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dynamical programming for off-the-grid dynamic inverse problems

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2024年第1期30卷 7-7页

作者： Duval, Vincent Tovey, Robert INRIA Paris MOKAPLAN F-75012 Paris France PSL Univ Univ Paris Dauphine CEREMADE CNRSUMR 7534 F-75016 Paris France

In this work we consider off-the-grid algorithms for the reconstruction of sparse measures from time-varying data. In particular, the reconstruction is a finite collection of Dirac measures whose locations and masses vary continuously in time. Recent work showed that this decomposition was possible by minimising a convex variational model which combined a quadratic data fidelity with dynamical Optimal Transport. We generalise this framework and propose new numerical methods which leverage efficient classical algorithms for computing shortest paths on directed acyclic graphs. Our theoretical analysis confirms that these methods converge to globally optimal reconstructions. Numerically, we show new examples for unbalanced Optimal Transport penalties, and for balanced examples we are 100 times faster in comparison to the previously known method.

关键词： Off-the-grid imaging dynamic inverse problems Frank-Wolfe dynamical programming optimal transport regularization

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A dynamical programming-Based Method to Generate Control Strategy for Air Traffic Flow 31

A Dynamical Programming-Based Method to Generate Control Str...

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31st Chinese Control And Decision Conference (CCDC)

作者： Huang, Jinglei Xu, Qiucheng Tian, Jing Yan, Yongjie China Elect Technol Grp Corp Res Inst 28 State Key Lab Air Traff Management Syst & Technol Nanjing 210007 Peoples R China

ISBN: (纸本)9781728101057

With the rapidly increasing of air traffic demand, air traffic problems are surfaced gradually. where the problems include air traffic control load, air traffic congestion, and the demand-capacity imbalances problem. And, the demand-capacity imbalances are typically occurred in the convection weather conditions. In this paper, a method based on dynamical programming is proposed to generate flow control strategy for flights that enter into a sector whose capacity is decreased from the normal operation capacity due to the convective weather. What is more, the air traffic flow from different directions are controlled in a more safe and efficient manner by restricting the maximum allowed number of flights and the minimal time interval between every two adjacent flights with minimization of delay cost. Experimental results show that, compared with the Rate-based method and Need-based method, the proposed method can reduce the average cost by 8.2% and 7.3%, respectively.

关键词： Air traffic management dynamical programming Flow control strategy Minutes-in-Trail

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An Efficient dynamical programming Algorithm for Bin Packing Problem

An Efficient Dynamical Programming Algorithm for Bin Packing...

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International Conference on Computational Science and Computational Intelligence (CSCI)

作者： Huyghe, Catherine Negre, Stephane Fontaine, Melanie Univ Picardie Jules Verne MIS Amiens France Univ Picardie Jules Verne EPROAD Amiens France Univ Picardie Jules Verne LTI Amiens France

In this paper, we propose a very efficient algorithm to solve the 2 dimensional bin packing problem. The algorithm can automatically place thousands of objects in bins using less than 1 minute with very near optimal r... 详细信息

ISBN: (纸本)9798350361513;9798350372304

关键词： bin packing problem heuristic dynamical programming algorithm lower bound

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Memetic algorithms and dynamic programming on vehicle routing problems in crisis situations

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OPERATIONAL RESEARCH 2025年第1期25卷 1-28页

作者： Vasalakis, Stamatios Spyridakos, Athanasios Univ West Attica Dept Business Adm Athens Greece

The Vehicle Routing Problem is a broad field of study and practice. In this article, we will introduce a general methodology to solve a Dial-a-Ride problem as proposed by Jean-Fran & ccedil;ois Cordeau in 2006, followed by a briefly presentation on its further development by Zhang et al. (Omega 54: 60-71, 2015. https://***/10.1016/***.2015.01.011), which involved the use of memetic algorithms to tackle the problem of transportation services regarding the moving of people or goods between locations. Memetic Algorithms are a type of optimization algorithms that have an evolutionary framework and include a list of local search components. Specifically, this kind of problems categorized as a multi-trip dial-a-ride problem, which involves designing multiple routes for each mode of transportation. Finally, an extensive presentation is made based on the principles of dynamical programming, which discretizes the optimization problems in stages and the techniques of Linear programming. The main objective is to utilize real-time information from electronic platforms to determine the most optimal transportation plan at each step. This type of problem is complex due to two main factors: (a) the urgent need to transport people based on their triage scale, and (b) the immediate movement towards the final destination. Additionally, other significant issues need to be taken into account, such as (a) the presence of multiple start and destination points for transportation with varying distances and availabilities, (b) the destination points of one stage becoming the start points for the next stage, (c) limited resources at destination points, and (d) the requirement to achieve global optimization of the response time concerning emergencies and priorities. A comparison will take place regarding these three methodological approaches (general Dial-a-Ride, memetic algorithm, dynamic programming), providing the benefits and the drawbacks of each one and illustrated through a case

