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Establishment and Solution of a Multi-Stage Decision Model Based on Hypothesis Testing and dynamic programming Algorithm

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arXiv 2025年

作者： Liu, Ziyang Hu, Yurui Deng, Yihan School of Future Science and Engineering Soochow University Suzhou China

This paper introduces a novel multi-stage decision-making model that integrates hypothesis testing and dynamic programming algorithms to address complex decision-making ***,we develop a sampling inspection scheme that controls for both Type I and Type II errors using a simple random sampling method without replacement,ensuring the randomness and representativeness of the sample while minimizing selection *** the application of hypothesis testing theory,a hypothesis testing model concerning the defect rate is established,and formulas for the approximate distribution of the sample defect rate and the minimum sample size required under two different scenarios are derived. Subsequently,a multi-stage dynamic programming decision model is *** involves defining the state transition functions and stage-specific objective functions,followed by obtaining six optimal decision strategies under various conditions through backward *** results demonstrate the model’s potent capability for multi-stage decision-making and its high interpretability,offering significant advantages in practical applications. © 2025, CC BY.

关键词： dynamic programming

Reinforcement Learning-Based Optimal Control for Continuous-Time Quantized Systems via Adaptive dynamic programming

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Reinforcement Learning-Based Optimal Control for Continuous-...

IEEE SSD International Multi-Conference on Systems, Signals and Devices

作者： Omar Qasem Weinan Gao Omar R. Daoud Electrical and Computer Engineering Department School of Engineering and Computing American International University Al-Jahra Kuwait State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang Lianning China

ISBN: (数字)9798331542726

ISBN: (纸本)9798331542733

Ahstract- This paper presents a comprehensive investigation into the stability analysis and design conditions for quantizers to ensure the closed-loop stability of continuous-time linear quantized systems, under the conditions derived by the small-gain theorem. The study begins by deriving explicit bounds on the quantizer parameters required for maintaining system stability. Building on this foundation, an optimal controller is designed using the linear quadratic regulator (LQR) framework, providing an efficient data-driven control strategy. To further enhance the system's performance, an adaptive dynamic programming (ADP) algorithm, referred to as the hybrid iteration (HI) method, is developed. This algorithm effectively learns the optimal control policy by leveraging the trajectories of the quantized states and inputs, thereby addressing the challenges posed by quantization constraints. The proposed HI approach combines the advantages of adaptive learning and optimization, making it well-suited for continuous-time systems with limited information. The simulation results confirm that the ADP approach with the provided conditions not only stabilizes the quantized system but also achieves optimal control performance under the specified quantization conditions. This study offers valuable insights and a robust methodological framework for addressing stability and control challenges, with insights to be expanded to continuous-time nonlinear quantized systems, with potential applications in various engineering domains, such as networked systems, robotics and autonomous systems.

关键词： Quantization (signal) Adaptive systems Regulators Simulation Heuristic algorithms Optimal control Stability analysis dynamic programming Trajectory Thermal stability

Engineering Configuration Optimization of Wind-Solar-Storage Systems Based on dynamic programming Model

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Engineering Configuration Optimization of Wind-Solar-Storage...

Electronics, Energy Systems and Power Engineering (EESPE), IEEE International Conference on

作者： Yiheng Zhang School of Mathematics and Statistics Beijing Jiaotong University Beijing China

ISBN: (数字)9798350389579

ISBN: (纸本)9798350389586

As the importance of optimizing resource management systems continues to grow, this paper focuses on the economic optimization of integrated systems through advanced computational models. First, we analyzed the economic feasibility of resource management systems without storage solutions, identifying that the configuration of power generation methods and dependence on external grids are key factors influencing economic outcomes. Subsequently, we introduced a dynamic programming model to optimize storage-integrated systems. By adjusting system constraints and solving linear programming projections, we significantly reduced the typical daily cost to 15,658 yuan. The optimization process, including charging and discharging strategies and the State of Charge (SOC) curve, was thoroughly visualized. Furthermore, considering fluctuations in demand and return on investment, a new coordinated configuration scheme was developed to optimize storage and resource acquisition under varying pricing conditions over time. This study highlights the crucial role of advanced optimization algorithms in enhancing the economic efficiency and reliability of future resource management systems, providing essential insights for the sustainable utilization of resources.

