimization procedure for the cooperative eco-driving control problem of a platoon of electric vehicles subject to safety and travel time constraints. Individual optimal trajectories are generated for each platoon member to account for heterogeneous vehicles and for the road slope. By rearranging the problem variables, the Riccati recursion can be applied along the chain-like structure of the platoon and be used to solve the problem by repeatedly transmitting information up and down the platoon. Since each vehicle is only responsible for its own part of the computations, the proposed control strategy is privacy-preserving and could therefore be deployed by any group of vehicles to form a platoon spontaneously while driving. The energy efficiency of this control strategy is evaluated in numerical experiments for platoons of electric trucks with different masses and rated motor powers.

关键词： Roads Force Vehicle dynamics Trajectory Indexes Electric vehicles Drag distributed optimal control Riccati recursion platooning eco-driving electric vehicles nonlinear programming

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Looking for the best constant in a Sobolev inequality: a numerical approach

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CALCOLO 2010年第4期47卷 211-238页

作者： Caboussat, Alexandre Glowinski, Roland Leonard, Allison Univ Houston Dept Math Houston TX 77204 USA Hong Kong Univ Sci & Technol Inst Adv Studies Kowloon Hong Kong Peoples R China

A numerical method for the computation of the best constant in a Sobolev inequality involving the spaces H (2)(Omega) C-0((Omega) over bar} is presented. Green's functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with two different strategies: an augmented Lagrangian method, together with finite element approximations, and a Green's functions based approach. Numerical experiments show the ability of the methods in computing this best constant for various two-dimensional domains, and the remarkable convergence properties of the augmented Lagrangian based iterative method.

关键词： Sobolev inequality Augmented Lagrangian algorithm Finite elements method distributed optimal control Uzawa algorithm

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