关键词： Memetic algorithm Linear programming dynamical programming Transportation Australasian triage scale

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Stochastic stabilization of quasi integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitation

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PROBABILISTIC ENGINEERING MECHANICS 2025年 79卷

作者： Liu, Weiyan Yin, Xunru Guo, Zhongjin Jiang, Shan Taishan Univ Sch Math & Stat Tai An 271000 Peoples R China

A stochastic stabilization control strategy is proposed for multi-degree-of-freedom (MDOF) quasi integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitation. At first, the averaged It & ocirc;stochastic differential equations (SDEs) for controlled first integrals are derived from the system motion equations by using the stochastic averaging method. Second, the dynamical programming equation of the averaged system with undetermined cost function is established based on the dynamical programming principle. The optimal control law is given through solving the dynamical programming equation. Third, the asymptotic Lyapunov stability with probability one of the controlled system is analyzed approximately by evaluating the largest Lyapunov exponent of the averaged system. Finally, the cost function and optimal control forces are determined based on the requirement of stabilizing the system. An example is delivered to illustrate the application and effectiveness of the proposed stochastic stabilization control strategy.

关键词： Stochastic stabilization Quasi integrable and non-resonant Hamiltonian system Asymptotic Lyapunov stability with probability one dynamical programming The largest Lyapunov exponent Stochastic averaging

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Two theorems on multilevel programming problems with dominated objective functions

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APPLIED MATHEMATICS LETTERS 2001年第8期14卷 927-932页

作者： Zhu, SS Wang, SY Coladas, L Chinese Acad Sci Acad Math & Syst Sci Inst Syst Sci Beijing 100080 Peoples R China Univ Tsukuba Inst Policy & Planning Sci Tsukuba Ibaraki 305 Japan Univ Santiago de Compostela Fac Math Santiago De Compostela 15782 Spain

In this paper, we present two theorems on the structure of a type of multilevel programming problems. The theorems explore relations among a multilevel programming problem, a dynamical programming, and a nonlinear pro... 详细信息

关键词： multilevel programming dynamical programming dominated objective functions

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Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

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Acta Mechanica Sinica 2007年第3期23卷 311-319页

作者： Ronghua Huan Maolin Deng Weiqiu Zhu Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang UniversityHangzhou 310027 China

In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged It^↑o stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged It^↑o equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged It^↑o equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.

关键词： Nonlinear system Stochastic excitation Stochastic averaging Optimal control dynamical programming

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Nonlinear stochastic optimal bounded control of hysteretic systems with actuator saturation

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2008年第3期9卷 351-357页

作者： Rong-hua HUAN Wei-qiu ZHU Yong-jun WU Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China College of Information Science and Engineering East China University of Science and Technology Shanghai 200237 China

A modified nonlinear stochastic optimal bounded control strategy for random excited hysteretic systems with actuator saturation is proposed. First, a controlled hysteretic system is converted into an equivalent nonlinear nonhysteretic stochastic system. Then, the partially averaged Itoe stochastic differential equation and dynamical programming equation are established, respectively, by using the stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov （FPK） equation associated with the fully averaged Itoe equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.

关键词： Hysteretic system Stochastic averaging Optimal control dynamical programming Actuator saturation

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Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems

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Acta Mechanica Sinica 2007年第4期23卷 437-444页

作者： Maolin Deng Weiqiu Zhu Department of Mechanics,State Key Laboratory of Fluid Power Transmission and Control,Zhejiang University,Hangzhou 310027,China Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

Abstract A nonlinear stochastic optimal control strategy for minimizing the first-passage failure of quasi integrable Hamiltonian systems （multi-degree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations） is proposed. The equations of motion for a controlled quasi integrable Hamiltonian system are reduced to a set of averaged It6 stochastic differential equations by using the stochastic averaging method. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximization of reliability and mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The final dynamical programming equations for these control problems are determined and their relationships to the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are separately established. The conditional reliability function and the mean first-passage time of the controlled system are obtained by solving the final dynamical programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illustrate the application and effectiveness of the proposed control strategy.

关键词： Nonlinear stochastic system First-passage time Reliability Stochastic control dynamical programming

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Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第9期10卷 1245-1251页

作者： Lin-cong CHEN Rong-hua HUAN Wei-qiu ZHU Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

We studied the feedback maximization of reliability of multi-degree-of-freedom （MDOF） quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged Ito equations are derived by using the stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Then, the dynamical programming equation and its boundary and final time conditions for the control problems of maximizing the reliability is established from the partially averaged equations by using the dynamical programming principle. The nonlinear stochastic optimal control for maximizing the reliability is determined from the dynamical programming equation and control constrains. The reliability function of optimally controlled systems is obtained by solving the final dynamical programming equation. Finally, the application of the proposed procedure and effectiveness of the control strategy are illustrated by using an example.

关键词： Stochastic optimal control dynamical programming Quasi integrable-Hamiltonian system Stochastic averaging Combined harmonic and white noise excitation Reliability

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