关键词： Wind Costs Biological system modeling Electricity Wind power generation dynamic programming Resource management State of charge Optimization Energy storage

Optimizing Return Distributions with Distributional dynamic programming

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arXiv 2025年

作者： Pires, Bernardo Ávila Rowland, Mark Borsa, Diana Guo, Zhaohan Daniel Khetarpal, Khimya Barreto, André Abel, David Munos, Rémi Dabney, Will Google DeepMind London United Kingdom FAIR Meta

We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond expected utilities, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained so far (since the first time step). We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we combine the core ideas of distributional value iteration with the deep RL agent DQN, and empirically evaluate it for solving instances of the applications discussed. © 2025, CC BY.

关键词： dynamic programming

A data-driven practical stabilization approach for solving stochastic dynamic programming problems

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Automatica 2025年 178卷

作者： Tipaldi, Massimo Iervolino, Raffaele Massenio, Paolo Roberto Forootani, Ali Department of Electrical and Information Engineering Polytechnic University of Bari Bari70126 Italy Department of Electrical Engineering and Information Technology University of Naples Napoli80125 Italy Helmholtz Centre for Environmental Research - UFZ Leipzig04318 Germany

This paper presents a data-driven practical stabilization approach for solving stochastic dynamic programming problems with unknown Markov Decision Process models over an infinite time horizon. The Bellman operator is modeled as a discrete-time switched affine system, with each mode representing a specific stationary stochastic policy and an external bounded disturbance term to account for such modeling issue. A two-step approach is followed. First, a model-based robust practical stabilization problem is solved to derive stabilization conditions which enable the practical convergence of the resulting closed-loop system trajectories towards a chosen reference value function. Then, by exploiting recent model-to-data Linear Matrix Inequality transformation tools, these results are further developed to obtain data-driven robust stabilization conditions for addressing the case of model-free problems. Such data-driven stabilization conditions are deployed into the Value Iteration algorithm, and finally tested on the recycling robot and the parking lot management problems to demonstrate the effectiveness of the proposed method. © 2025 The Author(s)

关键词： dynamic programming

Pontryagin-Bellman Differential dynamic programming for Low-Thrust Trajectory Optimization with Path Constraints

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arXiv 2025年

作者： Sidhoum, Yanis Oguri, Kenshiro Purdue University West LafayetteIN47907 United States School of Aeronautics and Astronautics United States

We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential dynamic programming (PDDP), is the result of the incorporation of Pontryagin’s Minimum Principle (PMP) into the Differential dynamic programming (DDP) formulation. Unlike traditional indirect methods that rely on first-order shooting techniques to determine the optimal costate, PDDP optimizes the costates using a null-space trust-region method, solving a series of quadratic subproblems derived from first- and second-order sensitivities. Terminal equality constraints are handled via a general augmented Lagrangian method, while state-path constraints are enforced using a quadratic penalty approach. The resulting solution method represents a significant improvement over classical indirect methods, which are known to be ineffective for state-constrained problems. The use of DDP to optimize the costate partially reduces the inherent sensitivities of indirect methods, thereby improving the robustness to poor initial guess. Finally, the incorporation of PMP within the DDP formulation enables the design of long-duration, multi-spiral low-thrust trajectories with fewer optimization variables compared to classical DDP formulations. Although the paper emphasizes the spacecraft low-thrust trajectory optimization problem, the theoretical foundations are general and applicable to any control-affine optimal control problem. Copyright © 2025, The Authors. All rights reserved.

关键词： dynamic programming

Exploring Dendritic Computation in Bio-Inspired Architectures for dynamic programming

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Exploring Dendritic Computation in Bio-Inspired Architecture...

Design, Automation and Test in Europe Conference and Exhibition

作者： Anup Das Electrical and Computer Engineering Drexel University Philadelphia USA

ISBN: (数字)9783982674100

ISBN: (纸本)9798331534646

dynamic programming is a classical optimization technique that systematically decomposes a complex problem into simpler sub-problems to find an optimal solution. We explore the use of bio-inspired architectures to find the shortest path between two nodes in a graph using dynamic programming. We leverage dendritic computations, which are linear and nonlinear mechanisms in neuronal dendrites that allow to implement different computational primitives. We exploit two key mechanisms: 1) a dendrite acts as a delay line to propagate an excitatory post-synaptic potential to the soma, and 2) a feedback mechanism from the soma into the dendrites to control this delay. Our key ideas are the following. First, we model each node on a graph as a leaky integrate-and-fire (LIF) neuron, supporting the two dendritic mechanisms. We use a countdown counter to implement forward propagation of a delayed synaptic potential and eligibility trace-based feedback to update the delay by incorporating the cost of edges in a graph. Next, we formulate dynamic programming in terms of the time to the first spike in neurons. We breakdown the shortest path problem into sub-problems of finding the earliest firing times of neurons, and iteratively building the final solution from these smaller sub-problems by tracing backward. We implement this approach for several real-world graphs and show its scalability. We also show early prototyping on a Virtex UltraScale FPGA.

关键词： Shortest path problem Firing Architecture Scalability Computer architecture dynamic programming Dendrites (neurons) Delays Optimization Field programmable gate arrays

Research on Quality Inspection and Optimal Decision-Making in Production Processes Based on dynamic programming Algorithm

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Research on Quality Inspection and Optimal Decision-Making i...

Digital Analysis and Processing, Intelligent Computation (DAPIC), International Conference on

作者： Yujie Lv Hanxin Chen Weichao Hong Fengwei Wang College of Science Xi'an Shiyou University Xi'an China College of Civil Engineering and Architecture Jinan University Jinan China College of Computer and Information Fujian Agriculture and Forestry University Fuzhou China College of Computer and Information Engineering Tianjin Agricultural University Tianjin China

ISBN: (数字)9798331536169

ISBN: (纸本)9798331536176

This study investigates the quality inspection and optimal decision-making in production processes using a dynamic programming algorithm. The primary objective is to develop a sampling inspection plan for components provided by suppliers, aiming to detect whether the defect rate of components is within the specified nominal value under different confidence levels (95% and 90%) while minimizing inspection costs. We propose a sampling model based on the Binomial Distribution and the approximate Normal Distribution to conduct hypothesis testing for defect rate detection. Additionally, a dynamic programming model is constructed to optimize decision-making in the production process, considering factors such as inspection costs, potential risk costs, and losses from defective products entering the market. The results show that the proposed models effectively balance inspection costs and quality control, leading to optimal decisions that maximize profit and minimize losses. Through Python-based simulations, we visualize the decision outcomes and validate the feasibility of the proposed approach.

关键词： Adaptation models Costs Accuracy Heuristic algorithms Decision making Process control Production Quality control Inspection dynamic programming

MINIMUM RIESZ S-ENERGY SUBSET SELECTION IN ORDERED POINT SETS VIA dynamic programming

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arXiv 2025年

作者： Emmerich, Michael T.M. Faculty of Information Technology University of Jyväskylä Finland

We present a dynamic programming algorithm for selecting a representative subset of size k from a given set with n points such that the Riesz s-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case can use the natural data ordering for efficient dynamic programming as an effective heuristic solution approach. This approach is then extended to problems related to two-dimensional Pareto front representations arising in biobjective optimization problems. Under the assumption of sorted (or non-dominated) input, the method typically yields near-optimal solutions in most cases. We also show that the approach avoids mistakes of greedy subset-selection by means of example. However, as we demonstrate, there are exceptions where DP does not identify the global minimum;for example, in one of our examples, the DP solution slightly deviates from the configuration found by a brute-force *** is because the DP scheme’s recurrence is approximate. The total time complexity of our algorithm is shown to be O(n2k). We provide computational examples with discontinuous Pareto fronts and an open-source Python implementation, demonstrating the approximate DP algorithm’s effectiveness across various problems with large point sets. © 2025, CC BY.

关键词： dynamic programming